# Induced Polarization of Clay Under Freeze-Thaw Cycling and Desiccation Processes: Effect of Surface Cracking Propagation

Haoliang Luo, Anne Jost, Julien Thiesson, Aida Mendieta, Emmanuel Leger, Damien Jougnot

► To cite this version:

Haoliang Luo, Anne Jost, Julien Thiesson, Aida Mendieta, Emmanuel Leger, et al.. Induced Polarization of Clay Under Freeze-Thaw Cycling and Desiccation Processes: Effect of Surface Cracking Propagation. Geophysical Research Letters, 2025, 52, pp.2024GL113424. 10.1029/2024GL113424. insu-05080907

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# Geophysical Research Letters®

## RESEARCH LETTER

10.1029/2024GL113424

**Key Points:**

* We propose a novel set-up for measuring the complex conductivity spectra and monitoring the soil surface crack patterns

* An exponential decline in both in-phase and quadrature conductivities with drying time, characterized by the same decay time ($r = 358$ min)

* We evidence a clear relationship between both in-phase and quadrature conductivities and the gravimetric water content or the surface crack ratio

**Supporting Information:**

Supporting Information may be found in the online version of this article.

**Correspondence to:**

H. Luo,
haoliang.luo@sorbonne-universite.fr

**Citation:**

Luo, H., Jost, A., Thiesson, J., Mendieta, A., Léger, E., & Jougnot, D. (2025). Induced polarization of clay under freeze-thaw cycling and desiccation processes: Effect of surface cracking propagation. *Geophysical Research Letters*, *52*, e2024GL113424. https://doi.org/10.1029/2024GL113424

Received 10 DEC 2024

Accepted 16 MAR 2025

**Author Contributions:**

**Conceptualization:** Anne Jost,
Damien Jougnot

**Funding acquisition:** Anne Jost,
Damien Jougnot

**Methodology:** Julien Thiesson

**Project administration:** Anne Jost,
Damien Jougnot

**Software:** Julien Thiesson, Aida Mendieta

**Supervision:** Anne Jost, Damien Jougnot

**Visualization:** Anne Jost, Damien Jougnot

**Writing – review & editing:** Anne Jost,
Julien Thiesson, Aida Mendieta,
Damien Jougnot

© 2025. The Author(s).

This is an open access article under the
terms of the Creative Commons

Attribution License, which permits use,
distribution and reproduction in any
medium, provided the original work is
properly cited.

<figure><img src="image_2.png" /></figure>

# Induced Polarization of Clay Under Freeze-Thaw Cycling and Desiccation Processes: Effect of Surface Cracking Propagation

Haoliang Luo<fnref n="1" /> ID, Anne Jost<fnref n="1" />, Julien Thiesson<fnref n="1" /> ID, Aida Mendieta², Emmanuel Léger³ ID, and Damien Jougnot<fnref n="1" /> ID

**Abstract** Freeze-thaw cycles and desiccation drastically affect soil surface cracking and shrinkage processes, altering soil pore structures and hydraulic properties. However, studies using geophysical methods to assess how soil crack patterns and shrinkage respond to climate change remain scarce. Induced polarization, a non-intrusive geophysical technique, is highly sensitive to the moisture content and pore structure of the porous media. For the first time, we investigate the effect of soil surface crack patterns on complex conductivity under freeze-thaw cycling and desiccation processes using a new experimental set-up. Results show that Y-junction-dominated crack patterns form on the sample surface after freeze-thaw cycling, and surface cracking network extends along existing cracks until desiccation ceases. Our findings from induced polarization experiments reveal that two components of complex conductivity are linearly sensitive to surface crack ratio and gravimetric water content. Additionally, they both exhibit a similar decay behavior with drying time. In summary, these results indicate that induced polarization provides a preliminary approach for monitoring the surface crack patterns of clayey soils.

**Plain Language Summary** Geophysical measurements (e.g., induced polarization) provide crucial information about pore structure and surface electrochemical properties, enabling the non-invasive identification of clay minerals. Despite growing concern about soil cracking due to global climate change, induced polarization is rarely used to monitor soil surface crack patterns. Laboratory experiments in this study demonstrate its usefulness in characterizing the cracks propagation of natural soils during freeze-thaw cycles and desiccation, highlighting the potential application for induced polarization in addressing this complex issue.

