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A laboratory method to evaluate the rates of water erosion of natural rock materials
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A laboratory method to evaluate the rates of water erosion of natural rock materials
Series Title:
Henderson, Matthew R
University of Florida -- Coastal and Oceanographic Engineering Dept
Place of Publication:
Gainesville Fla
Coastal & Oceanographic Engineering Program, Dept. of Civil & Coastal Engineering, University of Florida
Publication Date:
Physical Description:
xii, 85 leaves : ill., map ; 28 cm.
Subjects / Keywords:
Water-rock interaction ( lcsh )
Rocks ( lcsh )
Scour (Hydraulic engineering) -- Mathematical models ( lcsh )
Erosion -- Mathematical models ( lcsh )
government publication (state, provincial, terriorial, dependent) ( marcgt )
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )
Thesis (M.S.)--University of Florida, 1999.
Includes bibliographical references (leaves 81-84).
General Note:
"August 1999"--Cover.
Statement of Responsibility:
by Matthew R. Henderson.
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University of Florida
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University of Florida
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All applicable rights reserved by the source institution and holding location.
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Wetlands General Research Collections
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Full Text
Matthew P. Henderson Thesis
August 1999
Matthew R. Henderson
August 1999
I would like to thank Dr. Max Sheppard, my advisor and supervisory committee chairman, for his help and support during my research and Dr. Dave Bloomquist for his help in the design and construction of the testing device. Thanks also go to the staff of the Coastal & Oceanographic Engineering Laboratory and the Civil Engineering Laboratory. Special thanks go to Danny Brown and Vernon Sparkman for their efforts in the construction of the testing device. None of this would be possible without their help.
I would also like to thank Dr. Robert Dean and Dr. Ashish Mehta for serving on my supervisory committee. My appreciation also extends to Dr. Nick Cristescu and Dr. Oana Cazacu for their assistance in helping me understand the behavior and mechanics of rocks.
I am grateful to Mr. Shawn McLemore, P.E., of the Florida Department of
Transportation, for his financial support and professional interest. I am also grateful to Dr. Dave Horhota of the Florida Department of Transportation for providing us with rock samples to test. Thanks go to Dr. Rob Nairn, of Baird & Associates, and Dr. Andrew Cornett, of the Canadian Hydraulics Center, for providing me with information about the Northumberland Strait Crossing Bridge and the rock erosion experiments that they performed.
Many thanks go to my classmates and friends, especially Al, Greg, Judy, Joel,
Adam, Eduardo, Jennifer, Wendy, Tom, Bill, Becky, Justin, Ed, Lisa, and Thanasis all of whom acted as sounding boards and lent encouragement when necessary.
Finally, I would like to thank my family and especially my wife, Beth, who have always supported me in my endeavors.
LIST OF TABLES ............................................................................. vi
LIST OF FIGURES ........................................................................... vii
LIST OF SYM[BOLS........................................................................... ix
ABSTRACT .................................................................................x
1. 1 Types of Scour...................................................................... 3
1. 1.1 Long-term Aggradation and Degredation................................... 3
1. 1.2 Contraction Scour............................................................ 4
1.1.3 Local Scour................................................................... 5
1.2 Purpose and Scope ................................................................ 7
1.2.1 Purpose ....................................................................... 7
1.2.2 Scope ......................................................................... 8
2.1 What is Rock? ...................................................................... 9
2.2 How are Rocks Classified?7....................................................... 10
2.2.1 Origin or Genesis ........................................................... 11
2.2.2 Geological or Lithological. Classification.................................. 11
2.2.3 Engineering Classification of Intact Rock ................................. 12
2.3 Types of Rocks in Florida......................................................... 12
2.3.1 Types of Sedimentary Rocks ............................................... 13
2.3.2 Limestone.................................................................... 14
2.3.3 Sandstone.................................................................... 16
2.3.4 Coquina...................................................................... 16
2.3.5 Coral Rock .................................................................. 18
2.3.6 Locations of Rocks in Florida.............................................. 19
2.4 Current Methods for the Prediction of Rock Scour............................ 24
2.4.2 Scourability of Rock Formations Memorandum......................... 25
2.5 Previous Rock Erosion Experim ents ............................................................. 29
2.6 Rock Erosion Process .................................................................................. 32
2.7 Alternative Rock Erosion Predictive M ethod ................................................ 36
2.7. 1 Erodibility Index M ethod ..................................................................... 3 6
2.7.2 Application of Erodibility Index M ethod .............................................. 39
3.1 D esign Challenges ........................................................................................ 42
3.2 Previous Use of the Rotating Cylinder Testing Apparatus ............................. 44
3.3 Theoretical Hydrodynamic Aspects of the Rotating Cylinder Apparatus ........ 45 3.4 Advantages of Rotating Cylinder Apparatus ................................................. 48
3.5 Limitations and Bias of Rotating Cylinder Apparatus .................................... 49
3.6 Rotating Cylinder Testing Apparatus for Measuring Rock Erodibility ........... 50
3.6.1 Rotating Cylinder Testing Apparatus ................................................... 50
3.6.2 Torque Cell ......................................................................................... 54
3.6.3 Determination of End Effects ............................................................... 55
3.7 Experim ental Procedures .............................................................................. 57
3.7.1 Sam ple Preparation .............................................................................. 57
3.7.2 Erosion Testing ................................................................................... 59
3.7.3 Calculations ......................................................................................... 62
4.1 Cem ented Sand ............................................................................................ 64
4.2 Sandstone ..................................................................................................... 67
5.1 Analysis of Cemented Sand and Sandstone Tests .......................................... -70
5.2 Influence of NEcrocracks on Erosion ............................................................ 74
5.3 Further Experiments ..................................................................................... 75
5.4 Design Im provem ents ................................................................................... 75
Table pae
2.1 Classification of Sedimentary Rocks (Excluding Pyroclastic Rocks).............. 14
4.1 Loose Cemented Sand Dimensions................................................... 65
4.2 Loose Cemented Sand Test Results.................................................. 65
4.3 Dark Tan Sandstone Dimensions..................................................... 68
4.4 Dark Tan Sandstone Test Results .................................................... 68
Fiizure page
2.1 Gray Limerock, Soft with Intermittent Layers of Hard Limerock................. 15
2.2 Gray Sandstone........................................................................ 17
2.3 Coquina............................................................................... 17
2.4 Coral Rock...........................................................................18 I
2.5 Physiographic Divisions of Florida ................................................... 20
2.6 Definition Sketch for Hydraulic Fracturing of Rock................................ 33
2.7 Hydraulic Erosion..................................................................... 35
3. 1 Velocity profile between two consecutive cylinders ................................ 46
3.2 Velocity profile between two infinite parallel plates................................. 46
3.3 Rotating Cylinder Test Apparatus Schematic........................................ 51
3.4 Schematic of Acrylic Cylinder and Torque Cell ..................................... 52
3).5 Rotating Cylinder Test Apparatus .................................................... 52
3.6 Acrylic Cylinder and Torque Cell..................................................... 53
3.7 Torque Cell Calibration............................................................... 55
3.8 End Effects Experiment Set-Up ...................................................... 56
3.9 End Effects Determination............................................................ 57
3.10 Side Coring from Rock Core ......................................................... 59
4.1 Experimental results for Loose Cemented Sand..................................... 66
4.2 Dark Tan Sandstone ........................................................................................... 69
5.1 Cem ented Sand and Sandstone Erosion Rate Data .............................................. 71
5.2 Conceptual Rock Erosion Relationships ............................................................. 73
d width of gap between rotating and fixed cylinders
erosion rate
Js relative ground structure number
J, joint set number
Kb particle/block size number
Kd discontinuity or inter-particle bond strength
Kh material's resistance to erosion
k, Nikuradse Roughness Length
L unit length of channel
I length of thin horizontal crack
M. mass strength number
m bending moment in the rock above crack
N rotational speed
P Stream Power
P1 pressure outside thin horizontal crack
P2 pressure outside think horizontal crack
qu unconfined compressive strength
Rer critical Reynolds number for the onset of Taylor vorticies
Re external radius of rotating cylinder
Ri internal radius of fixed cylinder
St- slope of energy grade line
t height of thin horizontal crack
Ta Taylor number
U depth average velocity
friction velocity
ui steady flow velocity outside thin horizontal crack
U2 flow velocity inside thin horizontal crack
VC peripheral velocity of outer rotating cylinder
X variable being measured
AX unit error
(X ratio of external to internal radius
y unit weight of water
I-t dynamic viscosity
v kinematic viscosity
p fluid density
Cmax maximum axial stress
average shear stress
0 average shear stress on a bed
Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science A LABORATORY METHOD TO EVALUATE THE
RATES OF WATER EROSION OF NATURAL ROCK MATERIALS By
Matthew R. Henderson
August 1999
Chairman: D. Max Sheppard
Major Department: Coastal & Oceanographic Engineering
This thesis discusses the design and testing procedures developed to evaluate the rate of water erosion of natural rock material. A laboratory testing device the rotating cylinder erosion testing apparatus previously used for testing rates of erosion of cohesive soils was modified and improved to accept intact rock samples. Laboratory testing procedures and methods were developed for conducting erosion experiments using this apparatus on rock samples. Preliminary experiments were performed on samples of rock collected in Florida.
The results indicate that there are potential relationships between rock erosion rates and applied bed shear stress. In general, as the shear stress applied to the sample was increased, the erosion rate increased. The relationship between the shear stress and erosion rate appears be linear or similar to the relationships previously identified in cohesive soils. Even though the results have the anticipated trend, a number of additional
tests are needed before the variability of the samples and the locus of highest values can be established. Recommendations for additional testing and further design improvements are also provided.
It is a common engineering practice to support bridges over water with piles or footings that rest on individual piles. This design allows for water to continuously flow underneath the bridge and reduces the hydraulic force acting on the structure. One of the most important factors in the design of the supporting piles is the depth the piles must be installed in the river or sea bed to provide adequate support capacity for the structure.
However, in many cases, the bed can be eroded due to the action of flowing water. This process is known as scour. Scour, in turn, can reduce the support capacity of the bridge piers. It is therefore imperative to have accurate and dependable design equations that engineers can use to estimate the depth to which piles must be installed.
Scour at a bridge pier can cause the bridge to fail. The most common cause of bridge failures is floods, with the resulting scouring of bridge piles and foundations being the most common cause of flood damage to bridges (Richardson and Davis, 1995, p. 2). Such bridge failures can have tragic results. On April 5, 1987, the Schoharie Creek Bridge (part of the New York State Thruway System) collapsed. Four cars, a truck, and 10 lives were lost as a result (Shepard and Frost, 1995, p. 9). The failure was attributed to the loss of support capacity of the bridge footings due to scour. More recently, on March 10, 1995, the Arroyo Pasajero Twin Bridges (part of Interstate 5) near Coalinga in southern
California collapsed due to floodwaters. This resulted in the death of 7 people (Bobb, 1995).
The damage to bridges from scour has been documented to be widespread. For example, 17 bridges were destroyed or damaged in New York and New England during the floods that occurred in 1987. In 1985, floods in Pennsylvania, Virginia, and West Virginia destroyed 73 bridges. More recently, the 1993 flood in the upper Mississippi basin caused 23 bridge failures for an estimated damage of $15 million (Richardson and Davis, 1995, p. 2). Also, flooding from the storm Alberto in Georgia caused damage due to scour to over 500 state and locally owned bridges (Richardson and Davis, 1995, p. 2). It is evident from these figures that even the non-fatal failures can give rise to excessive costs.
It is clear from the situations described above that it is imperative to have an
understanding of flood-related scour, as such damage to bridges can present a danger to the public that frequently use these bridges. Since the failure of the Schoharie Creek Bridge, the Federal i-ghway Administration (FHWA) has taken a proactive approach to the evaluation of bridges susceptibleto scour and provided guidance on designing new bridges for scour (Pagan-Ortiz, 1998, p. 2). The guidance document currently used in practice by hydraulic engineers to evaluate and design for scour conditions is the FH\VA Hydraulic Engineering Circular No. 18, "Evaluating Scour at Bridges," which is known as HEC-18.
To understand the scour process, it is first important to provide explanations of scour, the different types of scour that occurs at a bridge site, and the current guidance document used by practicing hydraulic engineers to estimate the depth of scour at these
bridge sites. The definitions and explanations presented below are those that are currently used by hydraulic engineers and contained in HEC-l8.
