Preferential flow induced by desiccation cracks (PF-DC) has been proven to be an important hydrological effect that could cause various geotechnical engineering and ecological environment problems. Investigation on the PF-DC remains a great challenge due to the soil shrinking–swelling behavior. This work presents an experimental and numerical study of the PF-DC considering the dynamic changes of desiccation cracks. A soil column test was conducted under wetting–drying cycles to investigate the dynamic changes of desiccation cracks and their hydrological response. The ratios between the crack area and soil matrix area (crack ratio), crack aperture and depth were measured. The soil water content, matrix suction and water drainage were monitored. A new dynamic dual-permeability preferential flow model (DPMDy) was developed, which includes physically consistent functions in describing the variation of both porosity and hydraulic conductivity in crack and matrix domains. Its performance was compared to the single-domain model (SDM) and rigid dual-permeability model (DPM) with fixed crack ratio and hydraulic conductivity. The experimental results showed that the maximum crack ratio and aperture decreased when the evaporation intensity was excessively raised. The self-closure phenomenon of cracks and increased surficial water content was observed during low-evaporation periods. The simulation results showed that the matrix evaporation modeled by the DPMDy is lower than that of the SDM and DPM, but its crack evaporation is the highest. Compared to the DPM, the DPMDy simulated a faster pressure head building-up process in the crack domain and higher water exchange rates from the crack to the matrix domain during rainfall. Using a fixed crack ratio in the DPM, whether it is the maximum or the average value from the experiment data, will overestimate the infiltration fluxes of PF-DC but underestimate its contribution to the matrix domain. In conclusion, the DPMDy better described the underlying physics involving crack evolution and hydrological response with respect to the SDM and DPM. Further improvement of the DPMDy should focus on the hysteresis effect of the soil water retention curve and soil deformation during wetting–drying cycles.
Desiccation cracks are prevalent in clay-dominated soils due to water loss and often lead water to bypass the surface soil matrix and rapidly infiltrate into subsoil as preferential flow (Davidson, 1984; Weiler, 2005). Positively, the preferential flow induced by desiccation cracks (PF-DC) can promote the migration of farmland organic matter (Vervoort et al., 2003) and reduce surface runoff (Pei et al., 2020; Zhang et al., 2021a). Negatively, it also has proven to be an important hydrological mechanism that could lead to geotechnical engineering and ecological environment problems, such as dike and slope instability (Jamalinia et al., 2020; Zhang et al., 2021b), shallow landslides (Bogaard and Greco, 2015; Caris and Van Asch, 1991; Luo et al., 2021), groundwater pollution (Chaduvula et al., 2022; Chen et al., 2002; Mooney and Morris, 2008; Schlögl et al., 2022) and reduction of irrigation efficiency (Greve et al., 2010; Smith et al., 2005; Wang et al., 2018; Wang et al., 2022). Under the current background of frequent extreme flood–drought climate events, its negative effects will be more prominent (Tichavsky et al., 2019). Investigations on the PF-DC are of great significance in guiding scientific research and practical design in the above disciplines.
A unique characteristic of the desiccation cracks is their dynamic features, often causing instantaneous variation of crack proportion, depth and connectivity with moisture content. Previous efforts have attempted to reveal the effects of crack dynamics on the PF-DC through experimental studies, but most of them focused on the short-term wetting process and obtained only qualitative results, and debates remained. For instance, Favre et al. (1997) and Liu et al. (2003) stated that crack closure due to wetting can cause a significant reduction or even disappearances in the preferential flow. However, other studies found that the PF-DC also leads water to rapidly infiltrate into deep soil, even when desiccation cracks are nearly closed (Baram et al., 2012; Greve et al., 2010; Luo et al., 2021; Tuong et al., 1996; Sander and Gerke, 2007). Cheng et al. (2021) conducted a series of constant-head permeability tests with the hydraulic head gradient of 15 kPa. They stated that 4 % of surface crack ratio could be a critical value for determining whether desiccation cracks cause a significant increase in the infiltration rate or not. However, this value may vary with different soils, rainfall patterns and sample scales and thus lacks general applicability. Indeed, PF-DC has long-term and complex spatiotemporal variability due to crack dynamics during wetting–drying cycles. Therefore, short-term and small-scale infiltration tests (i.e., laboratory permeability tests) are not enough to reveal the complex hydrological process induced by PF-DC. Meanwhile, it is also difficult to quantitatively study PF-DC only through experiments. An improved understanding of the PF-DC combined with theoretical methods is also needed.