## 1. Introduction

Clayey soils are critical in various geological and engineering environments due to their hydraulic and mechanical properties (Li et al., 2023; Tang et al., 2021). They display significant structural heterogeneity and are affected by various environmental factors, such as soil mineral composition, hydrological conditions, and vegetation cover. Under complex environmental conditions, clayey soils are subject not only to seasonal wet-dry cycles but also to freeze-thaw cycles, which alter their structural characteristics and affect the formation and expansion of surface cracks (Hewage et al., 2023; Li et al., 2023; Wei et al., 2024). The growth of these cracks is attributed to the formation of ice crystals during the freezing process, which then open up during the thawing process. During desiccation, water evaporation causes the clay to shrink, further exacerbating the propagation of existing crack networks (Tang et al., 2011, 2021). These cracks promote significant changes in soil pore structures and hydraulic properties, thereby affect soil water balance and the hydrologic cycle. Therefore, using non-invasive geophysical measurements to study surface cracking patterns of clay soils under freeze-thaw cycles and desiccation is of great importance to prevent engineering failures.

Spectral induced polarization (SIP) is a non-invasive geophysical technique used to assess the electrical conduction and local charge storage properties of porous media in the low frequency range («10 kHz) using complex-valued conductivity (Schlumberger, 1920). When a primary electrical field is applied to a porous medium, the in-phase component of complex conductivity characterizes the electrical conduction of charge carriers, while the quadrature component describes the polarization phenomenon resulting from the local accumulation of electrical charge carriers in the porous medium (e.g., Binley & Slater, 2020; Kemna et al., 2012). These two components are highly sensitive to the properties of the pore fluid (e.g., saturation, salinity, and pH) and the physical

<footnote n="1">¹Sorbonne Université, CNRS, EPHE, UMR 7619 METIS, Paris, France, ²Université de Paris, Institut de Physique du Globe de Paris, Paris, France, ³Laboratoire GEOPS, Université Paris-Saclay, CNRS, Orsay cedex, France</footnote>
characteristics of the porous medium (e.g., soil pore structure, cation exchange capacity). Therefore, they can provide crucial information about fluid properties and soil pore structure (Hao et al., 2016; Luo, Jost, et al., 2024; Luo, Jougnot, et al., 2024; Luo et al., 2023; Peshtani et al., 2022; Revil et al., 2017).

The study of complex conductivity of clay materials has become increasingly common. For instance, induced polarization can be used to assess the low hydraulic conductivity and safety of clayey materials used as permeability barriers in landfills and radioactive waste repositories (e.g., Jougnot et al., 2010; Okay et al., 2013; Rodríguez et al., 2007). Recent works (e.g., Mendieta et al., 2021, 2023; Qi & Wu, 2024; Revil, Ghorbani, Jougnot, & Yven, 2023; Revil, Ghorbani, Jougnot, Yven, Grgic, et al., 2023) investigated how the mineral composition, salinity, and structural heterogeneity influence the low-frequency electrical responses, which are crucial for understanding the mineral-fluid interactions. Besides, external factors such as water content, temperature, and highly alkaline environment also significantly affect the complex conductivity (El Alam et al., 2023, 2024; Luo, Jougnot, et al., 2024). A comprehensive consideration of these factors helps to more accurately interpret the behaviors of clay minerals in real geological and engineering contexts. During wet-dry and freeze-thaw cycles, clay materials are particularly susceptible to shrinkage and surface cracking, which alter pore structure and, consequently, impact the low-frequency complex conductivity responses (An et al., 2020; Bore et al., 2022; Jougnot et al., 2010; Revil, Ghorbani, Jougnot, & Yven, 2023; Saneiyan et al., 2024). However, existing studies have not explicitly considered the effects of shrinkage and surface cracking on clay materials. Although climate change may amplify the potential for shrinkage, experimental studies investigating how these environmental factors influence low-frequency complex conductivity responses remain limited.