1. 1 Types of Scour
The FHWA defines scour in HEC- 18 as
Erosion or removal of streambed or bank material from bridge foundations
due to flowing water, usually considered as long-term bed degradation,
contraction, and local scour. (Richardson and Davis, 1995, p. xxiii)
The total scour at bridge sites consists of three specific types of scour: long-term aggradation and degradation, contraction scour, and local scour. A description of these different types of scour is provided below.
1.1.1 Long-term Aggradation and Degradation
FHWA describes this process in HEC-18 as
Aggradation and degradation of a river or tidal water body involves the
long term streambed elevation changes due to natural or man-induced
factors that can affect the reach of a river on which the bridge is located.
(Richardson and Davis, 1995, p. 6)
Aggradation is defined as "The general and progressive buildup of the longitudinal profile of a channel bed due to sediment deposition" (Richardson and Davis, 1995, p. xiii). Degradation is defined as "A general and progressive lowering of the channel bed due to scour" (Richardson and Davis, 1995, p. xvi).
Some examples of factors that affect long-term bed elevation changes include:
dams and reservoirs, changes in watershed land use, changes in downstream channel base level, diversion of water, natural lowering of the fluvial system, tidal ebb and flood, littoral drift (Richardson and Davis, 1995, p.7).
1. 1.2 Contraction Scour
Contraction scour is defined In HEC- 18 as "Scour in a channel or floodplain that is not localized at a pier, abutment, or other obstruction to flow" (Richardson and Davis, 1995, p. xvi).
In a channel, contraction scour results from the contraction of streamlines and usually affects all or most of the channel width (Richardson and Davis, 1995, p. 8). Contraction scour can occur when the flow area of a river or stream at flood stage is reduced, either by a natural contraction or a bridge, or when overbank flow is forced back to the channel by roadway embankments at the approaches to a bridge (Richardson and Davis, 1995, p. 8). Contraction scour is based on the continuity equation. That is, as the flow area decreases, the average velocity in the channel section increases. As a result, the bed shear stress through the contraction increases. The increase in shear stress causes an increase in sediment transport. As sediment is transported and the bed is lowered, the shear stress decreases, eventually to a magnitude where sediment is no longer transported and equilibrium is reached.
However, in coastal areas subjected to tidal flow, as the cross-sectional area increases, the discharge from the ocean may increase. If that occurs, the velocity and shear stress may not decrease. As a result, equilibrium may not be achieved. In this situation, the contraction scour may result in a continual lowering of the bed, similar to long-term bed degradation (Richardson and Davis, 1995, p. 8).
1.1.3 Local Scour
Local scour is defined in HEC-18 as 'Scour in a channel or on a floodplain that is localized at a pier, abutment, or other obstruction to flow" (Richardson and Davis, 1995, p. xx).
Local scour is caused by the formation of vortices at the base of either a pier or abutment. This vortex, known as a "horseshoe vortex," causes the bed material to be removed from the base of the structure (Richardson and Davis, 1995, p. 14).
HEC- 18 presents methods for estimating and designing for long-term bed aggradation and degradation, contraction scour, and local scour. The methods and equations presented within the guidance document were based upon laboratory studies that were conducted with beds consisting of cohesionless sediments (sand). It has been discovered by hydraulic and geotechnical engineers, utilizing the equations in HEC- 18 to design and construct bridges, that these equations provide reasonable estimates of scour depths for small structures in cohesionless sediments. However, the HEC- 18 equations overpredict the scour depths for larger or complex structures and for structures located in bed materials other than the cohesionless sediments. Currently, several researchers are investigating and attempting to improve on the design equations for larger and complex structures presented in HEC- 18.
The current approach used in calculating the scour depths around structures
located in bed materials other than sand is to apply the equations provided in HEC- 18 with the assumption that the bed materials will erode to the same depths, given sufficient time, as cohesionless sediments (Annandale et al., 1996, p. 59). The limitation of this approach is that it ignores the ability of materials such as rock to offer more resistance to scour than
sand (Annandale et al., 1996, p. 59). The sea or riverbeds at many bridge sites in the State of Florida are composed of materials other than cohesionless sediments (that is, other than sand or loose shells). This includes harder materials such as limestone and coquina. The erosion characteristics of these materials are quite different from those of cohesionless sediments. However, due to the current lack of understanding of their erosion characteristics, these rock materials are treated as cohesionless sediments in the current design scour prediction equations in HEC-18. Since the erosion of the rock materials can vary from cohesionless sediments, the present approach can be overly conservative in the prediction of scour depths. It is estimated by Florida Department of Transportation (FDOT) engineers that such overdesigns can lead to excessive costs on the order of millions of dollars for bridges. There is a clear need to improve the ability to predict design local and contraction scour depths in rock materials.
It should be noted that this problem is not limited to Florida, but applies to all states where bridges are located in erodible rock materials. For example, the Kentucky Transportation Center conducted a study that included on-site inspection of bridges with footings located on rock. An assessment was made of the validity of the FHWA guidance for assessing the scourability of piers and abutments founded on rock (Froehlich et al., 1995, p. 977). Scour hazards were assessed at 366 Kentucky bridges having at least one pier founded on rock. Analysis of the preliminary data collected during the on-site inspection found the scour hazard to be high at 8.5 percent of the bridges, moderate at 12.1 percent, and low at 79.4 percent of the structures (Froehlich et al., 1995, p. 979).
Along the same lines, on the Yellowstone River in Montana, a 50-year storm event caused a significant shift in the channel angle of attack on the Burlington Northern
Railroad Bridge piers. This resulted in severe scour at the piers and abutments. These piers were founded in a weathered shale, which is a rock material (Lewis, 1993, pp. 22552257).
There has been very little research performed in the area of the scour of rock materials. Chapter 2 of this thesis presents a description of rock materials found in the State of Florida and provides a summary of the previous experimental and engineering work that has been conducted on rock erosion and scour. It also presents a summary of the current state of knowledge of rock erosion as it relates to the scour process.
1.2 Purpose and Scope
1.2.1 Purpose
The scour at a bridge pier is a complex process, involving long-term aggradation and degradation, contraction scour, and local scour. Since extensive research into the rock scour process has been lacking as compared to research with cohesionless sediments, the goal of the work performed in this thesis was to develop a method for evaluating the rates of erosion of rock materials found in the State of Florida. By determining the erosion rate of a rock formation, estimates can be made about the amount of material that would be removed during the design life of a bridge. This information would be beneficial in estimating the long-term degradation and contraction scour at a bridge site located in rock in Florida. Local scour, which is the next step in the design process, in rock formations will need to be addressed in future research.
1.2.2 Scop
The scope of the research that was conducted as part of this thesis involved:
The design and construction of a laboratory apparatus to test the erosion rate
of rock materials from samples collected from bridge sites;
Development of procedures to perform the testing;
The measurement of erosion rates for rock samples collected at bridge sites in
Chapter 3 of this thesis presents a description of the design and construction of the rock erosion testing apparatus and describes the procedures developed for and the results of rock erosion experiments. Chapter 4 presents the results and analysis of the experimental data. Chapter 5 provides a summary of the analysis and the conclusions that were drawn from the experiments. Chapter 6 also presents recommendations for further research to be conducted in the field of rock erosion and scour.
This chapter presents a detailed description of the rock erosion process and a summary of the research that has been conducted in this field. It provides general descriptions of rock and the erosion process as well as the current methods used by practicing engineers to estimate scour in rock materials. It is important to note that the scope of this work does not include a detailed description of the geology of Florida or the rock formation processes. However, a brief description of the geology is included to provide some level of understanding of the rock materials that were evaluated. A detailed description of Florida's geology may be found in The Geology of Florida (Randazzo and Jones, 1997).
2.1 What is Rock?
Before a description of the rock erosion process can be undertaken, it is first
important to provide a definition and description of rock. The definition or interpretation of rock can vary depending on the level of detail required for the application. Simply stated, rock is an assemblage of minerals (Judson et al., 1987, p. 6). A more detailed geologic definition of rock is ". .any naturally occurring aggregates of minerals or mass of mineral matter, whether or not coherent, constituting an essential part of the earth's crust" (Jumikis, 1983, p. 37). However, to the civil engineer, in particular the geotechnical engineer, rock is considered to be a firm and coherent or consolidated substance that can
not be excavated by manual methods alone. The physical and strength properties of rocks are of primary concern to the engineer (Jumikis, 1983, pp. 37-38).
A simple concept of rock has been presented in Jumikis (1983):
Rock is a granular material composed of "grains and glue." There is
nothing else involved. The "glue" may be ferroginous, calcareous,
argillaceous, or siliceous material which cements the grains. (Jumikis,
1983, p. 38).
Rock is often assumed to be a homogeneous and isotropic medium for design purposes. However, in actuality, most rocks are not entirely sound, they are neither homogeneous nor isotropic (Jumikis, 1983, p. 38). Rock is a heterogeneous and anisotropic material, having preferred particle and crystal orientation. In addition, rocks typically have a great number of pores and microcracks that may open, close, or even multiply when a loading is applied (Cristescu, 1989, p. 1). Rocks react differently to forces in different directions, depending on the degree on anisotropy. In summary, rock is a multiple-body system and an extremely complex material difficult to work with (Jumikis, 1983, p. 39).
2.2 How is Rock Classified?
Rocks are typically classified according to several different principles. Jumikis (1983) lists some of these classification systems:
* By origin or genesis,
* Geological or lithological classification,
* Engineering classification of intact rock on the basis of rock strength, or
* A combination of the above items.
A brief description of each of these types of classifications is provided below.
2.2.1 Origin or Genesis
Rocks can be classified based upon the physical process by which they were formed. The three broad groups in which rocks can be placed are:
* Igneous rocks,
* Sedimentary rocks, and
* Metamorphic rocks.
Igneous rocks are formed from the solidification of magma the hot molten
silicate material from within the earth's crust. Sedimentary rocks are formed from the solidification of deposited and accumulated sediments of other rocks, plant remains and animal remains that have been weathered by wind or water at the earth's surface (Jumikis, 1983, p. 45). These are the primary types of rocks that are found in Florida's surface geology. The specific types of sedimentary rocks that are found in Florida will be discussed in Section 2.3 in further detail. Metamorphic rocks are formed when either igneous, sedimentary, and even metamorphic rocks undergo a change in mineralogy or texture due to application of heat, pressure and chemical reaction (Judson et al., 1987, p. 114).
The scope of the work of this thesis deals with sedimentary rocks, as these are the rocks primarily found in the state of Florida at the depths in which bridge piers will be located.
2.2.2 Geological or Lithological Classification
Lithology is the study of the physical character of rocks, such as its mineralogical composition and texture together with a descriptive term from some accepted rock classification system (Jumikis, 1983, p. 62). Examples of a lithologic classification would be limestone or coquina. From an engineering perspective, the geologic descriptions are
not adequate for classifying rocks based on their engineering properties (such as strength). This is due to the fact that a specific type of rock, limestone, for example, could exhibit varying strength characteristics.
2.2.3 Engineering Classification of Intact Rock
Engineering classification systems are based upon the material properties of the rocks. These include geomechanical engineering properties such as uniaxial compressive strength or the Modulus of Elasticity. Standard laboratory tests and examinations can evaluate these properties. An example of an engineering classification system is the rock strength classification system adopted by the International Society of Rock Mechanics (ISRM).
2.3 Types of Rocks in Florida
As described above, the predominate type of rocks that are found in the Florida at shallow (surface) depths are sedimentary rocks. Specifically, the types of rocks are limestone, coquina, sandstone, and coral rock. A description of each of these types of rocks is presented below:
2.3.1 Types of Sedimentar Rocks
As stated above, sedimentary rock is formed from accumulations of sediment,
which may consist of rock fragments of various sizes, remains or products of animals or plants, products of chemical action or of evaporation, or mixtures of these (Judson et al., 1987, p. 465). Sedimentary rocks or metamorphic rocks derived from them constitute approximately 75 percent of the rocks exposed at the surface of the earth (Judson et al., 1987, p. 90). Sedimentary rocks are generally distinguished in two groups detrital and
chemical. Detrital sedimentary rocks are formed from accumulations of minerals and rock fragments derived either from the erosion of existing rock or from the weathering products of these rocks (Judson et al., 1987, p. 91). Chemical sedimentary rocks are produced from chemical processes (Judson et al., 1987, p. 91). However, many sedimentary rocks are combinations or mixtures of the two different groups (Judson et al., 1987, p. 91).