Regarding the theoretical methods, explicit crack models (EMs) (Hendrickx and Flury, 2001; Khan et al., 2017; Xie et al., 2020), dual-porosity models (DPoMs) (van Genuchten, 1980; van Genuchten and Wierenga, 1976) and dual-permeability models (DPMs) (Aguilar-López et al., 2020; Gerke and van Genuchten, 1993b, a) were developed to simulate preferential flow in cracked clay soils. EMs were constructed based on the single-domain (or single-permeability) framework, which requires definition of the details involving the geometry, spatial distribution and hydrological properties of each crack. Such a requirement may be conceptually correct but makes it difficult to simulate network-distributed desiccation cracks due to considerable computational burden (Aguilar-López et al., 2020). The DPoM and DPM concepts belong to the dual-domain framework that assumes the soil pore system can be represented as two overlapping interacting regions, one which represents the matrix domain with micropores and the other one which represents the crack domain with mesopores–macropores (Šimùnek et al., 2003). Those models represent the cracks in the soil as an implicit form which need not prescribe geometrical and spatial features of the desiccation cracks. The DPoM concept holds the simplifying stipulation that water only flows through the shrinkage cracks rather than the soil matrix, which is unrealistic in many cases. To remedy this shortcoming, a classical DPM was developed, where the water flow in soil matrix and crack domain was simulated using the Richards' equation (Aguilar-López et al., 2020; Coppola et al., 2012; Gerke and Maximilian Köhne, 2004; Gerke and van Genuchten, 1993a) or Green–Ampt model (Davidson, 1984; Stewart, 2019; Weiler, 2005) building on Darcy's law. However, some critics emerged that the Richards' equation building on the capillarity, not existing in large PF paths (e.g., tensile cracks and biological holes), is not suitable to simulate the PF (Larsbo and Jarvis, 2003; Nimmo, 2010, Nimmo et al., 2021). Consequently, some improved DPMs were developed, where water flow in the crack domain was simulated by the Navier–Stokes equation (Germann and Karlen, 2016; Nimmo, 2010), kinematic wave equation (Greco, 2002; Larsbo and Jarvis, 2003) and Poiseuille model (Lepore et al., 2009). Although these improved DPMs better captured the characteristics of the water flow in the crack domain, the classical DPM concept has still been widely accepted and used in simulating preferential flow in soils due to its easily available parameters, reasonably satisfactory prediction to the measurements and high computation efficiency (Jarvis et al., 2016). Most importantly, a recent numerical study conducted by Aguilar-López et al. (2020) proved that effective parameter selection in the DPMs can achieve similar modeling results to the EMs.
Nevertheless, classical DPMs often adopt the assumption that crack volume and hydrological properties remain constant in both time and space, which is unfeasible to capture the full dynamics of PF-DC. Some attempts have been made to incorporate the dynamic nature of desiccation cracks into DPM including the SWAP family of models, i.e., LEACHM, which simulates PF-DC using a shrinkage characteristic and water loss (Kroes et al., 2000) but neglects the water exchange process occurring at the interface between two domains. Such a process has widely been confirmed to be significant in cracked soils (Greve et al., 2010; Krisnanto et al., 2016; Tuong et al., 1996). A later modification of SWAP incorporated the aforementioned process but at the cost of neglecting shrink–swell behavior of soil. The VIMAC model developed by Greco (2002) solved previous problems but against the cost of inducing many parameters which are difficult to determine from experiments or measurements. Coppola et al. (2012, 2015) took another step forward to allow crack volume and/or hydrological properties to vary as a function of soil shrinkage. However, the relationship proposed in the model, an empirical natural logarithm function involving the suction head and crack proportion, is not directly transferable to other types of soil. Stewart et al. (2016b) deduced a shrinking–swelling model, with relatively clear physical meaning and high consistency, and recently incorporated it into a Green–Ampt-based DPM (Stewart, 2018). While an analytical solution was obtained, the intrinsic limitation of the Green–Ampt approach (i.e., hypothesis of the wetting front and request for a constant boundary condition) hindered the further application of this model in complicated scenarios.
