A simple closed form force balanced solution for pore pressure, overburden and the principal effective stresses in the Earth

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Force balance in the Earth occurs through minerals and fluid, the constituents of the Earth. A simple set of equations rigorously defines the relationships between pore pressure, external confining loads, the principal effective stresses, mineralogy and strain in the Earth. The closed form solution applies The Effective Stress Theorem force conservation law through linkage of force balance definitions with granular mineral and fluid physical properties to a single absolute strain definition. Force balance for solids in the Earth is vectorial within volumetric. Volumetric effective stress is therein directly related to volumetric in situ strain. Force balanced means that all the static solid vectors and the fluid scalars individually and collectively sum to zero. All three principal confining loads, opposing effective stresses and strain are rigorously defined in the closed mathematical form. This set of equations represents a special case of Newtonian physics that applies in the Earth's sedimentary crust. The mathematical closure of the force balance and strain definitions has the fewest possible coefficients. The closed form involves only the density and compressibility coefficients of the minerals and fluid, which bear the external loads. Loading limb mineralogic stress/strain coefficients for the Newtonian closed form solution were measured in the Earth in sedimentary basins that closely fit the Newtonian gravitational biaxial idealization. More than half of the sedimentary basins of the world are extensional, dominated by normal faults and involving an approximately biaxial normal fault regime stress field. Assuming that continental drift is due to mantle convection, and that the Earth's volume is constant, all the horizontal stresses on the surface of the Earth's upper brittle crust would average to zero. Restating these assumptions more briefly, the average stress field of the Earth is biaxial with the maximum principle stress being vertical toward the Earth's center. The closed form equations exactly represent the average governing physics of the Earth. The closed form solution has been inverted and implemented to predict pore pressure and fracture pressure in hundreds of wells in several extensional basins. Wherever it was statistically tested in comparison to empirical methods to predict pore pressure and fracture pressure, the closed form force balanced method was found to be the most accurate. The physical conservation laws—rock properties relationships embodied in the closed form solution—touch every science and technology that deals with the Earth's sedimentary crust.