Sedimentary rocks may be composed of a variety of minerals. The detrital
sedimentary rocks are accumulations of igneous rocks (consisting of quartz, feldspar, ferromagnesian silicates) together with precipitated mineral matter that serves to cement the grains together (Judson et al., 1987, p. 93). In addition, sedimentary rocks may contain clays, quartz, and calcite (the most common cementing material in the coarsegrained sedimentary rocks).
Sedimentary rocks are further described based on the texture and particle size of the grains. In the case of chemical sedimentary rocks, they are described further based on the origin of the sediment inorganic or biochemical. Sandstone, which is considered a detrital sedimentary rock, is formed by the consolidation of grains of sand size between 1/16 (0.06) mm and 2 mm in diameter (Judson et al., 1987, p. 98). Sandstone is found in Florida's geology and is described in greater detail below.
Chemical sedimentary rocks that are of biological origin include limestone,
coquina, and coral rock. These rocks are explained in much greater detail below. It is important to know that limestone can also be formed from inorganic processes. Table 2.1 presents a classification of sedimentary rocks.
Table 2. 1. Classification of Sedimentary Rocks (Excluding Pyroclastic Rocks) (Judson et al., 1987, p.97)
Particle Size or
Origin Texture Composition Rock Name
Granule or larger Conglomerate (round grains) or Detrital Clastic Breccia (Angular
Sand Sandstone
Silt Siltstone
Clay Mudstone and
Calcite, CaCO3 Limestone
Chemical: Clastic or Nonclastic
Organic Dolomite, Dolostone
Halite, NaCl Salt
Gypsum,CaSO4 Gypsum
CaCO3 shells Limestone, chalk,
Chemical: Clastic or Nonclastic coquina
Si02 diatoms Diatomite
Plant remains Coal
2.3.2 Limestone
Jumikis (1983) provides a general description of limestone:
Limestone is a bedded carbonate rock and consists predominately of calcium carbonate (CaCO3) which has been formed by either organic
(biologic) or inorganic processes. If of biologic origin, limestone is formed from accumulation of lime shells from shellfish. Limestone responds to the
hydrochloric acid test, i.e., limestone effervesces in diluted HCL-acid.
The color of limestones vary from white through varying shades of gray
and black.
Most limestones have a clastic texture, but crystalline textures are
common. The carbonate rocks, dolomite and limestone, constitute about
22% of the sedimentary rocks exposed above sea level.
Limestones vary greatly in porosity, some being very impervious, some
very porous, hence, pervious. Because carbonate rocks are relatively
soluble, solution cavities in limestones may be abundant. One refers here
to Karst topography. In limestone areas are solution cavities and hence ready permeability should always be suspected until contrary evidence is
obtained. (p.52)
Figure 2.1 shows a sample of limestone from a FDOT rock core collected at a
bridge location in Fort Lauderdale, Florida. The boring log accompanying this rock core
describes this sample as "Gray Limerock, Soft with Intermittent Layers of Hard
Figure 2.1. Gray Limerock, Soft with Intermittent Layers of Hard Limerock
Specific descriptions of the locations of the limestone within Florida are presented in Section 2.3.6.
2.3.3 Sandstone
Jumikis (1983) provides a general description of sandstone:
Sandstone is a consolidated, porous and pervious rock composed mainly of
sand particles quartz grains cemented together by clayey, siliceous,
calcareous or limonitic material which fills the spaces between the grains.
A sandstone which is rich in quartz is stable over a wide range of
temperature and pressure. A siliceous cement usually produces the
strongest sandstone.
Calcareous cement may dissolve, and can be detected by means of the
hydrochloric acid test upon which test the calcareous material will
The flaking off of the sandstone at free surfaces, known as "spalling"
occurs in course of time. (pp. 52-53)
Figure 2.2 shows a sample of sandstone from a DOT rock core collected at a
bridge location in Fort Lauderdale, Florida. The boring log accompanying this rock core describes this sample as "Gray Sandstone."
It should be noted that in the surficial depths in Florida, sandstone is found in layers intermixed in the limestone rock formations.
2.3.4 Coquina
Coquina is a coarser type of limestone composed of organic remains and is
characterized by the accumulation of many large fragments of shells (Judson et al., 1987, p. 100). The name coquina derives from the Spanish for "shellfish" or "cockle". These are biochemical rocks, as described above, since they are a direct result of the
accumulation of shells, plant fragments and other organisms. Figure 23 shows a sample
of coquina.
Figure 2.2. Gray Sandstone
Figure 2,3. Coquina (from http://Index.ecu.edu/geology/harper/sedimentary/display)
Specific descriptions of the locations of the coquina within Florida are presented in Section 2.3.6.
2.3.5 Coral Rock
Coral rock is a biochemical limestone that is created by the action of plants and animals that extract calcium carbonate from the water in which they live. The calcium carbonate may be either incorporated into the skeleton of the organisms or precipitated directly. When the organism dies, it leaves behind a quantity of calcium carbonate. Large deposits of this material may be built up over long periods of time (Judson et al., 1987, p. 100). Reefs are examples of such accumulations. In Florida, the rock formed from such accumulations is described as coral rock. Figure 2.4 shows a sample of coral rock found in Florida (the exact location is not known).
Figure 2.4. Coral Rock
In should be noted that in tropical regions such as Florida Bay and the Florida Keys, there are virtual limestone "factories." These are shallow-water continental shelf regions, with warm climates and warm surface water temperatures that appear to be supersaturated with calcium carbonate, dominated by lime muds and lacking in terrigenous detritus (Judson et al., 1987, p. 100).
Specific descriptions of the locations of the limestone within Florida are presented in Section 2.3.6.
2.3.6 Locations of Rocks in Florida
This section describes the locations where the different types of rocks listed above may be found in Florida and is based on the work performed by Dr. H.K. Brooks for the Institute for Food and Agricultural Sciences at the University of Florida. Brooks (198 la, 198 1 b, 1981 c) characterized the natural features of Florida based on rock and soil types, geologic structure of the underlying rock, geomorphic process that constructed or sculpted the landscape, and relief Brooks (1981 a, 1981 c) developed maps, titled the "Physiographic Divisions of the State of Florida" and the "Geologic Map of Florida," that identify the various types of rocks that are located at the surface throughout the state.
Brooks subdivided the state into the following districts:
" Sea Island District,
* Eastern Flatwoods District,
Gold Coast Florida Bay District,
* Southwestern Flatwoods,
* Central Lake District, Ocala Uplift District,
* Tifton Upland District,
" Dougherty Karst District,
* Apalachicola Delta District, and
Southern Pine Hills District.
Figure 2.5 shows the approximate locations of the boundaries of these districts. The exact boundaries are shown on the "Physiographic Divisions of the State of Florida" Map. Detailed descriptions of these areas and the rocks that may be found within them are presented below.
In most locations in Florida, the solution of limestones have influenced the
landscape and courses of the creeks and rivers (Brooks, 1981b). It is important to stress that this is an overview and a general description of the type of rocks found in Florida. More specific and detailed information may be available on a site by site basis. To assist in the identification of the areas, the counties that are covered within the districts are presented.
Dougherty Karst District Tifton Uplands
f "I
Southern Pine Hills
Ocala Uplift District
.ST. PfERNBURG
Southwestern NAPu
fly ~Err
Sea Island District
*NM& Central Lake District
Eoas en a
Eastern Flatwoods District
-es .AL
Gold Coast and Florida Bay
Figure 2.5. Physiographic Divisions of Florida (after Brooks, 1981c)
126.96.36.199 Sea Island District
The Sea Island District is located in the northeast corner of the state. The district encompasses the counties of Nassau, Duval, Baker, and parts of Hamilton, Columbia, Union, Bradford, Clay, St. Johns, and Alachua Counties. The rock type present here is limestone, specifically Ocala Limestone. However, in most places, the Ocala Limestone is covered by an overburden too thick to influence the landscape or drainage. Outcrops of limestone occur along the St. Johns River in some locations (Brooks, 198 1b).
188.8.131.52 Eastern Flatwood District
The Eastern Flatwoods District extends from St. Johns County south along the Atlantic Ocean coast of Florida to Martin County. Limestone and coquina, are the rock types present in this district. Ocala Limestone is present at or near the surface in the vicinity of Cresent Lake in Flagler County. Coquina is present along the coast from St. Augustine, southeast past Cape Canaveral to Juno Beach (Brooks, 198 1b).
18.104.22.168 Gold Coast Florida Bay District
This district located in the southeastern part (Palm Beach, Broward, Dade, and Monroe Counties) of the Atlantic coastline of Florida, extending from West Palm Beach south to the Florida Keys. The District includes the Everglades and Florida Bay. The rock types present within this district include limestone, coquina, and coral rock (Brooks, 1981ib). The Atlantic coastal ridge is no longer underlain or influenced by coquina deposits in this district, as was the case with the Eastern Flatwoods District. However, the offshore barrier island in the vicinity of Palm Beach is perched upon coquina. Limestone formed as oolitic carbonate shoals are located in the vicinity of Miami. The
Florida Keys are islands of limestone or carbonate sand and mud. They are comprised of Coral Reef Keys containing coral rock and Oolitic Keys composed of oolitic limestone (Brooks, 1981b).
126.96.36.199 Southwestern Flatwoods District
This district includes the southwestern portion of Florida's coastline along the Gulf of Mexico. It includes the counties of Collier, Hendry, Lee, Charlotte, Glades, De Soto, Hardee, Sarasota, Manatee, Pinellas, and portions of Hillsborough County. It extends from St. Petersburg, along the Gulf Coast, south past Naples. The rock type that may be encountered within this district is limestone (Brooks, 198 1b).
18.104.22.168 Central Lake District
Located within the central part of the state, this district is the region of most active collapsed sinkhole development. This district is located between the Sea Island District, the Eastern Flatwood District, the Southwestern Flatwoods District, and the Ocala Uplift District. Limestone is the type of rock that may be encountered within this district. In certain areas, the limestone is very near the surface (Brooks, 198 lb).
220.127.116.11 Ocala Uplift District
The Ocala Uplift District extends along the northwest Gulf Coast up to but not
including the Panhandle. It extends from Tampa northeast to Apalachee Bay. Limestone is at or near the surface in most places within this district (Brooks, 198 lb). Ocala Limestone is present within this area. Brooks (1981 a) describes the Ocala Limestone as "limerock," consisting of the skeletons of fossils in a silt to sand size matrix, skeletons originally as argonite are now molds, 93-96% CaCO3, usually soft porous and friable, with
massive chert nodules occurring near the top and lower portion being rubbly where very small spheroidal fossils are dominant.
188.8.131.52 Tifton Upland District
This district is located on the border of Florida and Georgia and includes Gadsden County. Thick residual silty and clayey soil support a mixed forest in this area (Brooks, 1981b).
22.214.171.124 Dougherty Karst District
The Dougherty Karst District is located on the panhandle section of the state along the Florida and Alabama border. It includes Holmes, Jackson, and Washington Counties. The rock type present in this area is limestone. The limestone in this area is near enough to the surface to have influenced the landscape development (Brooks, 1981b).
126.96.36.199 Apalachicola Delta District
This district is located in the Panhandle along the Gulf Coast. It extends from Apalachee Bay west to Choctawhatchee Bay. This district has a clastic terrain with no karst, which is atypical of the Florida Section (Brooks, 198 Ib).
188.8.131.52 Southern Pine Hills District
This district is located on the western portion of the Panhandle on the FloridaAlabama border. It includes Escambia, Santa Rosa, Okaloosa, and portions of Walton County. This district contains clastic sediments and rocks that are very thick (Brooks, 1981b).
The Florida Geologic Survey (FGS) is currently publishing two new maps "The
Geologic Map of Florida" and "The Geomorphic Map of Florida." These maps may
include updated or refined information from the maps and information presented above.
2.4 Current Methods for the Prediction of Rock Scour
Based on the previous section, it has been demonstrated that rock materials are
present at surficial depths throughout the State of Florida. Bridge piers are being founded
within these materials. Therefore, it is necessary to estimate the depths of scour in rock
materials in Florida. This section describes the current methods used by hydraulic
engineers to estimate the scour of rock materials for bridge piers.
Chapter 3 of HEC- 18 titled Designing Bridges to Resist Scour describes the
approach for placing footings on erodible rock once the total scour for the worst case
condition as been estimated (Richardson and Davis, 1995):
Weathered or other potentially erodible rock formations need to be
carefully assessed for scour. An engineering geologist familiar with the
area geology should be consulted to determine if rock or soil or other criteria should be used to calculate the support for the spread footing
foundation. The decision should be based on analysis of intact rock cores, including rock quality designations and local geology, as well as hydraulic data and anticipated structure life. An important consideration may be the
existence of a high quality rock formation below a thin weathered zone.