The objective of this research was to investigate the PF-DC from the experimental perspective in combination with an effective modeling approach. Hence, a soil column test was conducted to investigate the dynamic changes of desiccation cracks and hydrological response. The variation of crack geometry, including crack ratio, width and depth, was measured. The soil moisture content, matrix suction and water drainage were also monitored. Meanwhile, we developed a dynamic dual-permeability preferential flow model by incorporating the shrinking–swelling model proposed by Stewart et al. (2016b). The performance of the model was evaluated by comparing the simulated results with measured data.
To investigate the effects of dynamic changes of desiccation cracks on preferential flow, a soil column infiltration test was conducted under wetting–drying cycles (abbreviated as WD cycles hereafter). The testing apparatus consisted of a rainfall-evaporation system, an environment monitoring device, a plexiglass column, a HD camera, hydrological sensors and a drainage measurement device (Fig. 1).
Schematic design and photos of the soil column test.
The rainfall-evaporation system included a rainfall simulator and two warm
lamps as well as a small fan. The rainfall simulator was 0.5 m above the
soil surface, which can produce rainfall with the intensity of 24–120 mm h
The plexiglass column was composed of a column (with a height of 60 cm and a diameter of 50 cm) placed on a catchment hopper which was used to collect and drain out water from the soil column.
The HD camera (TTQ-J2, constant focal length: 35 mm) was fixed on the slope above the soil surface to take photos at regular intervals during the drying periods.
Hydrological sensors, including five soil moisture content–temperature sensors
(Acclima, TDR-310s, with a measurement moisture content range of 0 %–100 % and
an accuracy of
The drainage measurement device, including two electronic balances, was used to record the cumulative water drainage from the soil column.
The soil used in the test was taken from Zongyang County, Anhui, China. Table 1 shows the basic physical parameters and main mineral composition of the
soil samples. The soil found in this study is classified as weak expansive
soil. The saturated hydraulic conductivity was measured on reconstituted
soil cores with a dry density of 1.55 g cm
Basic physical parameters of the soil sample.
Shrinkage curve of the test soil.
To ensure the homogeneity of the soil column, soil samples were compacted in
10 layers, and each layer was 5 cm thick. Prior to filling soil into the
plexiglass column, the soil samples with the total weight required for each
layer were prepared according to the designed density (dry density of
1.55 g cm
In the soil column test, the following data were collected:
Boundary conditions were collected, including rainfall intensity ( Hydrological data, including volume water content ( Crack geometric data, including the crack ratio (
Process of crack image processing.
The overall experimental process included two stages of WD cycles. The purpose of the first stage was to generate a relatively stable surface pattern of the desiccation cracks. The first stage was from 5 January 2022 at 15:00 to 28 February 2022 at 09:00 and included 13 WD cycles.
The second stage was from 28 February 2022 at 09:00 to 28 March 2022 at 22:30 and included seven WD cycles. Figure 4 presents the variation of rainfall, evaporation, temperature and relative humidity in the entire experiment process. Because the two warm lamps and fan were closed during the night, two kinds of evaporation intensity can be observed during the drying periods. In addition, the average environment temperature in the fifth WD cycle was higher because we turned up the power of the two warm lamps. In this current study, we mainly focus on the second stage of WD cycles.
Environmental conditions of the experiment.
