The relationship between suction and saturation (or volume water content) of unsaturated soil is called SWCC, which describes the water holding capacity of unsaturated soil under different suction conditions (Leong and Rahardjo, 1997). The SWCC of in situ soil at different depths are plotted in Figure 5.

The VG model is an effective SWCC model for fitting the soil-water characteristic curve (Van Genuchten, 1980). Considering that the residual saturation or residual matrix suction of the residual soil is difficult to determine, the VG model is modified (Chin et al., 2010) in the following form: S = 100 ( 1 + ( ψ a ) b ) c (3) where S is soil saturation, a, b and c are the fitting parameters. The experimental data are fitted by Eq. 3 and the fitting result is shown in Figure 5.

Figure 5 reveals that the SWCC curves of soil samples from different depths are not identical. This may be caused by the difference of stress, structure, and physical and chemical properties of soil. Combining with the analysis of Figure 3, with the increase of depth, the overlying soil stress increases, and the soil structure becomes more complete. The pore structure in soil has certain orientation, and the soil particles and clay minerals are arranged in a certain direction. As a result, the soil has an increasing air-entry value and an increasing water-holding capacity. The mineral composition of the soil varies at different depths. Combining with the analysis of Table 2, as the depth increases, the proportional content of quartz decreases and the proportional content of clay minerals increases. When the clay content increases, the water-holding capacity of the soil is stronger, and the dehumidification rate is smaller. This is in accordance with the experimental results in Figure 5. The above analysis confirms the reliability of the filter paper method for measuring matrix suction and the VG modified model.

Figure 6 shows the experimental relationship between the horizontal electric conductivity and soil saturation. The following rules can be found from the diagram: (1) The horizontal electric conductivity of soil increases with the increase of saturation degree. (2) With increasing saturation, a smaller saturation increment can lead to a large increase in horizontal conductivity.

When the saturation reached a certain value (in this test, about 80%), the horizontal conductivity increased rapidly with the increase of the saturation. The direct consequence of the increase of soil saturation is the enhancement of the conductivity of soil pores. This results in an increase in the thickness of electric double layer on the surface of soil particles, which enhances the surface conductivity of soil particles. The increase of saturation can significantly improve the connectivity of pore water, which improves the electrical conductivity of soil pore water and thus increases the overall electrical conductivity. It shows that the change of soil structure has an effect on its electric conductivity. In addition, the values of the horizontal conductivity of the soil at different depths with same saturation are different. The electrical conductivity of the shallow soil (z = 0.5 m) is obviously larger than that of the deeper soil. Combined with the analysis of soil’s physical and chemical properties in Table 2, it suggests the development of shallow roots and the retention of plant nutrients may cause high soil organic matter content and cation exchange capacity, leading to the higher electrical conductivity of shallow soil.

Archie (1942) first applied the theory of electrical conductivity to the study of soil microstructure and proposed the concept of structure factor F to reflect the microstructure characteristics of soil (Archie, 1942). The structure factor F is defined as the ratio of the total resistivity of porous media to the resistivity of its pore liquid and the structure factor is mainly related to the porosity and pore structure. Based on Archie’s research results, three basic conductivity structure parameters by measuring the horizontal, vertical, and pore water conductivity were proposed (Arulanandan and Muraleetharan, 1988). The physical meaning of conductivity structure parameters were clearly defined.

The average structure factor F ¯ reflects the size of soil porosity, pore structure characteristics, and its specific formula is: F ¯ = F V + 2 F H 3 (4) where F V and F H are the horizontal and vertical structure factor, respectively. The formula for calculating the horizontal (or vertical) structure factor is: F V = σ w σ V (5) F H = σ w σ H (6) where σ V and σ H are the vertical and horizontal electrical conductivity of soil respectively, and σ w is the electrical conductivity of pore water.

The average shape factor f ¯ describes the shape of soil particles and reflects the degree of cementation between soil particles. The correlation between the average structure factor and the average shape factor of soil is as follows: F ¯ = n − f ¯ (7) where n is the porosity of soil.

The anisotropy coefficient A reflects the anisotropy of soil and quantifies the directional arrangement of soil particles and its specific formula is: A = σ w σ V / σ w σ H = F V F H (8)

Based on the results of laboratory tests and the above formulas, the conductivity-related structural parameters of in situ soil with different depth and saturation degree are calculated. The conductivity-related structural parameters include average structure factor F ¯ , average shape factor f ¯ , and anisotropy coefficient A. The relationship between the conductivity-related structural parameters and soil saturation are shown in Figure 7. There is a certain correlation between the three conductivity-related structural parameters and saturation. The average structure factor and the average shape factor decrease with the increase of saturation, while the anisotropy coefficient increases first and then stabilizes with the increase of saturation.