For deep deposits of weathered rock, the potential scour depth should be
estimated (steps 4 and 5) and the footings placed below that depth.
Excavation into weathered rock should be made with care. If blasting is
required, light, closely spaced charges should be used to minimize
overbreak beneath the footing level. Loose rock pieces should be removed
and the zone filled with clean concrete. In any event, the final footing
should be poured in contact with the sides of the excavation for the full
designed footing thickness to minimize water intrusion below footing level.
Guidance on the scourability of rock formations is given in Fl-WA
memorandum "Scourability of Rock Formation" dated July 19, 1991. (p.
A summary of the FHWA memorandum referenced in HEC- 18 is presented below.
2.4.2 Scourability of Rock Formations Memorandum
As described above and in recognition that bridge foundation failures have occurred due to scour of rock or rock-like materials, FHWA developed an interim guidance to assess rock scourability using empirical methods and testing procedures (Gordon, 1991). These procedures were provided until the results of ongoing research would permit more accurate evaluation procedures.
The empirical methods presented in the interim guidance are commonly used by geotechnical engineers and geologists to determine rock mass engineering properties (Gordon, 1991). The guidance recommends that designers use a combination of the methods presented as no single index property correctly assesses the potential for scour. Several properties contribute to the quality, bearing capacity and soundness of rock (Gordon, 1991). The guidance recommends the following 7 methods to assess the scourability of rock:
* Subsurface Investigation;
* Geologic Formation/Discontinuities;
* Rock Quality Designation (RQD); Unconfined Compressive Strength;
* Slake Durability Index;
Soundness; and
* Abrasion.
A description of these items is presented below.
2.4.2. 1 Subsurface investigation
The purpose of a subsurface investigation for shallow foundations on rock is to identify rock types, determine the discontinuity frequency, and recover high quality rock cores for testing and evaluation (Gordon, 199 1). The guidance recommends the number of rock cores and type of cores to collect to obtain quality data.
126.96.36.199 Geologic formation/discontinuities
The type of rock and the number of discontinuities have a significant impact on the engineering properties (Gordon, 1991). Whether the rock is igneous, sedimentary, or metamorphic can impact a rock resistance to scour. In general, harder and more sound rock is less susceptible to scour (Gordon, 1991).
The spacing of discontinuities is an indication of overall rock quality and is
measured as the perpendicular distance between parallel discontinuities (Gordon, 1991). High fracture frequency (5 or 6 fractures per foot in a drill core) would indicate a poorer quality rock which would be considerably weaker and more susceptible to scour (Gordon, 1991).
220.127.116.11 Rock Quality Designation (ROD)
The RQD value is a modified computation of percent rock core recovery that
reflects the relative frequency of discontinuities and the compressibility of the rock mass. It is determined by measuring and summing all the pieces of sound rock in a 10.2 cm or longer length of core run, and subsequently dividing this by the total core run length. Rock with a RQD value less than 50% should be assumed to be soil-like with regard to scour potential (Gordon, 1991).
22.214.171.124 Unconfined compressive strengh
The unconfined compressive strength (q,), as determined by American Society of Testing and Materials (ASTM) D2938, is the primary intact rock property of interest for foundation design (Gordon, 1991). In general, samples with unconfined strengths below 1724 kPa (250 psi) are not considered to behave as rock (Gordon, 1991). There is only a generalized correlation between between unconfined compression strength and scourability as unconfined compressive strength increases, bearing capacity generally increases and scourability decreases (Gordon, 1991).
18.104.22.168 Slake Durability Index (SDI)
The International Society of Rock Mechanics (ISRM) SDI test is used on
metamorphic and sedimentary rocks such as slate and shale. SDI values less than 90 indicate poor rock quality. The lower the SDI value, the more scourable and less durable the rock material (Gordon, 1991).
18.104.22.168 Soundness
The laboratory test for soundness (based on AASHTO T 104) uses a soaking
procedure in magnesium or sodium sulfate solution. The samples are soaked for a total of
5 cycles with a duration of 16 to 18 hours per cycle. In general, the less sound the rock, the more susceptible to scour the rock will be. Loss rates of 12% (for the sodium sulfate solution) and 18% (for the magnesium sulfate solution) for the test duration can be used as an indirect measure of scour (Gordon, 1991).
18.104.22.168 Abrasion
The Los Angeles Abrasion Test (AASHTO T96) is an empirical test to assess the abrasion of aggregates. A rock sample is added with 12 steel balls in a rotating steel cylinder. The cylinder is rotated for 1000 revolutions at 30 to 33 revolutions per minute (RPMs). Rock with loss rates greater than 40% should be considered susceptible to scour (Gordon, 1991).
2.4.3 Geotechnical Data Comparisons for Rock Materials in Florida
The FHWA rock scourability guidance memorandum recommends that design
engineers perform several geotechnical tests to use as an evaluation for the susceptibility of rock to scour. The FDOT and University of Florida have conducted some of the recommended test on rock core samples to assess their values in relation to the values presented in the guidance document.
Limestone samples collected from the US 441 Bridge site over the Santa Fe River were tested for Unconfined Compressive Strength, Los Angeles Abrasion Test, and Magnesium Sulfate Soundness Test. Statistical analysis of the Unconfined compressivestrength (qu) test results indicate that the minimum qu expected is 1430 kPa or 207 psi (PSI, 1996, p. 5). The Los Angeles Abrasion Test that was performed yielded a loss of 72.3% (PSI, 1996, p. 9). The Magnesium Sulfate Soundness Test indicated a loss of 80.0% (PSI, 1996, p. 10).
The University of Florida conducted limited geotechnical tests on limestone
samples from Florida. The results from Unconfined Compressive Strength test indicated strengths ranging from 1372 kPa to 1475 kPa (199 psi to 214 psi). Magnesium Sulfate Soundness tests performed on limestone samples indicated losses from 58.7% to 9 1.1%.
In a review of FDOT and UF testing results, the qu are below the 1725 kPa (250 psi) threshold value. The Los Angeles Abrasion and Magnesium Sulfate Soundness test results also indicate that the rock materials should be considered scourable. In summary, based on these geotechnical tests, the rock materials in Florida may be susceptible to scour and must be considered in the design and scour protection for bridge sites.
2.5 Previous Rock Erosion Experiments
The HEC- 18 design manual recommends that rock materials either be considered "scourable" or "non-scourable", but does not provide guidance on the rates of erosion. There has been recent experimental work to evaluate the erosion of rock materials. Specifically, the National Research Council of Canada conducted experiments for the Northumberland Strait Bridge Crossing in Canada.
A series of laboratory experiments was conducted to evaluate the erosive response of sedimentary rock and glacial till at the bridge site in Canada. W. F. Baird & Associates retained the National Research Council (NRC) of Canada Institute for Marine Dynamics to investigate the erodibility of mudstone, siltstone, sandstone, and glacial till at the Northumberland Strait Bridge Crossing. The bridge is located on the Northumberland Strait connecting Prince Edward Island to New Brunswick. The experimental procedures and the results of the experiment are included in the NRC's report titled "Erosive Response of Northumberland Strait Till and Sedimentary Rock to Fluid Flow" dated September 1994. This section presents a brief overview of the tests that were performed and the results and conclusions of the experiments.
The primary goal of the experiments was to determine the critical shear stress of various materials obtained from the seabed of Northumberland Strait (Cornett et al., 1994, p. 1). For those materials that could be eroded, the secondary objective was to determine the rate of erosion of those materials. A total of 23 core samples and 5 slab samples from various locations along the bridge route were provided for testing. Two types of flows were then used to evaluate the rates of erosive nature of the seabed materials open channel flow and flow from a submerged jet (Cornett et al., 1994, p. 2).
The samples that were tested were categorized based on their hardness and
weathering (Cornett et al., 1994, p. 3). The system of rock strength classification and rock weathering classification were presented by the International Society of Rock Mechanics. The till was described as a very stiff, moist, reddish brown clayey silt containing a wide range of sand, gravel and cobbles (Cornett et al., 1994, p. 4). The mudstone was characterized as a finely graded silt or clay with mudstone gravel (Cornett et al., 1994, p. 4). The siltstone as a moderately to highly weathered, thinly laminated, reddish brown, micaceous extremely weak to very weak siltstone (Cornett et al., 1994, p. 5). The sandstone was described as a micaceous fine grained, thinly laminated sandstone with thin inter-beds of siltstone (Cornett et al., 1994, p. 5).
Tests were performed in a 12.5-in long open-channel titling flume with a 40-cm square cross-section. A false floor of PVC was installed in the base of the flume with 3 special test sections designed to receive test samples. An entrained abrasive granular material was also placed in the flow as an abrading agent to evaluate its influence on erosion. A submerged jet was placed in the flow when it was determined that the open channel flow was not sufficient to erode the more competent materials. The surface of the
test samples lay just above the floor (approximately 3 mm into the flow) of the flume (Cornett et al., 1994, p. 6). Core samples were cut and placed in a tray (containing 18 cores) to be inserted in the test sections. The shear stress exerted on the bed by the fluid was determined indirectly by measuring the vertical profile of velocity just above the bed (Cornett et al., 1994, p. 8). The velocity was measured with a laser doppler velocimeter system. Erosion of the upper surface of the test samples was measured at regular spatial intervals using an analogue dial pointer gage with an accuracy of 0.025 mm. (Cornett et al., 1994, p. 13). In the core samples, the elevation was measured at one point near the core. In the slab samples, the elevation was measured in a regular grid pattern across the sample and the average elevation was calculated (Cornett et al., 1994, p. 14).
The average depth of erosion was computed as the difference in average elevation between the initial and final profile. The rate of erosion is the average vertical velocity of the material su rface and was computed by dividing the depth of erosion by the duration of flow (Cornett et al., 1994, p. 15). In addition, a visual observation of the samples was used to assess the onset and extent of erosion.
The results indicated that the till and unconsolidated mudstone samples responded as cohesive soils and eroded in clear water open channel flows. However, the relation between shear stress acting on the bed and the erosion of material is complicated by the wide range of particle sizes within the material as well as the variable cohesive forces that exist between the smaller particles (Cornett et al., 1994, p. 1). For the glacial till, different components begin to erode at different shear stress values thereby making it difficult to characterize the erodibility of the material by a single shear stress value. For example, for a given flow, a sample of the glacial till may erode at a rate that decreases with time as the
easily eroded components are removed at first while the less erodible material remains as part of the sample (Cornett et al., 1994, p. 1).
The weak sedimentary rock that was tested tended to erode by breaking into
pieces along fractures, bedding planes, and other internal weaknesses (Cornett et al., 1994, p. 1). This result suggests that the erosion of the material is not related to shear stress. A suggested model presented by Cornett for the rock erosion process that describes the hydraulic fracturing of the samples is presented in the next section.
It should also be noted that a research project is underway at Oregon State
University to determine the relationship between the erodibility of rock materials and the Slake Durability Index (SDI) test. The results of this study were not available at this time.
2.6 Rock Erosion Process
The process of rock erosion by the action of a moving fluid is a complex one that may be influenced by several factors. On a fundamental level, rocks can be thought of as simply "grains" and "glue" (refer to Section 2. 1). The energy imparted by the moving fluid breaks the grains from the glue and subsequently transports the grains downstream. This fundamental description leads to the idea that there is a certain amount of energy required to initiate erosion of rock materials. In cohesionless sediments, this concept is known as a critical bed-shear stress. This is the shear stress required to initiate motion of the sediments.
Van Rijn (1993) describes the forces acting on a sediment particle resting on a horizontal bed. The fluid forces consist of skin friction forces and pressure forces. The skin friction force acts on the surface of the particles by viscous shear. The pressure
force, consisting of a drag and lift force, is generated by pressure differences along the surface of the particle. Particle movement will occur when the moments of the instantaneous fluid forces with respect to the point of contact are just larger than the stabilizing moment of the submerged particle weight (van Rijn, 1993, p. 4. 1). In rock materials, there are additional forces that act between the particles tending to keep the rock a solid body.
