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Unconfined compressive strength of clay soils at different temperatures: experimental and constitutive study

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Abstract

Unconfined compressive strength (\(S_{u}\)) is one of the soil engineering parameters used in geotechnical designs. Due to the temperature changes caused by some human activities, it is important to study the changes in \(S_{u}\) at different temperatures. On the other hand, due to the differences in the mineralogical composition of clay soils, it is important to study this subject in different clays. For this purpose, kaolin, illite and montmorillonite clays with a liquid limit (LL) of 47, 80 and 119, were tested in a temperature-controlled cell in temperature range of 20 to 60 \(^\circ\)C. Temperature was applied in undrained conditions and the results showed that the pore water pressure was a function of temperature and by heating, it increased in the samples. For specific temperature pore water pressure generated in montmorillonite was higher than Illite and kaolin. In all three types of clay, the \(S_{u}\) decreased linearly with increasing temperature. The reduction of \(S_{u}\) in kaolin was more than illite and in illite was more than montmorillonite. For all three samples, with increasing temperature, the modulus of elasticity (E) decreased non linearly. Increasing the temperature reduced strength and the stiffness of the clay samples.. The results of unconfined compressive tests at different temperatures were simulated using hypoplastic model. Impact of temperature was replicated by the model.

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Appendix

Appendix

Formulation of the hypoplastic model is as follows (Mašín 2013):

$$\begin{aligned} \mathring{\mathbf{T}}=f_{s} \varvec{\mathcal {L}}: {\textbf {D}} \frac{f_{d}}{f_{d}^{a}} \varvec{\mathcal {A}}: {\textbf {d}} ||\mathbf {D}|| \end{aligned}$$
(5)

with

$$\begin{aligned}&\varvec{\mathcal {L}} = \varvec{\mathcal {I}} + \frac{\nu }{1-2\nu } {\textbf {1}} \otimes {\textbf {1}} \end{aligned}$$
(6)
$$\begin{aligned}&\varvec{\mathcal {A}} = f_{s} \varvec{\mathcal {L}} + \frac{\mathbf{T}}{\lambda ^{*}} \otimes {\textbf {1}} \end{aligned}$$
(7)
$$\begin{aligned}&f_{s} = \frac{3p}{2} \left(\frac{1}{\lambda ^{*}}+\frac{1}{\kappa ^{*}}\right) \frac{1-2\nu }{1+\nu } \end{aligned}$$
(8)

where \(\nu\), \(\lambda ^{*}\) and \(\kappa ^{*}\) are model parameters, p = − trT/3, and 1 and \(\varvec{\mathcal {I}}\) are second- and fourth-order unity tensors, respectively. The factor \(f_{d}\) reads

$$\begin{aligned} f_{d} = \left(\frac{2p}{p_{e}}\right)^\alpha \end{aligned}$$
(9)

with \(\alpha\) = 2 and the equivalent pressure

$$\begin{aligned} p_{e}=p_{r} exp\left[\frac{N - ln(1+e)}{\lambda ^{*}}\right] \end{aligned}$$
(10)

where N is a parameter and \(p_{r}\) is a reference stress equal to 1 kPa. The factor \(f^{A}_{d}\) reads

$$\begin{aligned} f^{A}_{d}=2^{\alpha }(1-F_{m})^{\alpha /\omega } \end{aligned}$$
(11)

where \(F_{m}\) is the Matsuoka-Nakai factor calculated from

$$\begin{aligned} F_{m}=\frac{9I_{3}+I_{1}I_{2}}{I_{3}+I_{1}I_{2}} \end{aligned}$$
(12)

and the exponent \(\omega\) reads

$$\begin{aligned}&\omega =-\frac{ln(cos^{2}\phi _{c})}{ln2}+a(F_{m}-sin^{2}\phi _{c}) \end{aligned}$$
(13)
$$\begin{aligned}&I_{1}=tr{\textbf {T}} \end{aligned}$$
(14)
$$\begin{aligned}&I_{2}=\frac{1}{2}[{\textbf {T}}:{\textbf {T}}-(I_{1})^{2}] \end{aligned}$$
(15)
$$\begin{aligned}&I_{3}=det{\textbf {T}} \end{aligned}$$
(16)

Finally, the asymptotic strain rate direction d is calculated as

$$\begin{aligned}&{\textbf {d}}=\frac{\mathbf{d}^{A}}{||\mathbf{d}^{A}||} \end{aligned}$$
(17)
$$\begin{aligned}&{\textbf {d}}=-\widehat{{\textbf {T}}}^{*}+1\left[\frac{2}{3}-\frac{cos3\theta +1}{4}F_{m}^{1/4}\right]\frac{F_{m}^{\zeta /2}-sin^{\zeta }\phi _{c}}{1-sin^{\zeta }\phi _{c}} \end{aligned}$$
(18)

with the Lode angle \(\theta\)

$$\begin{aligned} cos3\theta =-\sqrt{6}\frac{tr(\widehat{{\textbf {T}}}^{*}.\widehat{{\textbf {T}}}^{*}.\widehat{{\textbf {T}}}^{*})}{[\widehat{{\textbf {T}}}^{*}:\widehat{{\textbf {T}}}^{*}]^{3/2}} \end{aligned}$$
(19)

exponent \(\zeta\)

$$\begin{aligned} \zeta = 1.7 + 3.9 sin^{2}\phi _{c} \end{aligned}$$
(20)

and the stress measure \(\widehat{{\textbf {T}}}^{*}={\textbf {T}}/tr {\textbf {T}}-\varvec{1}/3\). The model requires five parameters \(\phi _{c}\), \(\lambda\), \(\kappa\), N and \(\nu\), and state variables \(\varvec{T}\) and void ratio e.

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Mohammadi, F., Maghsoodi, S., Cheshomi, A. et al. Unconfined compressive strength of clay soils at different temperatures: experimental and constitutive study. Environ Earth Sci 81, 387 (2022). https://doi.org/10.1007/s12665-022-10473-y

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