A novel semianalytical method for evaluating the average consolidation degree of a two-soil-layer deposit

Abstract

Two-soil-layer deposits are sometimes encountered in engineering practice. To accurately assess the consolidation condition of a two-soil-layer deposit, it is necessary to fairly estimate both the settlement- and excess pore water pressure-defined average degrees of consolidation of the system. In this study, the consolidation behavior of a two-soil-layer deposit is first experimentally and numerically investigated, and the results show that the average degree of consolidation defined by the excess pore water pressure (ADCu) is generally less than that defined by the settlement (ADCs), and the difference can be distinct when a softer and less permeable layer is located adjacent to the drainage boundary. A new index (β) denoting the permeability reduction in the soil layer adjacent to the drainage boundary is introduced to indirectly quantify the difference between the ADCu and ADCs. The β value is quantitatively correlated to the permeability, compressibility, soil layer thickness, and loading condition of a two-soil-layer deposit, and a simple method with general application procedures is finally proposed to evaluate the ADCu of a two-soil-layer deposit by modifying a theory that was originally developed to predict the ADCs. Application of the proposed method to another two consolidation tests of two-soil-layer deposits demonstrates that the method has satisfactory validity.

Appendix

According to Zhu and Yin (1999), the ADCs of a two-soil-layer deposit subjected to instantaneous constant loading is

$$U=1-\sum_{i=1}^{n}\frac{{c}_{i}}{{\lambda }_{i}^{2}}{\text{exp}}\left(-{\lambda }_{i}^{2}{T}_{v}\right)$$

(15)

T_v is expressed as

$${T}_{v}=\frac{{c}_{v1}{c}_{v2}t}{{\left({H}_{1}\sqrt{{c}_{v2}}+{H}_{2}\sqrt{{c}_{v1}}\right)}^{2}}$$

(16)

For one-way drainage condition, c_i can be expressed as

$${c}_{i}=\frac{2{\left[{H}_{1}{m}_{v1}\kappa {\text{cos}}\left({\lambda }_{i}\kappa \right)\right]}^{2}}{{\alpha }^{2}\left({H}_{1}{m}_{v1}+{H}_{2}{m}_{v2}\right)\left[{H}_{1}{m}_{v1}{\mathrm{cos}}^{2}\left({\lambda }_{i}\kappa \right)+{H}_{2}{m}_{v2}{\mathrm{sin}}^{2}\left({\lambda }_{i}\alpha \right)\right]}$$

(17)

in which α and κ are

$$\alpha =\frac{{H}_{1}\sqrt{{c}_{v2}}}{{H}_{1}\sqrt{{c}_{v2}}+{H}_{2}\sqrt{{c}_{v1}}}$$

(18)

$$\kappa =\frac{{H}_{2}\sqrt{{c}_{v1}}}{{H}_{1}\sqrt{{c}_{v2}}+{H}_{2}\sqrt{{c}_{v1}}}$$

(19)

and λ_i is the ith positive root of the following equation

$${\text{cos}}\lambda -m{\text{cos}}\left(n\lambda \right)=0$$

(20)

where m is

$$m=\frac{\sqrt{{k}_{v2}{m}_{v2}}-\sqrt{{k}_{v1}{m}_{v{1}}}}{\sqrt{{k}_{v2}{m}_{v2}}+\sqrt{{k}_{v1}{m}_{v1}}}$$

(21)

and n is

$$n=\frac{{H}_{1}\sqrt{{c}_{v2}}-{H}_{2}\sqrt{{c}_{v1}}}{{H}_{1}\sqrt{{c}_{v2}}+{H}_{2}\sqrt{{c}_{v1}}}$$

(22)