The erosion process in rock can be more complex than just the shear stress acting on a body. Experimental work performed at the NRC found that the weak sedimentary rock that was tested tended to erode by breaking into pieces along fractures, bedding planes, and other internal weaknesses. Cornett et al. (1994) presents a simple model for the hydraulic fracturing of rock. The erosion of the rock materials at the fracture planes was not directly related to the shear stress. The results of the study suggest that the erosion of rock may be driven by hydrodynamic pressures within fractures (Cornett et al., 1994, p.26). Cornett et al. proposed the sketch presented in Figure 2.6:
10 Ul
Ul slab sample
Figure 2.6. Definition Sketch for Hydraulic Fracturing of Rock (Cornett et al., 1994, p.27)
The model proposed by Cornett et al. (1994) for the hydraulic fracturing of rock is based on a thin horizontal crack in a rock sample of length I and height t that is subjected to a steady flow with velocity ul. The crack is a point of stagnation. Through the application of the Bernoulli's equation, a pressure difference develops between the crack and the external flow, which can be expressed as: AP= -P =- 11 122 gt ,I Equation 2.1
The pressure differential represents the velocity head of the flow that acts to open the crack. The fracture, or removal, or rock occurs when the pressure in the crack exceeds the rock strength to resist flexural failure at the base of the crack (Cornett et al., 1994, p. 26).
The bending moment M in the rock above the crack base (assuming a unit width) can be written as:
2=-P=PPl2 Equation 2.2
The maximum axial stress amax required to carry this moment is given by:
a ma = 1.5pV,)2 11 Equation 2.3
This representation suggests that for a fixed crack geometry, the rock strength required to resist failure is proportional to the square of external fluid velocity. Flexure failure would occur when the rock strength is exceeded by the maximum axial stress (Cornett et al., 1994, p. 27).
Annandale, who has developed a method for estimating rock erosion that will be
discussed in the next section, has suggested the following framework for hydraulic erosion
of rock materials. Annandale's approach is based on a rational correlation between the rate of energy dissipation of flowing water and an erodibility classification of the materials (Annandale, 1995, p. 471). The removal of rock material occurs in three stages: jacking, dislodgment, and displacement. Figure 2.7 presents these processes.
Figure 2.7. Hydraulic Erosion (Annandale, 1995, p. 473)
Flowing water is subject to turbulence which, in turn, is associated with a loss in energy. Annandale suggests that turbulence causes pressure fluctuations that result in an action that progressively jacks out material from its position. Once removed, the material is then dislodged and displaced (Annandale, 1995, p. 472). Annandale selected the rate of energy dissipation as the parameter to represent the relative strength of the fluctuating pressure disturbance. Annandale states:
Turbulence causes both pressure fluctuations and energy loss. Increases in
turbulence intensity will concurrently result in increased rates of energy
dissipation and increases in the magnitude of fluctuation pressures.
Estimates of the rate of energy dissipation should therefore represent the relative magnitude of fluctuating pressure, and thus the erosive power of
water (p. 473).
Details of this method are presented in the following section.
2.7 Alternative Rock Erosion Predictive Methods
2.7.1 Erodibility Index Method
A method that has been developed for use in estimating the erosion of rock
materials as well as the erosion of cohesionless and cohesive soils is the Erodibility Index method. This method, developed by Annandale (1995), compares a material's ability to resist erosion, which has been designated as the Erodibility Index, with the erosive power of flowing water. As described above, the erosive power of water has been defined in terms of the stream power. The comparison of these two values determines if a material will or will not erode. This method has been further developed for use in estimating the scour at piles for bridges, which is presented in the Interim Report by the Colorado Department of Transportation titled "Preliminary Procedure to Predict Bridge Scour in Bedrock" (Smith, 1994). A brief description of the components of the Erodibility Index method is presented below. The reader is referenced to the above mentioned report for the details of this method.
2.7. 1.1 Erosive power of water
Hydraulic erosion occurs when the erosive power of flowing water exceeds a material's ability to resist erosion. The erosive power of flowing water is based on the rate of energy dissipation. In this method, the correlation between the rate of energy dissipation (P) and a material's resistance to erosion (Kh) can be expressed as
P = f(Kh), Equation 2.4
(Annandale, 1995, p. 472).
If P > f(Kh), then the material should erode. However, if P < f(Kh), then the material should not erode (Annandale, 1995, p. 472). For an open channel flow condition, the rate of energy dissipation (P) per unit width of flow (based on a unit discharge per unit width q) can be expressed as (Annandale, 1995, p. 480): P = yqsfL = yqAE, Equation 2.5
where y = unit weight of water,
sf = energy slope, and
L = unit length of the channel.
188.8.131.52 Material's resistance to erosion (K_)
As described above, Kh is the parameter used to describe a material's ability to
resist erosion by water. This parameter was based on Kirsten's ripability index, which is a classification system for indexing the effort required for material excavation (Smith, 1994, p. 6). Kirsten developed a rational relationship between the flywheel power of excavation equipment and the ripability of any given earth material (Annandale, 1995, p. 481). The classification system is the product of several parameters which influence excavation and summarizes the most important variables into a single dimensionless number (Smith, 1994, p. 6).
The primary geotechnical parameters that are used in the calculation of the
Erodibility Index are earth mass strength, block or particle size, discontinuity/inter-particle
bond shear strength, and the shape of material units and their orientation relative to the flow (Annandale, 1995, p. 48 1). The relationship is: K = MSKbKdS Equation 2.6
where M, mass strength number,
Kb = particle/block size number,
Kd = disconitunity or inter-particle bond strength, and
J= relative ground structure number.
A description of these parameters is presented below. The tables containing the values for these parameters have not been reproduced in this work.
Mass Strength Number. The mass strength number represents the material
strength of an intact representative sample without regard to geologic heterogeneity within the mass (Annandale, 1995. p. 482). This parameter can be determined for different earth materials such as cohesionless sediment, cohesive sediment, and rock materials.
Particle/Block Size Number. The particle/block size factor is the material
parameter used to represent the rock mass quality or the median particle diameter for granular material (Smith, 1994). The larger the block and particle sizes, the greater the material will offer resistance to erosion. The particle/block size number is evaluated for rock by the ratio of rock quality designation (RQD) to the number of different joints, the joint set number (Jn).
Interparticle Bond Strength Factor. This parameter represents the relative strength of discontinuities in rock and the strength of particle bonding in granular material (Smith, 1994). It is determined by the ratio between joint wall roughness and joint wall alteration in rock material. Visual observations are required to evaluate the condition of the joint
such as tightness, alteration material and separation. Joints that are tighter and rougher with a sound alteration material within the joints will offer a greater resistance to erosion (Smith, 1994).
Relative Shape and Orientation Factor. The relative ground structure number developed by Kirsten (1982) relates the relative shape of the material particles or blocks and the orientation and spacing of the structural features to the direction of effort during excavation (Smith, 1994). For the purposes of hydraulic erosion, the direction of excavation is analogous to the direction of flowing water (Smith, 1994). This parameter can be determined from the dip angle and direction of the least favorable discontinuity relative to stream flow and the ratio of joint spacing (Smith, 1994).
188.8.131.52 Erodibility threshold
The erodibility threshold of earth materials was established by Annandale by relating the erosive power of water (stream power) and the relative ability of the earth materials to resist erosion for 150 field observations and published data on initiation of sediment motion (Annandale, 1995, p. 488). The 150 field observations were from several spillways and dams (Annandale, 1995, p. 472). A material will erode if for a given stream power and Erodibility Index is above the threshold. If it is below the threshold, it will not erode. Annandale provides graphical representations of the erodibility threshold for various earth materials that have not been reproduced here (Annandale, 1995, pp. 489491).
2.7.2 Application of Erodibility Method
W. F. Baird & Associates applied the method in estimating the scour in cohesive
soils and rock materials for the Northumberland Strait Bridge in Canada. The method was
applied by W. F. Baird & Associates in the assessment of scour protection for the 65 bridge piers for the Northumberland Strait Crossing bridge that links New Brunswick and Prince Edward Island in the Canadian Maritimes (Anglin et al., 1997, p. 89). One of the factors at this bridge location that precluded the use of standard scour prediction techniques was the presence of the highly weathered/fractured and variable bedrock seabed. An extensive literature survey was undertaken by Baird & Associates to identify scour assessment techniques that could be applied (Anglin et al., 1997, p. 92). After reviewing the available information, including HEC-18, W. F. Baird & Associates concluded that there was no acceptable technique to define scour potential for the bridge piers due to the following unique conditions:
combined waves and currents; conical shape of the pier bases;
location of some pier bases in dredged pits (up to 7 m deep); and
highly weathered/fractured and variable bedrock seabed (Anglin et al., 1997, p.
Initially, a laboratory study was performed in an attempt to characterize and quantify the erosion potential of the various seabed materials at the crossing location (Anglin et al., 1997, p. 92). The procedures and results of this study were discussed in a Section 2.5. In this experiment, the erosion process was found to be complex and it was not possible to reliably quantify the erosion of these materials as a function of either near bed velocity or shear stress (Anglin et al., 1997, p. 92).
Subsequent to these experiments, the literature review was updated. The
Erodibility Index approach was identified as a potential method for estimating erosion in complex earth materials. To estimate the scour potential, both the stream power and the seabed's resistance to erosion was identified. The stream power of the ambient flow
conditions (tidal surges and currents) was identified through numerical modeling techniques. The 1 00-year stream power event (which considers the combined effect of waves and tidal surges/currents) was selected as the ambient design event for the project (Anglin et at., 1997, p.,94). The stream power at the bridge pier locations were evaluated and a geotechnical investigation was performed to identify, the erodibility indices for the material the bridge piers were to be founded (Anglin et al., 1997, p. 97).
A pier by pier assessment was performed to assess the requirement for scour
protection. A factor of safety was incorporated to address the uncertainties associated with the driving force for erosion, resisting forces, and the erosion threshold relationship. A higher factor of safety was applied at piers with a greater variation in seabed conditions or where the tolerance for scour was lower (Anglin et al., 1997, p. 99).
Currently, a monitoring program is in place to document scour which may occur around the base of the bridge piers. This is being conducted for the following reasons:
" the erodibility index method used for scour evaluation was new and had not
previously been applied to bridge piers, waves, currents, or a design;
" the uncertainties associated with the estimation of the driving force for and the
seabed's resistance to scour; and
" the desire to minimize seabed survey requirements around the bridge piers
(Anglin et al., 1997, p. 101).
The previous chapter provides a brief overview of the current state of knowledge and practice in the field of rock erosion and scour. As can be seen from previous investigations, even though methods have been proposed for predicting water scour in rock materials, much work is still needed. To evaluate the scour of specific rock materials, it is important to examine several factors. At first, it is important to understand a materials reaction to fluid flow. A laboratory study is most suited for this type of investigation since it allows much better control of important variables and, in general, more accurate measurements. The work performed under this study consisted of the development of a methodology for the evaluation a rock's erosion reaction to fluid flow. A laboratory-testing device was required to measure and evaluate the rates of erosion of the various rock materials found in Florida.
3.1 Design Challenges
To develop a laboratory method for testing the erosion rates of rock materials, the following challenges had to be addressed.
There are difficulties in working with rock as a matrix. First, drilling rigs are required to extract samples of rock (called cores). This is the most common
method of collecting rock samples for analysis. Secondly, rock has the
propensity to fracture along weak planes, leaving broken pieces of samples.
Therefore, the testing device must be able to work with limited amount of
sample material and be able to utilize rock cores that are routinely collected by
the FDOT as part of bridge pier design and construction.
" The laboratory-testing device must be able to simulate the action of flowing
water over a bed of rock materials, similar to that found in field conditions.
Specifically, the device must be able to apply a hydraulic shear stress to the
rock surface.
" Along the same lines as described above, the laboratory-testing device must be
able to measure the shear stress that is applied to the rock sample being tested.
" The testing device must be able to generate shear stresses at the levels that will
be encountered in design storm flow conditions. Therefore, the laboratorytesting device must be able to operate at shear stresses that range from ambient
to beyond design conditions.
" Based on information obtained from the literature review, rock can be highly
resistant to erosion. Since the erosion rates are very low as compared with cohesionless and cohesive sediments, the laboratory-testing device must be
able to measure small amounts of lost material while continuously operating for
An extensive literature survey was performed to evaluate the different types of devices used to measure the rates of erosion of natural earth materials with the thought that one of these devices may be able to be applied to rock materials. Based on the above described criteria, the rotating cylinder erosion testing apparatus was selected. This type of device has been used by several researchers in the evaluation of critical stress and rates
of erosion of cohesive sediments. A description of this type of device, which is similar to the viscometer used by Couette, and the improvements that have been implemented are discussed in detail below.