This study aims to evaluate the effect of soil surface crack patterns on complex conductivity during freeze-thaw cycling and desiccation processes. To achieve this, we propose a novel experimental setup for measuring complex conductivity and monitoring surface crack patterns during freeze-thaw cycling and desiccation processes under controlled environmental conditions. The first objective of this study is to investigate dependences of the two components of complex conductivity (in-phase and quadrature conductivities) on gravimetric water content and surface crack ratio. The second objective is to assess how the induced polarization response evolves with time during desiccation.

## 2. Materials and Methods

We propose the first experimental set-up able to jointly investigate the surface crack behavior and determine the complex conductivity of a clay sample, considering the effects of freeze-thaw cycling and desiccation processes. Figure 1a presents pictures of the experimental setup, where the sample holders for electrical conductivity measurement and temperature monitoring have identical structures (see Text S1 in Supporting Information S1). Ag-AgCl non-polarizing electrodes are used in this study to measure the impedance and phase (see Figure S1 in Supporting Information S1). A key point in evaluating complex conductivity is determining the geometrical factor of the sample holder. As shown in Figures 1c and S1 in Supporting Information S1, electrodes P1 and P2 served as current electrodes, while electrodes P5 and P6 were used as voltage electrodes. A geometrical factor of 0.2337 m was used to convert the impedances into the conductivities of the clay sample in this configuration.

We used the same illite material as described in Mendieta et al. (2021). Its porosity range varies in a 0.52–0.56 range and exhibits a cation exchange capacity of 47 meq/100 g. The illite sample was first dried in an oven at 105°C for 12 hr to remove the residual liquid water. The oven-dried clay was then blended with a given amount of brine (NaCl solution) at a specific salinity (i.e., 0.01 mol/L, conductivity: 0.123 S/m at 25°C) to produce samples with the desired water content, until the soil sample reached equilibrium. The initial gravimetric water content of the illite sample was measured to be 0.574 g/g. The equilibrium soil sample was divided into two parts: (a) the first part was compacted into the conductivity cell, and the surface of the specimen was leveled. The electrodes were inserted 1.0 cm into the sample to accommodate the sample desiccation and crack formation while maintaining the electrical contact. (b) The other part was compacted with the same bulk density into the temperature cell, and temperature sensors (arranged along the radial direction) were inserted into the sample for monitoring temperature variations.

We then placed the two experimental cells containing illite in the climatic chamber, installed and calibrated the analytical balance and digital camera. The experiment is separated in two portions (see Figure 1b): a freeze-thaw cycle and a desiccation stage. For the freeze-thaw cycle we used a range of temperature from +5 to –20°C, with step-wise temperature changes and a constant relative humidity of 90%. Every temperature step was held constant
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Experimental equipment, temperature and relative humidity test conditions, evolutions of water evaporation and soil surface cracking in the specimen with different experimental stages. (a) A picture of the laboratory experimental setup. (b) The temperature (including set and actual curves) and relative humidity test conditions for the studied sample. Evolution of surface crack patterns on the specimen under varying experimental states from the digital camera and successive pictures at (c) initial state, (d) after freeze-thaw cycling state, and (e) final state. (f) Change in gravimetric water content (w) with elapsed time. The star represents the initial gravimetric water content of the clay sample. Note that water evaporation occurs within the specimen during the freeze-thaw cycle in an open system, resulting in the loss of liquid water. (g) Change in water evaporation rate with drying time. (h) Change in surface crack ratio ($R_s$) with drying time.</figcaption></figure>

for 6 hr to ensure thermal equilibrium; except for the -3, -20 and +5°C steps that were held for 12 hr. The desiccation portion of the experiment was carried out at 25°C and a relative humidity of 20%. All SIP measurements (from 0.1 Hz to 10 kHz) were taken after the temperature in the chamber had stabilized and were repeated twice. Additionally, we monitored the surface crack patterns as well as the gravimetric water content in one of the samples.
## 3. Experimental Results

### 3.1. Water Evaporation and Cracking Behavior

Figures 1c–1e show the evolution of crack patterns on the specimen surface at different experimental stages. The clay sample exhibits distinct patterns of crack formation and growth during freeze-thaw cycling and desiccation processes. After a freeze-thaw cycle, the crack pattern of the clay sample displays an interconnected network of cracks with Y-shaped connections (i.e., resembling the branches of a “Y”: Figure 1d). As desiccation progresses, the geometric structure of the crack network tends to stabilize, with no new sub-cracks forming. This stage mainly involves the lateral and vertical expansion of existing cracks until desiccation ceases (Figure 1e).