The DPM concept used in this study corresponds to the one developed by
Gerke and van Genuchten (1993a). The model divides the flow domain
into two overlapping and interacting continua according to the volumetric
ratios of each domain, where two coupled 2-D Richards' equations are used to
describe the matrix flow and preferential flow as
The hydraulic properties of the two domains are parameterized based on the
Mualem–van Genuchten soil water retention curves (SWRCs)
(Mualem, 1976; van Genuchten, 1980) as
According to Gerke and van Genuchten (1993a), the total porosity
In the case of a DPM, a specified flux
Considering a rainfall condition, the effective boundary fluxes of the two
domains are initially equal to rainfall intensity (
Considering an evaporation condition, the Wilson–Fredlund–Barbour–Penman
experimental function model (Wilson et al., 1997) was used to
calculate the actual evaporation of each domain:
In Stewart et al. (2016a, b) and Stewart (2018), the total porosity (
Stewart et al. (2016a) then deduced the porosities of each
domain as
Substituting
In terms of Eq. (8), the total water content of the soil volume can be
expressed as
However, the
Eventually, we can simulate the hydrological process considering the dynamic changes of desiccation cracks by incorporating Eqs. (19), (21), (26), (27) and (28) into the DPM.
Figure 5 presents typical images of crack evolution during each WD cycle.
Intuitively, it seems that the crack area and width did not show an obvious
increasing trend with the WD cycles as expected. Conversely, during the
first to fourth WD cycles, the cracks at the same moment after rainfall
(Fig. 5b2–4) and the final state (Fig. 5c2–4) decreased significantly, even
though the environmental temperature (
Typical images of crack evolution in seven wetting–drying
cycles.
Figure 6 quantitatively shows the variation of crack ratio
(
Time series of crack geometries.
The maximum crack depth measured after each wetting–drying cycle.
Table 2 presents the manually recorded results of external hydrological responses involving ponding and drainage during each WD cycle. It can be seen that the ponding occurred on the soil surface within 5 min after each rainfall event. The ponding duration in each rainfall event mainly decreased with WD cycles. Note that the ponding depth in each rainfall event was below the upper drainage outlet. Regarding the water drainage, approximately 1.4 kg of water (the total water mass was 8 kg) was leaked during the first rainfall event due to the interspace between the soil and the plexiglass column and the hydrological sensors. Then, we sealed the interspace using clay powder and polyurethane cement (soft materials without constraining effects on the soil swelling) after each drying process, and subsequently, no water drainage was observed at the bottom outlet.
Manual readings of external hydrological responses.
Figure 8 shows the internal hydrological responses recorded by the soil moisture and water potential sensors. Because the M2 and M4 were damaged during soil compaction, no matric suction data were obtained at their depths. Overall, water content at all depths increased during rainfall and decreased during evaporation, where T1 showed the most sensitive responses to the WD cycles. During rainfall, the time for water content to respond to each rainfall event increased with depth, but the time difference among all depths decreased significantly from the second WD cycle on. During the drying periods, an interesting phenomenon was that the water content at 5 cm depth showed an overall decline trend, but transient increases of water content frequently appeared during low-evaporation periods. Such transient increases seem to be related to the slow decrease of crack ratio as mentioned in Sect. 4.1. Regarding the matric suction, its variation trend was similar to the water content but showed more delayed responses to the environmental conditions, especially in the last three WD cycles. Additionally, Fig. 8b also implies that soil at 5 cm depth reached saturation during each rainfall event, while soil below the 25 cm depth was in the unsaturated state in the whole experiment process.
Time series of volume water content
The single-domain model (SDM), dual-permeability model (DPM) and dynamic DPM (DPMDy) were implemented in a finite element solver for Richards' equation as part of the COMSOL Multiphysics® software (COMSOL 5.6). As shown in Fig. 9, they have the same 2-D size, boundary conditions, mesh structure and initial condition. The model domain is 0.5 m by 0.5 m, the same as the soil column. Because the measured maximum crack depth was 23.8 cm, we specified the crack domain existing within the upper 25 cm depth of the soil column.
