Derivation of the nonlinearity parameter B/A of saturated, unconsolidated marine sediments via a statistical approach

Marine sediments are known to exhibit the nonlinearity parameter B/A that is much greater than that of homogeneous fluids and solids. The enormous value of B/A is particularly sensitive to the state of grain contacts. Although there exists a large body of literature that deals with the B/A of marine sediments, few studies have addressed how the random nature of grain contacts affects B/A. Here, we develop a model for the B/A of saturated, unconsolidated marine sediments, which accounts for random grain contacts. The number of contacts per grain and the distribution of contact stress between grains are treated statistically. The quadratic nonlinearity of the equivalent suspension of grains and the interstitial fluid is then combined with the nonlinearity arising from the random Hertzian contacts to produce the effective B/A of marine sediments.