Figures 1f and 1g describe the evolution of the gravimetric water content (w) and water evaporation rate with drying time. Note that water evaporation within the specimen occurs during the freeze-thaw cycle in an open system, resulting in the loss of the liquid water. During the first stage of the desiccation portion, the gravimetric water content decreases linearly, while the water evaporation rate (mass of water loss per minute) remains constant at around 0.208 g/min. After approximately 700 min, the decline of water content gradually slows and water content eventually stabilizes at a residual value of about 0.061. Simultaneously, the water evaporation rate begins to decrease at this stage, and once the residual moisture content is reached, the evaporation rate drops to nearly zero. Additionally, we fitted the water evaporation rate of the desiccation portion using the Boltzmann function (Zhang et al., 2016). Figure 1g shows that this expression effectively describes the typical characteristics and transitions between different evaporation stages of the specimen.

The surface crack ratio ($R_s$), defined as the ratio of the surface area of cracks to the total surface area of the specimen, is used to quantify crack networks at different water contents (see Figure S2 in Supporting Information S1). Figure 1h shows the variation of the surface crack ratio with gravimetric water content. During the freeze-thaw cycling and initial drying stage, the ratio increases rapidly as the water content decreases. With further desiccation, the surface crack ratio tends to a maximum value of approximately 12%. Once the water content reaches the shrinkage limit (the minimum water content at which the volume no longer decreases during desiccation), the surface crack ratio of the specimen eventually stabilizes.

### 3.2. Complex Conductivity Spectra

The complex conductivity, including in-phase conductivity $\sigma^*(\omega)$ and quadrature conductivity $\sigma''(\omega)$, is inferred from the measured impedance and the geometric factor of the sample holder and expressed as,

$$ \sigma^*(\omega) = \sigma'(\omega) + i\sigma''(\omega). \quad (1) $$

Figure 2 shows the complex conductivity spectra at different temperatures and gravimetric water contents. In Figures 2a and 2b, it can be seen that the in-phase conductivity increases with an increase in the temperature during the freeze-thaw cycling process. The in-phase conductivity is roughly two orders of magnitude lower in the frozen state than in the unfrozen state. We also observe that the sample has an initial higher in-phase conductivity than after undergoing the freeze-thaw cycling. For the desiccation process, Figure 2c illustrates that as the gravimetric water content decreases, the in-phase conductivity of the specimen also decreases.

Figures 2d and 2e describe that the quadrature conductivity increases with rising temperature at low frequencies. However, the curves are superimposed regardless of temperature at high frequencies, especially during the thawing process. This suggests that there is no significant correlation between quadrature conductivity and temperature. Figure 2f shows that the quadrature conductivity of the specimen decreases as the gravimetric water content decreases during desiccation. We also observed that at low gravimetric water contents and low frequencies, the experimental data exhibit higher noise and uncertainty.

## 4. Discussion

In cold and arid regions, clayey soils are frequently subjected to freeze-thaw cycles and drying processes that significantly influence the formation and propagation of surface cracks. During the freezing process, pore water freezes into ice, water freezing causes volume expansion and results in the formation of freeze cracks. These cracks then open up during the thawing process (Hewage et al., 2023; Li et al., 2023). After the freeze-thaw cycle, Y-junction-dominated crack patterns have formed on the sample surface (Figure 1d). These crack patterns are
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Complex conductivity spectra of the clay sample (0.01 mol/L NaCl, conductivity: 0.123 S/m at 25°C). (a) In-phase and (d) quadrature conductivity spectra at different equilibrium temperatures during the freezing process. (b) In-phase and (e) quadrature conductivity spectra at different equilibrium temperatures during the thawing process. (c) In-phase and (f) quadrature conductivity spectra at different gravimetric water contents during desiccation.</figcaption></figure>

