Elastic Modulus of Rock Calculator

Young's modulus of a rock is the slope of the linear portion of its axial stress-strain curve, E = stress divided by strain, with stress in MPa and strain dimensionless, so E is normally quoted in GPa. Because strain is typically only a few thousandths, a granite core loaded to 80 MPa at a strain of 0.0012 returns about 67 GPa. Rock is not perfectly linear: the curve begins concave-up while microcracks close, straightens through the elastic range, then softens as new cracks grow. ISRM and ASTM procedures therefore specify where the slope is taken - tangent modulus at 50 percent of peak strength, secant modulus from the origin, or an average over the straight segment. The dynamic route uses seismic velocities instead: G = rho times Vs squared, nu = (Vp squared - 2 Vs squared) divided by 2(Vp squared - Vs squared), and E = 2G(1 + nu). Typical inputs are Vp of 2,000 to 7,000 m/s, Vs near Vp divided by 1.7, and density around 2,650 kg/m3. Dynamic values usually exceed static ones by 10 to 80 percent because the tiny, fast strains of a passing wave do not mobilize the microcracks and joints that soften a loaded specimen; correlations such as E static near 0.7 times E dynamic are rough and rock-specific. Common bands run below 5 GPa for chalk and weak shale, 5 to 15 GPa for sandstone, 15 to 40 GPa for limestone, 40 to 70 GPa for granite, and above 70 GPa for quartzite and basalt. Porosity, saturation and confining pressure shift these figures substantially.

The proportionality between load and extension was stated by Robert Hooke in 1678 as ut tensio sic vis, and Thomas Young supplied the modulus form in 1807, but applying it to rock waited on mining and dam engineering. Systematic laboratory compression testing of rock cores developed through the first half of the twentieth century as tunnels, hydroelectric dams and deep mines demanded numbers for deformability rather than strength alone. The Malpasset dam failure in France in December 1959 and the Vaiont slide in Italy in October 1963 pushed rock deformability measurement from a research topic into a required design input. The International Society for Rock Mechanics was founded in Salzburg in 1962, largely at the initiative of Leopold Muller, and its Suggested Methods series - including the 1979 method for determining the deformability of rock materials in uniaxial compression - standardized how the modulus is picked off a stress-strain curve. ASTM issued parallel standards, now consolidated in D7012. The dynamic branch grew alongside seismic exploration, as laboratory ultrasonic pulse measurements and borehole sonic logs gave velocities from which moduli could be computed without breaking the sample. Gene Simmons and William Brace documented the systematic gap between static and dynamic compressibility of rocks in a 1965 Journal of Geophysical Research paper, and reconciling the two remains an active problem in reservoir geomechanics.