STADYN Wave Equation Program 6: Revision of Soil Properties (Cohesion)

In our last post we discussed the overhaul of STADYN’s $\xi-\eta$ system relative to the modulus of elasticity, which additionally involved revising the way the program estimated dry unit weight and void ratio. The last is necessary because the modulus of elasticity is estimated using the Hardin and Black formulation. In this post we will discuss revision of another parameter, namely soil cohesion.

We based the relationship of $\rho$ to $\eta$ based on work for the TAMWAVE program. It would doubtless be useful to state the relationship between $\eta$ and the consistency/density of the soil, and this is as follows:

$\eta$	Cohesive Designation	Cohesionless Designation
-1	Very Soft	Very Loose
-0.6	Soft	Loose
-0.2	Medium	Medium
0.2	Stiff	Dense
0.6	Very Stiff	Dense
1	Hard	Very Dense

Doing it this way enabled us to have a linear relationship between $\rho$ and $\eta$ . It is too much to expect for the linear relationship to extend to other variables, and this is certainly the case with cohesion. Unfortunately, a conventional $\xi-\eta$ interpolation dictates such a relationship. The original $\xi-\eta$ function for cohesion can be seen below, for values of cohesion in kPa.

Note that the relationship between cohesion and $\eta$ is linear for the purely cohesionless state at $\xi = 1$ . If extended past the bounds of the graph for lower values of $\eta$ , the cohesion becomes negative. STADYN prevents this from happening but this essentially deprives soft soils of any cohesion.

Baseon on the TAMWAVE values, for purely cohesive soils the following approximate relationship can be established for cohesion:

$\frac{c}{p_{atm}} = 0.5e^{1.5\eta},\,\xi=1$

where $c$ is the soil cohesion and $p_{atm}$ is the atmospheric pressure. The left hand side of the equation is the “normalised” cohesion using the atmospheric pressure. Doing this for parameters such as effective stress makes for an interesting look at soil properties. The best known use of this is in the SPT correction for overburden.

For cases where $\xi < 1$ , the value can be reduced linearly so that $c = 0$ when $\xi = -1$ . The result of all this can be seen in the graph below.