primarily governed by heterogeneous stress conditions generated by the crystallization process and the clay tensile strength, which is consistent with the findings of previous studies (e.g., Hewage et al., 2023; Lu et al., 2016). During desiccation, the surface cracking network extends longitudinally and transversely along existing cracks until desiccation ceases (Figure 1e). This occurs because the stress concentration increases at the tips and surrounding areas of the existing cracks, promoting the propagation of new cracks in the same direction. Additionally, after the freeze-thaw cycle, uneven moisture distribution accelerates shrinkage and crack propagation, especially near the existing cracks where moisture evaporates more readily (Tang et al., 2011; Wei et al., 2024).

The water evaporation rate of soils is closely associated with the soil pore structure and external environmental factors. The results presented in Figure 1g indicate that the water evaporation rate during drying consists of three stages: a brief constant rate, a falling rate, and a residual stages. After being exposed to the freeze-thaw cycle, the internal pore structure of the specimen is loosened, and micro-cracks form on the surface. They provide more surface area for water evaporation, facilitating water migration and escape (Hewage et al., 2023; Wei et al., 2024). As a result, the water evaporation rate remains relatively constant, supported by internal capillary flow (Shokri et al., 2009). With further desiccation, the water-air interface gradually moves deeper into the specimen, and the amount of liquid water decreases with time. Increased effective stress between soil particles restrict the flow of liquid water from the inner soil pores to the evaporation surface (Tang et al., 2011, 2021). During this period, the evaporation rate gradually decreases, reflecting a transition to diffusion-limited vapor transport (DeCarlo & Shokri, 2014; Or et al., 2013). Once the residual moisture content is reached, the evaporation rate stabilizes at this residual stage.

The in-phase and quadrature components of complex conductivity represent the ability of geological materials to conduct electrical current and reversibly store electric charges, respectively (Jougnot et al., 2010). These components are sensitive to the pore structure, water content, and surface crack propagation of porous media. Additionally, the frequency dependence of in-phase and quadrature conductivities can help to interpret the relevant hydrogeophysical properties of the porous medium (Coperey, Revil, & Stutz, 2019; Duvillard et al., 2018; Revil, Ghorbani, Jougnot, & Yven, 2023; Revil, Ghorbani, Jougnot, Yven, Grgic, et al., 2023; Revil et al., 2017). Figure 2 shows a sharp decline in the magnitude of both components of the complex conductivity for the frozen state at low frequencies. This decline is due to the effects of unfrozen water content and surface crack propagation. The decrease in unfrozen water content, along with the growth of surface cracks, results in a sharp decrease in complex conductivity. However, Figures 2d and 2e show that quadrature conductivity curves are
<figure><img src="image_5.png" /><figcaption>**Figure 3.** The dependence of two components of complex conductivity at 10 Hz on gravimetric water content, elapsed time, and surface crack ratio. (a) Relationship between in-phase and quadrature conductivities and gravimetric water content. The solid lines represent the power-law fit of the experimental data during desiccation. (b) Relationship between in-phase and quadrature conductivities and elapsed time. The elapsed time is recorded from the end of the freeze-thaw cycle. The decay time $\tau$ is determined from the best fit of the exponential decline. (c) Relationship between in-phase and quadrature conductivities and surface crack ratio ($R_s$). The solid lines represent the linear fit of the experimental data during desiccation.</figcaption></figure>

superimposed regardless of the temperature at high frequencies, indicating another possible ice polarization mechanism (Coperey, Revil, Abdulsamad, et al., 2019). During desiccation, quadrature conductivity curves were noisy and exhibited high uncertainties, particularly at low gravimetric water contents and low frequencies. This may be attributed to the increase in contact resistance between the electrodes and the soil sample, as surface cracks propagate deeper into the sample (Jougnot et al., 2010). Additionally, the sudden decrease in relative humidity (from 80% to 20%) causes significant changes in the applied suction, which may affect the steady-state conditions of the clay sample during the SIP measurements. To avoid misinterpretation, we will focus on the experimental data at high frequencies only (from 1 Hz to 1 kHz).