Setup of the 2-D numerical model for the SDM, DPM and DPMDy.
The boundary conditions at the top were set as a combined type of boundary conditions (as mentioned in Sect. 3.1) for representing the rainfall, ponding and evaporation process recorded in the experiment; the bottom side is a seepage boundary condition; and the left and right sides of the model are no-flux boundaries.
Because the pressure head in the surface area may change frequently and drastically during WD cycles, a refined mesh structure with dense boundary layers was used to capture the transient hydrological conditions. The boundary layers included 15 layers of rectangular grid, with a minimum and maximum thickness of approximately 0.04 and 0.3 cm, respectively. A coarser free-triangle mesh (average length of 1.8 cm) was defined below the boundary layers. The initial condition both in matrix and crack domains was set as the distribution of porewater pressure measured from the experiment prior to the first WD cycle.
As shown in Fig. 10, using Eq. (18) to fit the measured shrinkage curve in
Fig. 2, we obtained the four shrinkage parameters as
Fitted shrinkage curve (solid line) and modeled porosity variation of matrix (dashed line) and crack domains (dashed–dotted line).
Figure 11 shows the measured matric suction versus volume water
content at different depths. The SWRCs were estimated using a best fit of
the van Genuchten–Mualem equation to measured soil water retention data. It
can be seen that the WD cycles lead to hysteretic curves in the SWRC at 5 cm
and 25 cm depths, while those at the 45 cm depth rarely show hysteretic
curves. This result may also indicate that most of the cracks exist within
the upper 25 cm depth of the soil column. In this study, we simply estimated
an approximate single SWRC of the soil matrix through experiment data
instead of incorporating the hysteretic curves into the model. For instance,
the estimated SWRC in Fig. 11a lies between the wetting SWRC
and drying SWRC to capture the overall characteristics of wetting–drying
SWRCs as far as possible. Note that the shape parameter
Measured and estimated SWRC at different depths:
As mentioned in Eq. (29), the maximum saturated hydraulic conductivity of
matrix domain (
Modeled hydraulic conductivity of each domain in the three
models.
In the dual-permeability concept, another important parameter is the
hydraulic conductivity of the interface between matrix and crack domains
(
Regarding the
All parameters and parametric methods for the SDM, DPM and DPMDy are listed in Table 3.
Summary of parameters and parametric methods for the SDM, DPM and DPMDy.
SDM: single-domain model. DPM: dual-permeability model neglecting crack dynamic changes. DPMDy: dynamic DPM.
Figure 13 shows the temporal evolution of the boundary flow velocity
simulated by the SDM, DPM and DPMDy. As shown in Fig. 13a1 and a3,
during drying periods, the matrix domain dominates the soil evaporation
process and was responsible for 97 %–99 % of the total evaporation in
all the dual-permeability models. The matrix evaporation rate (
Boundary flow simulated by the SDM, DPM and DPMDy.
With regard to the wetting process, Fig. 13a2 and a4 represent two typical infiltration patterns before and after the fifth drying period (with significantly increased evaporation intensity). Overall, matrix flow still dominated the infiltration process in all the dual-permeability models due to the relatively small crack ratio and depth. For the SDM, all the rainfall infiltrates into the soil during the beginning of rainfall events. When the soil surface gets saturated, water ponding occurred, and the soil infiltration rate gradually decreased. In the DPM and DPMDy, the surplus water after matrix ponding infiltrates into the crack domain as preferential flow, and water will pond on the overall soil surface when the crack domain reached its storage capacity. Recall that the crack volume in the DPMDy decreases with the matrix getting moist, while that in the DPM keeps constant. Consequently, the ponding time of the crack domain simulated by the DPMDy in the third rainfall event (inflection point of the dashed red line in Fig. 13a2) was 1.6 and 4.8 min earlier than that of the DPM-0.01 and DPM-0.03 (rigid dual-permeability model with crack ratio of 0.01 and 0.03, respectively), respectively. The cumulative preferential flow simulated by the DPMDy was 87.4 % and 95.2 % less than that of the DPM-0.01 and DPM-0.03, respectively. A similar rainfall pattern was obtained during the sixth rainfall event.
