Determination of volumetric changes in cracked expansive clays

Abstract

The main objective of this research was to determine volumetric changes in cracked expansive clays. The presence of soil discontinuities was captured by using appropriate soil property functions, namely: a bimodal water retention curve and a sigmoidal swell–shrink curve. Field measurements were used in empirical equations to predict volume changes, and the results were validated using published data (laboratory testing, numerical modeling, or site monitoring). The results indicated that the average swell potential and swell pressure of the expansive Regina clay are 18 ± 2% and 155 ± 15 kPa, respectively. Likewise, heave was found to be 20–30 mm at surface and gradually diminished at 1.75 m depth. The predicted results closely matched the ranges and trends as validated using published data of laboratory testing, numerical modeling, or site monitoring. It is concluded that for natural and compacted expansive soils, the bimodal water retention curve differentiates between flow through the cracks and through the soil matrix. Likewise, the proposed sigmoidal equation accurately describes the swell–shrink curve with most of the deformations between the shrinkage limit and the crack limit.

Appendix

Slope of water retention curve

$$D = \frac{{{\text{d}}w}}{{{\text{d}}\varphi }} = w^{{\prime }} = w_{\text{s}} \left[ {\left( {A + B} \right)F} \right]^{{\prime }} = w_{\text{s}} \left[ {F\left( {A + B} \right)^{{\prime }} + \left( {A + B} \right)F^{{\prime }} } \right]$$

where

$$\begin{aligned} \left( {A + B} \right)^{\prime } & = \left\{ {\frac{V}{{\ln \left[ {2.718 + \left( {\frac{a}{\varphi }} \right)^{n} } \right]^{m} }} + \frac{1 - V}{{\ln \left[ {2.718 + \left( {\frac{j}{\varphi }} \right)^{k} } \right]^{l} }}} \right\}^{'} \\ & = - \frac{V}{{m\ln^{2} \left[ {2.718 + \left( {\frac{a}{\varphi }} \right)^{n} } \right]}}\left\{ {\frac{1}{{2.718 + \left( {\frac{a}{\varphi }} \right)^{n} }}\left[ {2.718 + \left( {\frac{a}{\varphi }} \right)^{n} } \right]^{'} } \right\} \\ & \quad - \frac{1 - V}{{ l\ln^{2} \left[ {2.718 + \left( {\frac{j}{\varphi }} \right)^{k} } \right]}} \left\{ {\frac{1}{{2.718 + \left( {\frac{j}{\varphi }} \right)^{k} }}\left[ {2.718 + \left( {\frac{j}{\varphi }} \right)^{k} } \right]^{'} } \right\} \\ & = \frac{{Vn\left( {\frac{a}{\varphi }} \right)^{n} }}{{m\left[ {2.718 + \left( {\frac{a}{\varphi }} \right)^{n} } \right]\varphi \ln^{2} \left[ {2.718 + \left( {\frac{a}{\varphi }} \right)^{n} } \right]}} + \frac{{\left( {1 - V} \right)k\left( {\frac{j}{\varphi }} \right)^{k} }}{{l\left[ {2.718 + \left( {\frac{j}{\varphi }} \right)^{k} } \right]\varphi \ln^{2} \left[ {2.718 + \left( {\frac{j}{\varphi }} \right)^{k} } \right]}} \\ \end{aligned}$$

And,

$$F^{\prime } \left[ {1 - \frac{{\ln \left( {1 + \frac{\varphi }{3000}} \right)}}{5.812}} \right]^{\prime } = - \frac{{\left[ {1 + \frac{\varphi }{3000}} \right]^{\prime } }}{{5.812\left( {1 + \frac{\varphi }{3000}} \right)}} = - \frac{1}{{\left( {\varphi + 3000} \right)5.812}}$$

Therefore,

$$D = \frac{{w_{\text{s}} FVn\left( {\frac{a}{\varphi }} \right)^{n} }}{{m\ln^{2} \left[ {2.718 + \left( {\frac{a}{\varphi }} \right)^{n} } \right]\left[ {2.718 + \left( {\frac{a}{\varphi }} \right)^{n} } \right]\varphi }} + \frac{{w_{\text{s}} F \left( {1 - V} \right)k\left( {\frac{j}{\varphi }} \right)^{k} }}{{l\ln^{2} \left[ {2.718 + \left( {\frac{j}{\varphi }} \right)^{k} } \right]\left[ {2.718 + \left( {\frac{j}{\varphi }} \right)^{k} } \right]\varphi }} - \frac{{w_{\text{s}} \left( {A + B} \right)}}{{5.812\left( {\varphi + 3000} \right)}}$$

(7)

Slope of swell–shrink curve

$$E = \frac{{{\text{d}}e}}{{{\text{d}}w}} = e^{{\prime }} = \left[ {e_{\text{d}} + \frac{{e_{\text{s}} - e_{\text{d}} }}{{1 + \left( {\frac{1}{{{\text{d}}w_{\text{b}} }}} \right)^{{w_{\text{b}} - w}} }}} \right]^{{\prime }} = \frac{{ - \left( {e_{\text{s}} - e_{\text{d}} } \right)\left[ {1 + \left( {\frac{1}{{{\text{d}}w_{\text{b}} }}} \right)^{{w_{\text{b}} - w}} } \right]^{{\prime }} }}{{\left[ {1 + \left( {\frac{1}{{{\text{d}}w_{\text{b}} }}} \right)^{{w_{\text{b}} - w}} } \right]^{2} }}$$

Therefore,

$$E = \frac{{\left( {e_{\text{s}} - e_{\text{d}} } \right)\ln \left( {\frac{1}{{{\text{d}}w_{\text{b}} }}} \right)\left( {\frac{1}{{{\text{d}}w_{\text{b}} }}} \right)^{{w_{\text{b}} - w}} }}{{\left[ {1 + \left( {\frac{1}{{{\text{d}}w_{\text{b}} }}} \right)^{{w_{\text{b}} - w}} } \right]^{2} }}$$

(8)