3.2 Previous Use of the Rotating Cylinder Testing Apparatus
Moore and Masch (1962) applied the rotating cylinder principle used in
viscometers to measure the scour resistance of cohesive soils. The device was called the rotating cylinder erosion test apparatus. The apparatus consisted of a cylindrical cohesive soil sample mounted coaxially inside a slightly larger transparent cylinder. The cohesive soil sample is suspended and supported by a hollow tube. The outer cylinder is free to rotate about its axis. The annular gap between the cylinder and sample is filled with fluid. As the outer cylinder is rotated, momentum is imparted to the fluid and the fluid moves, imparting a shear stress to the face of the sample. The cohesive soil sample is stationary but mounted on flexure pivots so that the shear stress transmitted to the sample surface resulted in a slight rotation of the supporting tube. The resulting rotation was calibrated to measure the torque on the sample and, thereby, the shear stress (Moore and Masch, 1962, p. 1444).
As a shear stress was applied to the sample, material was eroded from the face of the sample. The amount of material eroded was measured and the duration that the shear stress was applied was also recorded. Therefore, the average rate of erosion could be computed for a given applied shear stress.
Several researchers including Rektorik et al. (1964), Arulanandan et al. (1973),
Sargunam et al. (1973), Alizadeh (1974) and Chapius and Gatien (1986) have used similar
devices with improvements and enhancements. Akky and Shen (1973) used the rotating cylinder apparatus developed by Arulanandan to evaluate the erosion of cement-stabilized soil. In fact, Chapius and Gatien improved the testing apparatus to accept either intact or remolded cohesive soils, with improved rotation guidance, better alignment, a lower internal friction, and a reduction of the influence of end conditions on the fluid annular flow (Chapius and Gatien, 1986, p. 86). These researchers evaluated the rate of erosion of cohesive sediments with the rotating cylinder device.
3.3 Theoretical Hydrodynamic Aspects of the Rotating Cylinder Apparatus
Essentially, the rotating cylinder works along the same principle as a rotational viscometer. Rotational viscometers operate on the principle that when a cylinder is suspended and immersed in a liquid contained in a vessel which rotates at a steady speed, a balancing couple will be required to keep the cylinder at rest. This couple may be produced by the torsion of a wire from which it is suspended (Merrington, 1949, p. 30). One of the earliest types of rotational viscometers is the Couette viscometer. The outer cylinder is supported by a spindle that rotates at a fixed speed. The inner cylinder is suspended from a torsion wire (Merrington, 1949, p. 32). The fluid is contained in the gap between the two cylinders.
For a newtonian fluid, the velocity distribution increases linearly from zero at the stationary inner cylinder (no-slip condition) to the velocity of the outer rotating cylinder at the wall of the outer cylinder, as shown in Figures 3.1 and 3.2. This equates to laminar flow between two infinite parallel plates.
Figure 3. 1. Velocity profile between two concentric cylinders
Outer Cylinder
Figure 3.2. Velocity profile between two infinite parallel plates
Equating the flow to the linear velocity profile between the two concentric
cylinders occurs only during laminar (tangential only) flow conditions. However, as the speed of the outer cylinder is increased (an increase in the RPMs of the motor) there are changes in the flow regime. The flow begins as a laminar flow and then, at a certain outer cylinder velocity or RPM (depending on cylinders' dimensions), the flow becomes
unstable. The instability grows until a secondary flow is achieved. The secondary flows, described by G.I. Taylor, are a succession of stable toroids or vortices, which have been termed Taylor's rotational vortices. These vorticies are well-defined counter-rotating circulation cells. As the outer cylinder speed is increased, the Taylor vortices can become unstable. Several pictures of Taylor vorticies can be found in An Album of Fluid Motion (Van Dyke, 1982, pp. 76-77).
Rohan and Lefebvre (199 1) investigated certain hydrodynamic aspects of the
rotating cylinder erosion tests. The critical Reynolds number between a laminar flow and the formation of the above mentioned Taylor vortices can be calculated by the following equation (Rohan and Lefebvre, 1991, p. 167): Recr =2'Np a L5R2 > 41.3, Equation 3.1
where N = fQ (radians/s)/27r = rotational speed in cycles/s,
p (kg/m3) fluid density,
t (Ns/m2) = dynamic viscosity,
R, (m) = external radius,
Ri (m) = internal radius, and
cc = RC/Ri.
Viscous stability in the presence of three-dimensional disturbances is obtained for values of Taylor's number (Ta)
Equation 3.2
Ta= Vd d
where d = width of the gap between the cylinders,
Ri=inner radius,
V0 = peripheral velocity of the outer cylinder, and
v =kinematic viscosity (Rohan and Lefebvre, 199 1, p. 169).
In fact, there are three regimes of flow which can be distinguished based upon the calculation of the Taylor number (Rohan and Lefebvre, 1991, p. 169):
1. Ta <41.3 = laminar Couette flow;
2. 41.3 < Ta < 400 = laminar flow with Taylor vortices;
3. Ta > 400 = turbulent flow.
In the cases where the flow consists of secondary flows (vortices) or turbulent flow, the velocity profile is no longer a linear relationship from the wall of the stationary inner cylinder to the rotating outer cylinder.
3.4 Advantages of Rotating Cylinder Apparatus
The rotating cylinder test apparatus met several of the design criteria presented in Section 3. 1. Specifically:
*a small sample quantity of rock samples can be used in this type of device as
the outer cylinder can be sized to accommodate the size of the rock cores and
*water can be applied to a rock sample to produce a shear stress on the sample, *the average shear stress on the sample can be measured easily by measuring the
torque that is being applied to the sample,
*small quantities of material being eroded can be measured using precision
balances, and
0 the apparatus can be operated for a long period of time as the outer cylinder
can be driven by a continuous duty motor.
3.5 Limitations and Bias of Rotating Cylinder Apparatus
It is important to discuss the limitations of this type of testing device to understand where uncertainty and bias may be present in the results from these experiments. In the measurement of the shear stress, the shear stress is computed by measuring the torque on the sample. However, the torque being measured is the torque being applied to the entire sample. Therefore, the calculation of the shear stress results in the average shear stress over the entire sample surface. The results from the experiments assume that the shear stress is uniform across the entire surface of the sample. In actuality, the surface of rock samples can be pitted and uneven (as can be seen from the pictures presented in Section
2.3). Therefore, there may be variations in the shear stress distribution over the face.
Secondly, there may be bias in the measurement of shear stress. Rohan and
Lefebvre (1991) suggest that the shear stress on the sample may be underestimated. The authors suggest that in a curved flow (such as in a curved rectangular pipe), the fluid flowing on the exterior of the curve is exposed to a centrifugal force superior to that found on the interior of the curve. This causes an external "depression"~ and the liquid moves toward the rotating exterior cylinder which favors helicodial flow (Rohan and Lefebvre, 1991. p. 167). In addition, Rohan and Lefebvre (1991) suggest that in the turbulent flow regime, the shear stress may be underestimated due to the fluctuations of the radial components of velocity. Authors are not unanimous in evaluating the influence of the radial component of fluctuation of velocity (Rohan and Lefebvre, 1991. p. 169). In summary, Rohan and Lefebvre (1991) suggest that in interpreting test results, the shear
stress may be underestimated due to streamline curvature and the fluctuations in the radial component of velocity (Rohan and Lefebvre, 199 1. p. 170).
In essence, this indicates that the torque, and therefore shear stress, measured may be biased in the direction of underestimating the shear stress acting on the sample. In practical terms, there may be components of the flow acting on the surface of the sample in directions other than the direction in which the torque is being measured. Thus, there may be a component of shear stress which is eroding the surface of the sample that is not being accounted for in the measurements. These components are difficult to measure.
In the application of these results, the underestimation of shear stress would
provide conservative estimates of the critical shear stress and rates of erosion. That is, the results would show greater erosion rates for a given shear stress. The conservative nature of these results would be appropriate for design applications. Chapter 6 provides recommendations for further research as to evaluating the magnitudes of these biases.
3.6 Rotating Cylinder Testing Apparatus for Measuring Rock Erodibilit
The rotating cylinder testing apparatus used in this study was similar to the devices previously used; however, some modifications have been made. Figures 3.3 and 3.4 are schematic drawings of the rotating device used in this study and Figures 3.5 and 3.6 are photographs of the actual device itself
3.6. 1 Rotating Cylinder Testing Apparatus
This section describes the details of the rotating cylinder testing apparatus. The major components of the apparatus consist of the following:
*Bodine 1/8-hp Frame 42A motor (2500 RPMs at 50 in-oz [353 mm-N] of
torque) with contoller,
* 3-in (7.62-cm) outside diameter (2.5-in [6.35-cm] inside diameter) acrylic
* Omega digital readout, and
* Sensotec Model QWFK-8M Miniature Reaction Torque Transducer (torque
cell) with a range from 0 to 25 in-oz (0 to 176.5 mm-N).
Figure 3.3. Rotating Cylinder Test Apparatus Schematic
English units are shown for equipment dimensions as they were used by the
manufacturers to specify equipment sizes. The metric equivalents are also provided. The testing apparatus consists of a prefabricated metal stand with a motor access panel placed on the front of the stand. The prefabricated metal stand has adjustable feet, which is used
4- 12-in Support Bracing
Torque Cell
Rotating Acrylic Cylinder
S. 33.5-in
22.25-in Not to Scale
Not to scale
Figure 3.4. Schematic of Acrylic Cylinder and Torque Cell
Figure 3.5. Rotating Cylinder Test Apparatus
orque Cell
1.75-in dia. x 3-in long sample
3-in OD 2.5-in ID Acrylic Cylinder
Figure 3.6. Acrylic Cylinder and Torque Cell
to level the apparatus, and handles mounted to the sides that can be used to transport the device. The motor is mounted beneath the top of the prefabricated metal stand. The acrylic cylinder is mounted to a '/2-in (1.27-cm) diameter steel shaft that extends beneath the top of the metal stand. Two pulleys and a belt connect the motor and shaft. The motor controller is mounted on the outside of the access panel.
The rock sample that is being tested is fixed between 2 thin plates and is secured by a 3/16-in (0.48-cm) threaded rod placed through the center of the sample. The rock sample/rod system is connected to the torque cell, which is held stationary by the support bracing fixed directly to the apparatus. The output from the torque cell is displayed by the Omega digital readout, which was programmed (following the manufacturers' recommended procedures) to provide the torque output in mm-N. The readout is
mounted on the outside of the access panel next to the motor controller. A tare switch is connected to the readout. This allows the readout to be set to zero before a test to facilitate the torque reading. The tare switch is also mounted on the face of the access panel just below the readout.
3.6.2 Torque Cell
The addition of the torque cell is an improvement over the previous methods for measuring torque. The torque cell allows for the elimination of bearings or flexure pivots to support the sample and for the measurement of the torque contributions due to end effects. In the previous devices, the cohesive soil sample was mounted to pivots or bearings so that the shear stress transmitted to the sample surface resulted in a slight rotation of the supporting tube. The resulting rotation was calibrated to measure the torque on the sample by using either torsion wires or by a pulley and weight system. In this type of set-up, the friction within the bearings must be accounted for in the torque measurements.
The addition of the torque cell allows for the direct measurement of torque with minimal rotation of the sample. Thus the need for bearings is eliminated. One end of the torque cell is mounted to the fixed support bracing and the sample is mounted to the other end as shown in Figures 3.4 and 3.6.
To calibrate the torque cell, a moment arm was attached to the shaft where the sample would normally be located. A wire was run from the moment arm, over a pulley, to a pan where brass weights were placed. This allowed a known torque to be placed on the torque cell. The torque reading was plotted versus the expected value. Figure 3.7 shows the torque cell calibration. Notice that the cell is very linear.
; 100 80 60
" 40 ~2o
0 20 40 60 80 100 120
Expected Torque (mm-N) Figure 3.7. Torque Cell Calibration
The torque cell measurements agreed with the expected values, indicating that the torque cell is accurate in recording the torque.
3.6.3 Determination of End Effects
In this type of erosion testing device, the torque measurements are for the total torque exerted on the sample. Water flow over the top and bottom ends of the sample also produces a torque that is measured by the torque cell. Since the ends are protected from being eroded by thin metal plates, the torque being produced on the end of the sample must be taken into consideration. A method to evaluate the end effects with the torque cell was developed.
The dimensions of the rock samples used in this experiment are 1.75-in in diameter by approximately 3-in in length (4.45-cm x 7.62-cm). A detailed explanation of the preparation of the rock samples is included in Section 3.7.1.
Experiments were performed to measure the torque exerted on the bottom plate. The experiments consisted of placing the threaded rod with the bottom plate only within the acrylic cylinder. Enough water is added in the rotating cylinder at each RPM tested to cover the underside of the bottom plate only. The torque at each RPM tested was recorded and a plot was developed. Figure 3.8 shows the set-up for the end effects determination experiment.