By integrating the boundary flow velocity in Fig. 13a, the total cumulative
flux for the experiment and the three models was obtained (Fig. 14a). In the experiment, the variation of water flux was estimated by
calculating the sum of the difference between
Water balance for the measured and simulated results.
In Fig. 14a, the results show that the total infiltration (
Figure 15 shows part of the comparison results between the measured data and the three models. Detailed descriptions of all the comparison results are presented in Appendix A. Overall, all models show similar response trends with the measured data. Divergences among the three models mainly appeared during drying.
Temporal evolution of the measured and simulated crack
ratio, matric suction and volumetric water content.
In Fig. 15a, the simulated surficial
In Fig. 15b, the matric suction (
In Fig. 15c, the total volumetric water content
Our experimental results demonstrated that the crack evolution is not always
positively correlated to the increase of the WD cycles,
Crack images at
In addition, another interesting phenomenon is the transient decrease in
Variation of boundary
As mentioned in Sect. 5.3.1, during the drying process, the matrix and
crack evaporation simulated by the DPMDy are overall lower and higher than
other models, respectively. It can be explained by looking at the variation
of boundary
For the dual-permeability model, the two domains are coupled by the water
exchange term (Eq. 3) that is governed by the pressure head difference
between the two domains (
Pressure head difference
As shown in Fig. 18a1–a3,
This result means that the crack closure during wetting benefits the building-up process of the pressure head in the crack domain and thus can promote water exchange from the crack into the matrix domain. It corresponds to some experimental results that the PF-DC also exists and leads water to rapidly infiltrate into soils even if desiccation cracks are nearly closed (Baram et al., 2012; Greve et al., 2010; Luo et al., 2021; Sander and Gerke, 2007; Tuong et al., 1996). It also means using the DPM may overestimate the flux of PF-DC but underestimate the water exchange coming from the PF-DC. Because the experimental scale, crack ratio and depth in this study are small, the difference of simulation result involving the matric suction and water content between the DPM and DPMDy is not very significant. However, we can imagine that the deviation caused by the DPM at a larger scale will be more significant, especially in a typical shrinking–swelling soil slope under long-term WD cycles.
We evaluated the prediction errors of different models to the measured
matric suction, water content and crack ratio using a fixed slope line as
the same in Sect. 5.3.2 (see Fig. A3 and Table 4). Overall, the DPMDy,
which incorporates the dynamic changes of desiccation cracks and hydraulic
conductivity into the dual-permeability model, has an overall better
performance than the SDM and DPM, as indicated by the small intercept and high
Summary of fitting performance of different models to measured data.
Compared to other dynamic preferential flow models, the DPMDy developed in
this study also has its unique advantages. Firstly, the variation of crack
volume (or crack ratio) in our model is deduced from the changes of matrix
porosity due to shrinkage and thus has a universal definition. Instead,
Coppola et al. (2012, 2015) linked the crack ratio to the suction head
with an empirical natural logarithm function, which is not transferable to
other types of soils. Secondly, the results support the suitability, in the
crack domain, where capillarity has little effect, of
However, in the current study, the hysteresis effect was neglected in both the soil deformation and SWRC because we assumed the soil shrinking–swelling behavior has less influence on the pore-size distribution (or SWRC shape) but more influence on the porosity (or hydraulic conductivity). This assumption inevitably caused some errors when compared to the measured water content, especially for the surficial soil layer that has been significantly affected by the WD cycles. Our future work will try to incorporate the hysteresis effect into the current model to further improve the prediction strength. In addition, we have to remind the reader again that because the shrinking–swelling model in our method is developed based on the hydrological-driven perspective, it may be more suitable in the natural soil layer where the crack pattern already has a stable state after long-term WD cycles.
