Abstract
A theory for nonlinear waves in marine sediments must account for the presence of a granular frame filled with water and possibly gas bubbles. When grains are in full contact, the stress–strain relation for the sediment contains a contribution varying as strain to the power 3/2, referred to as the Hertz force. The quadratic nonlinearity parameter derived from the second pressure derivative with respect to density thus diverges in the limit of small strain. We present a simple nonlinear wave equation model (a variant of the NPE) for compressional waves in marine sediments that avoids Taylor expansion and the problem of diverging nonlinearity parameter. An equation of state for partially consolidated sediments is derived from consolidation test results. Pressure is found to increase with overdensity to the power 5/2, indicating an increase in the number of contacts per grain as density increases. Numerical results for nonlinear compressional waves show agreement with analytic self-similar profiles derived from the nonlinear wave equation. [Work supported by the ONR.]
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