We also analyze the dependence of in-phase and quadrature conductivities at 10 Hz on the gravimetric water content and drying time. Figure 3a describes the relationship between in-phase conductivity and quadrature conductivity versus gravimetric water content during the desiccation process. The solid lines represent the power-law fit of the experimental data. We observe that the in-phase and quadrature conductivities are highly correlated with gravimetric water content, with power-law exponents of 3.1 and 4.1, respectively. Additionally, the power-law exponent for the quadrature component is higher than that for the in-phase component ($p = n+1$), consistent with the previous works (e.g., El Alam et al., 2023, 2024; Vinegar & Waxman, 1984). Here, we introduce an exponential decay with an evaporation characteristic decay time ($\tau$) to describe the decrease in both in-phase and quadrature conductivities with the drying time:

$$ \sigma'(t) = (\sigma_i' - \sigma_f') \exp[-\frac{t}{\tau}] + \sigma_f', \qquad (2) $$

$$ \sigma''(t) = (\sigma_i'' - \sigma_f'') \exp[-\frac{t}{\tau}] + \sigma_f'', \qquad (3) $$

where the subscripts i and f represent the initial and final values of in-phase and quadrature conductivities, respectively. Figure 3b shows the relationship between in-phase and quadrature conductivities and elapsed time. The elapsed time is recorded from the end of the freeze-thaw cycle. Exponential decay was observed in both components of the complex conductivity, indicating that the same process affects both in-phase and quadrature conductivities. We observe that the in-phase and quadrature components exhibit the same decay over the drying time characterized by the same decay time ($\tau = 358$ min). Furthermore, this decay phenomenon may be due to the interaction between moisture loss and the expansion of surface cracks during the desiccation process.

Figure 3c shows the dependence of in-phase and quadrature conductivities at 10 Hz on the surface crack ratio during desiccation. We note that the linear expressions for both conductivities are in fairly good agreement with experimental data. Indeed, as expected, the surface crack ratio increases with decreasing gravimetric water content, leading to higher effective porosity in the clay sample. Since the complex conductivity is sensitive to the water content and effective porosity of the porous medium, the in-phase and quadrature conductivities are reduced. Surface crack dynamics (i.e., surface crack ratio) can affect the hydrological and mechanical properties of clayey soils, thereby affecting the soil water balance and the hydrologic cycle. The results of this work therefore fill a gap in the current literature by demonstrating that complex conductivity can characterize the pore
structure and hydraulic properties, which helps to interpret and monitor the surface cracking and shrinkage dynamics of clayey soils.

## 5. Conclusions

Induced polarization shows promise as a method for assessing and monitoring the physical characteristics of crack propagation in natural soils during freeze-thaw cycling and desiccation processes. In this study, a clay sample has been subjected to laboratory freeze-thaw and desiccation experiments with SIP monitoring. After the freeze-thaw cycle, Y-junction-dominated crack patterns formed on the sample surface. During desiccation, the surface crack network extends along existing cracks until desiccation ceased. The magnitudes of the in-phase and quadrature conductivities exhibited a sharp decline below the freezing/thawing point, while a distinct signal of ice polarization appeared at high frequencies. Both components of complex conductivities exhibited the same exponential decline with drying time, characterized by the same decay time ($\tau = 358$ min). Additionally, a clear relationship was observed between both conductivities and the surface crack ratio, noting that in-phase and quadrature conductivities decrease linearly as the surface crack ratio increases. These findings provide valuable insights into the application of time-lapse tomography for field monitoring on clayey slopes, particularly in evaluating the dynamics of subsurface water transport and crack patterns in clayey slope structures.

## Data Availability Statement

Data is available at Luo, Jost, et al. (2024).

## Acknowledgments

H.L. Luo acknowledges the financial support by China Scholarship Council (CSC) project (Grant 202106370053). The authors also thank the Pierre-Simon Laplace Institute (IPSL) for its financial support through the “Water Cycle” theme. D. Jougnot acknowledges the ANR EXCITING project (Grant ANR-17-CE06-0012) and the ANR-DFG BARRIERS (ANR-24-CE92-0052) projects for funding the instruments and part of the salary of H. Luo.

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