To Torque Cell
Acrylic Cylinder Threaded Rod
Water level
(varies depending
on RPMs) Bottom Plate
Figure 3.8. End Effects Experiment Set-up
The end effects experiments were conducted on two different dates. The results of those experiments are shown in Figure 3.9.
The results of the two end effects experiments agree. The manufacturer reported the values for the uncertainty bars shown in the figure. As will be discussed in the experimental procedures section, the torque on the bottom plate for a given RPM can be obtained from the plot. This torque is subtracted from the total torque reading. The
---Bottom Plate Only 3-T
.-Bottom Plate Only
An I
0 500 1000 1500 2000 2500 3000 3500
Figure 3.9. End Effects Determination
resulting torque value is that exerted on the outer surface of the sample. It should be noted that during a particular erosion test, only enough water is added to the cylinder annulus to wet the sides and not the end plate on the top of the sample. Therefore, only the end effects from the bottom plate need to be considered.
3.7 Experimental Procedures
This section describes the procedures that were used to perform the experiments. First, the sample preparation procedures are described. The experimental procedures are then described along with the calculations that are performed.
3.7.1 Sample Preparation
Samples that were tested in the rotating cylinder apparatus were collected from rock cores obtained by the FDOT. The sample was formed by drilling a horizontal solid cylinder through a vertical core. The rationale for collecting a sample from the side of a
core was based on the results of a preliminary experiment performed at the University of Florida. A sample of limestone was collected from a FDOT core and then cut into a cube. To obtain qualitative information about the anisotropy of these samples, a pressure washer was directed at each face of the sample. While this does not simulate field conditions (tangential flow over a bed), it did provide some insight into the erosion properties of the sample. It was discovered that there were differences in the rates at which various faces eroded. These differences in erosion can be attributed to the non-homogeneity and anisotropy of rock samples. It was concluded that in order to most accurately simulate the field condition, the sample face being eroded should be in the same orientation as in the field. By cutting a horizontal solid cylinder from the core, the eroding surface will be closer to that of a field situation. Figure 3. 10 illustrates this point.
The samples for erosion testing were taken from 4-in (10.16-cm) nominal diameter cores collected by the FDOT. The samples were cored from the sides using a concrete wet corer with a 2-in (5.08-cm) diameter core bit. This produced a sample of 1.75-in (4.45-cm) in diameter. The ends of the sample were leveled with a concrete wet saw. This left a sample with a length of approximately 3-in (7.62-cm).
A hole must be drilled in the center of the rock material to connect the end plates as well as allow the sample to be connected to the torque cell.
In preparing the samples, it was discovered that during coring, the samples could fracture easily. Care had to be taken in the coring of the samples. To minimize the fracturing, a 3/16-in (0.48-cm) diameter hole was drilled through the center. This minimized the disturbance to the sample and kept the sample intact.
Side Core
: : . . : ::::: ::: ::: ::: ::: :::: ::: ::: ::: :::.:::." .' .: . .:
. ........ : ... .. ... .... !ii ::::::::::::::::: :. . . . . ..::: "
Rock /
... : . . .... ....
Field Cr
Figure 3. 10. Side Coring from Rock Core
3.7.2 Erosion Testing
The procedures described herein were developed to perform the rock erosion
experiments. Below is a list of equipment required for these experiments:
.:rotating cylinder erosion device,
*concrete wet corer,
*2.00-in (5.08-cm) OD/1.75-in (4.45-cm) ID wet core bit,
*3/16-in (0.48-cm) masonry drill bit,
*drying dish,
*drying oven (Located in UF's Geotechnical Engineering Lab),
*calipers, *Pi tape,
*mass balance (with an accuracy of +0. 0 1 g),
*1000 ml graduated cylinder,
hand held tachometer, and
The erosion testing procedures are described in detail below.
1. Prepare the sample for erosion testing as described in Section 3.7.1 by using
the concrete wet corer and masonry drill bit.
2. Record the mass of the sample with the mass balance.
3. Place the sample in the drying oven for at least 16 hours to dry. After that
time, record the mass of the sample. The sample is considered dry when the
mass change is less than 0. 1% in a period greater than I hour. Record the
sample dry mass.
4. Measure the diameter of the sample with the Pi Tape at a minimum of 3
locations with the calipers and record the average diameter of the sample.
5. Measure the length of the sample with the calipers.
6. Measure the volume of the sample by gently submerging the sample in a
graduated cylinder and measure the volume of water displaced.
7. Compute the sample dry density from the above measurements in g/cm .
8. Collect the water and loose material in a drying dish. Place the drying dish in
the drying oven to remove the water. Record the mass of remaining material. 9. Completely immerse the sample in water for at least 16 hours to hydrate. The
sample is hydrated to simulate a saturated rock formation as may be found in a
waterway bed. After that time, record the mass of the sample. The sample is
considered hydrated when the mass change is less than 0. 1% in a period
greater than I hour.
Rock Erosion Test:
1. Secure sample on the threaded rod with the platens and place the sample in the
rotating cylinder erosion-testing device.
2. Fill the rotating cylinder annulus with water to the proper level. It is important
to note that water from the actual field site where the sample was collected
should be used.
3. Place the rubber stopper on the acrylic cylinder and then attach sample to
torque cell.
4. Set the offset of the torque cell with the tare switch to 0.000 mm-N.
5. Turn on the motor and increase the RPMs (as measured by the tachometer)
until the desired torque is achieved.
6. Allow the test to run for a minimum of 72 hours. Record the duration of the
experiment in min with the stopwatch. Periodically adjust the motor speed to keep a constant torque on the sample. Record the torque in mm-N applied to
the sample.
7. Turn off the motor and allow the water within the annulus to cease motion.
8. Remove the sample from the torque cell and cylinder.
9. Empty the water out of the cylinder and clean out the eroded particles in the
10. Place the sample in the drying oven for at least 16 hours to dry. After that
time, record the mass of the sample. The sample is considered dry when the
mass change is less than 0. 1% in a period greater than I hour. Record the
sample dry mass.
There are a few important items to note with regards to the experimental
procedures. First, prior to beginning the actual erosion experiments, a preparation run is required. The preparation run is required to remove loose material from the surface of the
rock sample prior to measuring the erosion. The coring process disturbs the surface of the sample and this may cause an excessive amount of material to erode that may not have eroded otherwise. The preparation run was conducted after the sample dimensions were recorded but prior to the first experiment.
Also, at times, a slight amount of material would be removed from the sample
during the saturation process. This material was collected and weighed (dry weight). This value was then subtracted from mass lost prior to the experiment so the change in mass would reflect the amount of material lost during the experimental run.
3.7.3 Calculations
This section explains the calculations that were made from measurements collected
during the experiments. The calculations consisted of determining the mass lost
during an erosion test, the shear stress acting on the surface sample and the rate of
erosion. The calculations are as follows:
1. Mass lost (g) =Sample dry mass (g) Sample dry mass after experiment (g)
-mass lost from hydration (g)
Torque (mm N)
2. Shear Stress (Pa) = Sample Radius (mm) Sample Surface Area (in2)
Mass Lost (g)
3. Erosion Rate (cm! /min) = Dry Density (g / cm')
Sample Surface Area (cm2)
Experiment Duration (min)
4. Convert to mm!/ hr and plot Erosion Rate (mm / hr) vs. Shear Stress (Pa)
In the calculations above, the erosion rate is expressed as mm/hr. In
cohesive soil studies, this erosion rate is typically expressed as mass/area-time
(such as g/m2-min). In this study, the erosion was converted as a length/time or an effectivev" erosion rate. The purpose of this conversion was to provide an estimate of erosion in terms of a design situation. That is, how much will the bed level be lowered in a finite amount of time.
This chapter discusses the results of the experiments that were performed to
evaluate the critical stress and rates of erosion of rock materials. Erosion experiments were performed on two samples collected from rock corings at a bridge site in Florida. The conclusions that can be drawn from these experiments are presented in the next chapter.
4.1 Cemented Sand
The first experiment was conducted on a rock sample from the 1 7t Street
Temporary Bridge in Fort Lauderdale, Florida collected on April 16, 1997. The boring log that accompanied the sample described the rock as a "Loose Cemented Sand". The sample was collected from a proposed bridge pier location at a depth interval of 27.92 mn and 30.97 mn (91.58 ft and 101.58 ft) below the mudline.
Experiments on this sample were conducted at the University of Florida between March 25, 1999, and April 23, 1999, in the rotating cylinder testing apparatus. The sample was tested at 4 different shear stresses. Table 4.1 presents the dimensions of the sample. Table 4.2 presents the results of the experiments. Figure 4. 1 presents a plot of the erosion rate, versus average shear stress, -T.
Table 4.1. Loose Cemented Sand Dimensions Dry mass (g) 147.48
Diameter (cm) 4.45
Height (cm) 7.34
Volume (cm3) 72.02
Density (g/cm3) 2.05
Surface Area (cm2) 102.53
Table 4.2. Loose Cemented Sand Test Results
Run Torque T Duration Mass lost Erosion rate
No. RPMs N-mm Pa Min mm/hr
1 2280 4.4 19.3 4307.57 0.47 3.12 x 10-4
2 1500 1.5 6.6 4389.85 0.12 7.81 x 10.'
3 1856 2.7 11.8 4436.92 0.09 5.80 x 10.5
4 2010 3.6 15.8 3185.07 0.35 3.14 x 10-4
Since the amount of material being eroded was less than 1 g and the torque being measured was between I and 5 N-mm, uncertainty bars were assigned to the data collected. The purpose of assigning uncertainty bars in this case is to provide an understanding of the possible ranges of values especially in dealing with small quantities. The method used to estimate the uncertainty was proposed by Stein (1964). The method provides an estimate of the largest possible error that the uncertainties of individual quantities create on the final result. Stein states that the method is not entirely defensible
on statistical grounds but it represents an excellent technique for checking the general tolerances on predicted or measured values (Stein, 1964, p. 4 1).
The procedure consists of first determining the uncertainty for an individual measurement (AX for variable X). The unit error for a measurement is expressed as AX/X. The final answer is expressed in terms of the measured variables. The logarithm is taken of each side of the equation and then the derivative of both sides is taken. It is then assumed that the unit errors are sufficiently small to substitute into the equation. That is, AX/X (the unit error) can be substituted for the derivative of Log X. The signs for the individual quantities are placed in the same direction. This procedure assumes that all measurement errors are combined in the most unfavorable way to result in maximum error (Stein, 1964, pp. 41-42).
0.0 5.0 10.0 15.0 20.0 25.0
Shear Stress (Pa)
Figure 4.1. Experimental results for Loose Cemented Sand
It should be noted that the experimental run at 15.8 Pa (Run No. 4), which was the last experiment run on this sample, was performed for 53 hours as opposed to the minimum 72 hours that was described in the previous chapter. This was due to a vibration in the system that was observed. It was determined that the bearing holding the /-in diameter shaft was showing the results of wear. The test was terminated at 53 hours as there was a concern that the vibrations may "shake" the sample within the cylinder and cause material to shake loose from the samples. This may have caused a greater erosion rate than would have occurred without the vibration.
Based on the above results, for the loose cemented sand sample, the erosion rates ranged between 5.80 x 10~ mm/hr and 3.14 x 10- mm/hr for a range of shear stresses between 6.6 Pa and 19.3 Pa.
4.2 Sandstone
The second experiment was conducted on a rock sample from the 17 7h Street
Temporary Bridge in Fort Lauderdale, Florida collected on April 14, 1997. The boring log that accompanied the sample described the rock as a "Dark Tan sandstone with Small Voids and No Shells." The sample was collected from a proposed bridge pier location at a depth interval of 29.93 ma and 30.54 m (98.18 ft and 100. 18 ft) below the mudline. This sample was collected at the same bridge location but different pier as the Cemented Sand sample described in Section 4. 1.
Experiments on this sample were conducted at the University of Florida between April 12, 1999 and April 26, 1999 in the rotating cylinder testing apparatus. The sample was tested at one shear stress. Table 4.3 presents the dimensions of the sample. Table 4.4
presents the result of the experiment. Figure 4.2 presents a plot of the erosion rate, 6,
versus average shear stress, T.
