1. A method for performing an operation on an earth formation using an estimated property of the earth formation, the method comprising: obtaining a sample of rock from the earth formation; scanning the sample with a volumetric imaging device to obtain a three-dimensional volume representation of the sample; determining internal rock damage of the sample using the three-dimensional volume representation of the sample; performing one or more tests on the sample using a rock test device; measuring a deformation parameter of the sample using a deformation sensor; constructing a mathematical model of the sample that replicates the determined and measured internal rock damage and damage distribution of the sample; simulating the one or more tests using the mathematical model; obtaining a rock deformation parameter using the one or more simulated tests corresponding to the measured rock deformation parameter; comparing the rock deformation parameter obtained from the one or more simulated tests to the corresponding measured rock deformation parameter; adjusting parameters of the mathematical model based upon the rock parameter obtained from simulation not being within a selected range of the measured rock parameter; providing the mathematical model as a verified mathematical model based upon the rock parameter obtained from simulation being within a selected range of the measured rock parameter; estimating an unconfined compressive strength (UCS) of the earth formation using the verified mathematical model; and at least one of (a) pumping hydrocarbons from the earth formation using a pump and a controller at a flow rate determined by the estimated unconfined compressive strength (UCS) in order to avoid sand grains from being pumped with the hydrocarbons, and (b) pumping drilling fluid for drilling a borehole using drilling equipment, the drilling fluid having a weight that is selected using the estimated unconfined compressive strength (UCS) to avoid collapse of the borehole; wherein the determining, constructing, obtaining a rock deformation parameter, comparing adjusting, providing, and estimating are performed using a processor.