This study combined an experimental study and a numerical simulation to quantify the preferential flow induced by dynamic changes of desiccation cracks (PF-DC). A soil column infiltration test under wetting–drying conditions was conducted to investigate dynamic changes of desiccation cracks and the accompanying water infiltration process. The variation of crack geometry, including crack ratio, width and depth, was measured. The soil volumetric water content, matric suction and water drainage were also monitored. A new dynamic dual-permeability model (DPMDy) was developed to account for the PF-DC, which includes physically consistent functions in describing the variation of both porosity and hydraulic conductivity in crack and matrix domains. The performance of the single-domain model (SDM), rigid dual-permeability model (DPM) and DPMDy was evaluated by comparing their simulation results to the monitoring data.
Overall, the DPMDy performed not only better in its prediction of the crack evolution and hydrological response with respect to the SDM and DPM, but it also provided much better descriptions of the underlying physics involving the PF-DC. During the drying periods, the matrix evaporation modeled by the DPMDy is lower than that of the SDM and DPM due to considering the permeability decay induced by soil shrinkage. But the crack evaporation modeled in the DPMDy approach is the highest because it managed to capture the raised crack permeability induced by drying–enlarging desiccation cracks. Compared to the DPM with a fixed crack volume, the DPMDy revealed that the crack closure process during wetting will lead to a faster pressure head building-up process in the crack domain and higher water exchange rates from the crack to the matrix domain. Additionally, using a fixed crack ratio in the DPM, whether it is the maximum or the average value from the experiment data, will overestimate the infiltration fluxes of PF-DC but underestimate its contribution to the matrix domain.
The DPMDy developed here has a physically consistent definition. It remedies the shortcomings DPM and other dynamic preferential flow models in defining the dynamic changes of desiccation cracks and hydraulic properties of the crack domain and interface. Future works should focus on considering the hysteresis effect of the SWRC during wetting–drying cycles in the model and its application to complex field situations.
Figures A1 and A2 show the temporal evolution of the measured and simulated crack ratio on the soil surface, matric suction (negative porewater pressure) and volumetric water contents at the five monitoring depths (5, 15, 25, 35 and 45 cm).
In Fig. A1a, the simulated
In Fig. A1b–f, the matric suction (
In Fig. A2a–e, the volumetric water content
Temporal evolution of the measured and simulated crack
ratio and matric suction at different depths.
Temporal evolution of the measured and simulated volumetric water content at depths of 5, 15, 25, 35 and 45 cm. Note that the simulated volumetric water content demonstrated here is the total volumetric water content that was combined with the combined matrix and crack domains using Eq. (8).
Scatter plots of modeled vs. measured data. Panels
The source code and the data generated from this study are available from the corresponding author upon reasonable request.
YL: conceptualization, methodology, investigation and writing (original draft preparation). JZ: supervision, writing (review and editing) and project administration. ZZ: resources, software and investigation. JPAL: writing (review and editing). RG: writing (review and editing). TB: supervision, writing (review and editing) and funding acquisition.
At least one of the (co-)authors is a member of the editorial board of
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This paper was written during the visiting research exchange of Yi Luo at TU Delft in summer 2022. The experiment was conducted from January to March 2022 in China. Ming-jian Hu and his research group are thanked for their great help in providing TDR probes. Yi Luo's Chinese colleagues Yuhao Li, Zhan Yang, Xiang Li and Zijian Shen are thanked for their contribution to the experiment monitoring. The authors would also like to thank the editor and anonymous reviewers for their valuable comments that substantially improved this paper.
This work was financially supported by the National Natural Science Foundation of China (grant no. 42177166) and the Fundamental Research Funds for National University, China University of Geosciences (Wuhan). It was also partially funded by the Plan of Anhui Province Transport Technology Progress (grant no. 2018030) and the Engineering Research Center of Rock-Soil Drilling & Excavation and Protection, Ministry of Education (grant no. 202210).
This paper was edited by Alberto Guadagnini and reviewed by two anonymous referees.