Table 4.3. Dark Tan Sandstone Dimensions Dry mass (g) 191.24
Diameter (cm) 4.47
Height (cm) 6.93
Volume (cm3) 90.03
Density (g/cm3) 2.12
Surface Area (cm2) 97.19
Table 4.4. Dark Tan Sandstone Test Results
Run Torque Duration Mass lost Erosion rate
No. RPMs N-mm Pa Min Ag mm/hr
1 2080 2.3 10.6 4334.00 0.25 1.68 x 10-4
A second experimental run was conducted for this sample at a shear stress of 2.3 Pa (approximately 900 RPMs). This run was performed immediately after the Run No. J of the Loose Cemented Sand sample (at 15.8 Pa). This experimental run was unsuccessful, as excessive vibrations were visible. The sandstone sample was visibly "shaking" which most likely altered the erosion rate and thus invalidated the test.
0.0 5.0 10.0 15.0 20.0 25.0
Shear Stress (Pa)
Figure 4.2. Dark Tan Sandstone
This chapter discusses the conclusions that can be drawn from the data collected from the rotating cylinder apparatus. It is important to note that the data collected from the experiments should be considered preliminary as additional tests are needed at the same shear stresses and the range should be extended.
5.1 Analysis of Cemented Sand and Sandstone Tests
Figure 5.1 is a plot of both the Loose Cemented Sand and Dark Tan Sandstone erosion data A trend line was fitted through the Cemented Sand data with the Microsoft Excel software. The Cemented Sand and Sandstone samples were similar samples in appearance and texture. This linear relationship is based on only 4 data points for the Cemented Sand. Research conducted by Chapius and Gatien in the area of cohesive soil erosion found that between 6 and 10 samples were required to be tested to achieve a good evaluation of the erodibility of a clayey material for a given eroding water. The number of samples allow for a statistical determination of the critical shear stress and the mean erosion rate as a function of shear stress (Chapius and Gatien, 1986, p. 86).
As described in Chapter 2, rock is a non-homogenous and anisotropic material. It is anticipated that, similar to the results found by Chapius and Gatien, that several samples must be tested to develop the erosion relationship. Therefore, the results presented here are preliminary, as only one sample was tested. The test results have the anticipated trend
but a number of additional tests are needed before the variability of the samples and the locus of highest values can be established.
Figure 5.1. Cemented Sand and Sandstone Erosion Rate Data
To provide an estimate of the type of flow conditions that would produce the
range of shear stresses tested in the apparatus, the Prandtl-von Karman formula was used. For hydraulically rough beds
U = 2.57. Inl Il1.d),
Equation 5.1
where U = depth average velocity,
U. = friction velocity,
* Cemented Sand
S2.50E-04 0 Sandstone
- Linear (Cemented Sand)
0.00 5.00 10.00 15.00 20.00 25.00
Shear Stress (Pa)
d =water depth, and
k, Nikuradse Roughness Length.
The average shear stress on the bed can be calculated from
T= ui. 2p. Equation 5.2
A water depth of 7.6 m (25 ft) in freshwater and k, = 0.20 m (0.66 ft) was used for the calculation. A shear stress of 3.6 Pa is produced for a depth averaged velocity of 0.91 ni/s (3 ft/s), 6.5 for Pa for 1. 22 m/s (4 if's), and 10. 1 Pa for 1. 52 ni/s (5 ft/s). For example, if a bed of cemented sand (Figure 5. 1) was subjected to a shear stress of 10 Pa 24 hours per day, 365 days a year, for 50 years, a total of only 5.5 cm (0.2 ft) of material would be eroded based on the preliminary test data.
Figure 5.2 is a plot of the data for the Cemented Sand sample with conceptual relationships provided. Figure 5.1 shows a linear relationship. However, researchers studying cohesive soil erosion, including Chapius and Gatien (1986), showed that the erosion rate relationship can be represented by a composite of two straight lines with different slopes. The point of intersection of the two lines is referred to as the characteristic value. The first line is followed by a second line with a larger slope, which indicates a greater erosion rate. The line with the larger slope may be extrapolated to intersect the Erosion Rate = 0 axis to determine the critical shear stress for cohesive soil erosion (Mehta, 198 1, p. 124). The data collected in this study may support a similar relationship as shown on Figure 5.2.
Mehta (198 1) suggested that there may be several factors that influence the
location of the characteristic value in cohesive soils. These include the sampling method, grain size, salinity, temperature, pH, water content, shear strength, consolidation, and pre-
erosion contact time. In addition, the characteristic values of cohesive soils may vary between experiments. Mehta (1981) suggests that this may be a result of erosion being a stochastic phenomenon. That is, the distribution of the instantaneous bed shear stress and the spatial distribution of the orientation and of the bond strength of the surficial particles are factors that influence the rate of erosion.
Also, for design purposes where a conservative estimate is needed, the conceptual design curve shown in Figure 5.2 would be appropriate. This is a linear relationship through points on the extremes of the uncertainty bars. This relationship would provide the greatest erosion rates.
Conservative Relationship
(Conceptual)- Increase in
/ "Erosion Rate (Conceptual)
/ / Characteristic Value (Conceptual)
,." Extrapolation (Conceptual)
10.00 15.00
Shear Stress (Pa)
Figure 5.2. Conceptual Rock Erosion Relationships
For comparison purposes with erosion rates for other types of materials, the
erosion rates for the Cemented Sand samples were converted to g/(m2-min). The erosion rates for the Cemented Sand samples tested in this study ranged from 0.00198 0.011 g/(m2-min). As described in Chapter 3, Akky and Shen (1973) tested the erodibility of cement-stabilized sandy soil under various physical and environmental conditions. Akky and Shen (1973) varied the amount of cement mixed with the sandy soil and also applied various numbers of wet-dry and freeze-thaw cycles to the samples. The erosion rates ranged from 0 375 g/(m2-min) (which occurred for a sample after 12 freeze-thaw cycles). Chapius and Gatien (1986) noted that the usual range for natural clays was 0 30 g/(mE-min) as compared to 0 100 to 1000 g/(mE-min) for artificial clays.
5.2 Influence of Microcracks on Erosion
As described in Section 3.7 Experimental Procedures, prior to performing the
experiments, a sample preparation run must be performed. The purpose of the preparation is to remove the layer of material that has been disturbed due to the coring procedure. It is likely that the stresses placed on the rock sample from may influence increases the number of microcracks in the sample and alters the stress state. It is noticed that for the same shear stress, a greater amount of material was eroded during the preparation run than an experimental run. The number of microcracks may increase the erosion rate for a sample. Microcracks were discussed in Section 2.1. Chapter 6 recommends additional research to investigate the possible influences of the state of stress and microcracks on the rate of ersoion.
5.3 Further Experiments
The experiments have shown that erosion relationships for rock may be developed. However, additional testing is required to establish definitive testing procedures. The tests that should be conducted include:
" performing multiple tests on the same sample and similar samples to evaluate
the variability of the erosion properties and the repeatability of the tests,
* for a given sample, perform an experiment from the lowest shear stress to the
highest shear stress and vice versa to evaluate if the magnitude and timing of
the shear stress have any influence on the test results,
* measuring the calcium carbonate (CaCO3) content of the eroding fluid before
and after the experiments to evaluate if there is any dissolution of the sample
during the test,
* varying the water chemistry parameters such as salinity to evaluate their
influences on the rates of erosion, and
* adding a cohesionless sediment such as sand to the eroding fluid to evaluate if
it would act as an abrading agent and influence the rates of erosion.
5.4 Design Improvements
After working with the rotating cylinder apparatus for rock erosion, there are
several design improvements suggested to improve the existing device. Particularly, it was noticed during start-up activities that there was a vibration in the motor/shaft/acrylic cylinder system between 3000 and 4000 RPMs. This vibration was significant enough to preclude tests from being run between these speeds. The vibration was attributed to the difficulty in finely balancing the system for high speeds. It is suggested that the '/2-in diameter shaft be replaced by a larger shaft and the top and bottom acrylic pieces of the acrylic cylinder be replaced by a larger diameter and heavier material. This would assist in damping the vibrations at high speeds. In addition, the cylinder could be supported at a
second point, near the top of the cylinder. This would provide support and help reduce vibrations at the higher speeds.
As discussed in the conclusions presented in Chapter 5, a laboratory apparatus and testing method has been developed to estimate the rate of erosion of soft rock materials. The results can be used to estimate contraction scour depths at proposed bridge sites and may be used to estimate local scour depths. Based on the results and conclusions of this work, the following is a list of proposed research efforts: Evaluate rock erosion at actual bridge site To build a database of the erosion rates
of several different types of rock materials found in the State of Florida, samples of erodable rock materials can be collected from design and construction borings being performed at actual bridge sites. The samples can be tested and the rates of erosion
should be established for these rock materials. This information can be used for
evaluation purposes by hydraulic engineers to assess potential erosion depths and
scour severity for different types of rock materials in Florida. While it will most likely
be necessary to actually test the rock materials at a specific site to assess the scour depths, estimates of scour depths based on the type of material may aid in the predesign and conceptual design phases of the project.
" Comparison of sample orientation with the rate of erosion It is necessary to design
and construct a laboratory device that can test a rock sample from a core at different
orientations. As described previously, the current laboratory device tests a sample that
is extracted from the side of a rock core. The purpose of this is to test, as best as possible, the stress plane that is parallel to the flow. However, in a case of local scour, the face or planes of the rock materials may not be oriented parallel to the flow. In addition, it would be advantageous for the FDOT to be able to test the rock cores directly from a boring as opposed to coring from the side of the sample. A modified rotating device should be constructed to be able to test the 4-in diameter rock cores. This would allow for a comparison of the results with the 1.75-in diameter cores to evaluate if there is indeed a difference between the rates of erosion and the stress plane's orientation to the flow. The preliminary tests used to gain insight into the order of magnitude of the rate of erosion indicated that the vertical planes eroded faster than the horizontal planes for the same flow conditions. If this is true in general, then using the vertical cores as samples would provide conservative results (i.e. yield higher erosion rates for the same shear stress). Comparison of the measurement of the rates of erosion with va[ying measurement devices The rotating cylinder laboratory testing device is one type of device to estimate the rates of erosion. As described in Chapter 3, there are certain limitations to this type of device. A second type of erosion testing device is currently being designed and constructed by the University of Florida to test the erosion rates of both cohesive sediments and erodible rock materials. This device is an annular flume where the sample is raised into the flow as the material is eroded. Samples of the same rock materials can be tested in both types of devices and their respective erosion rates can be compared. This will provide an estimate as to the effects of the limitations of the rotating device on the measured rates of erosion.
* Evaluation of the Erodibility Index Method and the laboratory measurement of the
rates of erosion To evaluate the estimates of the depth of scour that can be
computed using the Erodibility Index Method described in Chapter 2, rock samples
can be collected and tested at a specific bridge site. The necessary geotechnical
engineering properties can be collected during the boring process and the depth of scour can be computed. Then samples of the rock material from the coring can be
tested in the rotating cylinder laboratory testing device to estimate the rates of erosion.
Estimates and assumptions can be made to evaluate the design flow condition (500year storm) and the depth of scour can be compared for both methods. This will
provide estimates as to the difference and the degrees of conservatism, if any, between
the estimates.
" Effect of dilitancy and compressibility in rates of erosion By pre-stressing the rock
samples prior to testing in the rotating cylinder laboratory testing device, the dilitancy, compressibility, and number of microcracks can be varied. The erosion rates for each
of these states can be compared to evaluate the influence that they may have on the erosion rates. This may be very important in design considerations. The method of
construction (such as drilled shafts or driven piles) of the bridge piers can influence the state of stress in the underlying rock materials. It may be necessary to take the method
of construction into account in the estimates of the scour depths based on the
measured data.
These further research items are necessary and important in continuing to provide a better understanding of not only the rock erosion process itself, but the factors that
influence the rates of erosion and the methods for estimating the depths of scour. The University of Florida is currently proceeding with the additional research in many of these areas.
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Matthew Henderson was born in New Hartford, New York, in 1968. He grew up in Central New York and spent many summers on the shores of Lake Ontario with his family.
He received a bachelor of science degree with distinction in civil engineering from Worcester Polytechnic Institute in 199 1. Upon graduation, he accepted employment with O'Brien & Gere Engineers, Inc., in Syracuse, New York, as a Civil and Environmental Engineer. He was promoted from Staff Engineer to Design Engineer in 1992 and to Project Engineer in 1994.
In 1996, he left the firm to pursue a graduate degree in Coastal & Oceanographic Engineering at the University of Florida in Gainesville, Florida. After his August 1999 graduation with a master of science degree from the University of Florida, he looks forward to a career in coastal engineering.