Viscous Nucleus Function of Soft Clay Derived from Hydrostatic Stress Relaxation

Abstract

Perzyna’s overstress models are often used to predict the creep behavior of soft clays. In long-term predictions, the performance of these models relies heavily on the choice of the viscous nucleus function. Exponential laws and power laws are common choices. Rather than just assuming a viscous nucleus function, in this study we propose deriving it from the hydrostatic stress relaxation test. To do so, we present a new method for interpreting the results of such test applying Perzyna’s viscoplasticity theory. We demonstrate the method using experimental data from San Francisco Bay mud and Rio de Janeiro soft clay. We conclude that hydrostatic stress relaxation testing is a simple, yet overlooked, way to define and calibrate the viscous nucleus function of soft clays.

Appendix: Derivation of Equation 11

At $t=\infty$ the yield stress balances the mean effective stress, $p'_{y\infty }=p'_\infty$. Thus, Eq. 9 can be rewritten as:

$$\begin{aligned} p'_y = p'_\infty \left( \frac{p'_\infty }{p'} \right) ^\frac{\kappa ^*}{\lambda ^*-\kappa ^*} \end{aligned}$$

Dividing both sides by $p'$, we get:

$$\begin{aligned}{} \frac{p'_y}{p'} &= \frac{p'_\infty }{p'} \left( \frac{p'_\infty }{p'} \right) ^\frac{\kappa ^*}{\lambda ^*-\kappa ^*} = \left( \frac{p'_\infty }{p'} \right) ^{1+\frac{\kappa ^*}{\lambda ^*-\kappa ^*}}\\{} &= \left( \frac{p'_\infty }{p'} \right) ^\frac{\lambda ^*}{\lambda ^*-\kappa ^*} = \left( \frac{p'_\infty }{p'} \right) ^{1/\Lambda } \end{aligned}$$

By defining the overstress function as $F = p'/p'_y - 1$, Eq. 11 is obtained:

$$\begin{aligned} F = \frac{p'}{p'_y} - 1 = \left( \frac{p'}{p'_\infty } \right) ^{1/\Lambda } - 1 \end{aligned}$$

This definition holds true under a hydrostatic stress state, being the mean effective stress the only stress acting on the soil skeleton.