For unsaturated soil, the electrical conductivity and matrix suction are closely related to the soil saturation, which are the comprehensive reflection of the microstructure of unsaturated soil. Therefore, there must be an essential relationship between the conductivity-related structural parameters and its matrix suction. The conductivity-related structural parameters can be used to describe the suction of unsaturated soil and its change law. However, neither of them can individually and accurately describe the variation of matrix suction in soils. Matrix suction in unsaturated soils is the result of the combined effect of soil structure, particle composition, particle arrangement, saturation, and other factors. Zha et al. (2010) proposed a new method to characterize the matrix suction by the comprehensive structural parameter R _e (Zha et al., 2010) and its formula is: R e = A F ¯ f ¯ (9)

Figure 8 shows the relationship between comprehensive structural parameter and soil saturation. It can be seen from the diagram that there is a good correlation between the parameter R _e and the saturation. When the soil saturation is high, the comprehensive parameter R _e is small, and the influence of saturation it is minimal. When the saturation is low (<35%), the change of the saturation has a great influence on the comprehensive parameter. A slight decrease of saturation leads to a dramatic increase of the comprehensive parameter R _e .

Figure 9 shows the relationship between comprehensive structural parameter and matrix suction. It indicates that there is a parabola relationship between the parameter R _e and the matrix suction. The matrix suction of unsaturated soil increases with the increase of parameter R _e . In this way, a simple parabola equation between matrix suction and comprehensive structural parameter (R _e ) can be established and the R _e can be used to predict the matrix suction.

Based on the test results in Figure 9, a general functional relationship between matrix suction and comprehensive structural parameter of unsaturated soils is established: ψ = α + β R e + λ R e 2 (10) where ψ is matrix suction, α , β  and  λ are model parameters that are related to the properties of soil. In this work, the model parameters of soil samples at different depths are shown in Table 3.

Finally, the matrix suction is obtained by this prediction model. The procedure of this method is summarized using a flowchart in Figure 10, which can be divided into five steps: (1) measurement of horizontal conductivity, vertical conductivity and pore water conductivity of unsaturated soil using TDR-310H sensor; (2) the temperature calibration of the electrical conductivity using Eq. 1; (3) calculation of the conductivity-related structural parameters ( F ¯ , f ¯ and A) using Eqs 4, 7, 8; (4) calculation of the comprehensive structural parameter using Eq. 9; (5) calculation of the matrix suction of unsaturated soil using Eq. 10. Therefore, the matrix suction can be predicted by testing the electrical conductivity. This solves the problem of matrix suction being difficult to be measured in a practical engineering application, especially for in situ soil.

It should be noted that the prediction model is established in the condition that R _e is in the range of 0–8 and the matrix suction is in the range of 0–800 kPa. The vertex of the quadratic function is about to be reached when R _e = 8. There is a negative correlation between R _e and matrix suction in the range of R _e > 8. Accordingly, the prediction model may be invalid when R _e > 8.

A conductivity-matrix suction prediction model was established for shallow unsaturated soil samples in laboratory tests. An artificially simulated rainfall test was carried out on Yandou landslide to verify this model. Once the model was proven to be effective, the response of matrix suction of soil samples at different slope depths to rainfall infiltration were investigated.

The height H of the artificial trench was 2.2 m, the width B was 2.8 m (see Figure 2). A monitoring point was arranged every 0.5 m on the trench surface, and a vertical monitoring line was formed by four monitoring points from top to bottom. Three monitoring lines were successively arranged on the trench surface, with an interval of 0.5 m for each line. The rainfall simulation device was arranged on the natural surface (trench edge). The length of device l was 2.4 m, the width b was 1.2 m, the distance between each rainfall nozzle d was 0.6 m, the average height of nozzle from ground h was 1.8 m. A PVC pipe was buried at the top of the edge of the trench as a runoff collecting trench. Water was stored in a water tank and supplied by a water pump. The flow valve was used to regulate the rainfall intensity. The monitoring instruments were TDR-310H sensor probe and WATERMARK-200SS matrix suction sensor probe (Irrometer Company). The data logger was CR-1000 from Campbell Scientific Company. The data collection interval was 10 min. For the problem of rainfall-induced shallow slope instability, the intensity of rainfall must be large enough and exceed the saturation permeability coefficient of the surface soil of the slope (De Vita et al., 2012). For this reason, the rainfall intensity I of 20 mm/h and the rainfall duration T of 6 h were selected for the site rainfall in this work. Simulated rainfall started at 8:00 a.m. The duration of data acquisition was 48 h. The detailed site diagram is shown in Figure 11.

WATERMARK-200SS matrix suction sensor is a granular matrix sensor. The resistance R _x of sensor is measured by a known built-in voltage divider circuit and the matrix suction of the soil is determined by the calibration equation. The default calibration equation for the sensor was developed by Clinton Shock in 1998 (Shock et al., 1998), as shown in Eq. 11: ψ x = − 3.213 R x − 4.093 1 − 0.009733 R x − 0.01205 T (11) where ψ x matrix suction signal value of sensor output,R _x is the resistance of sensor, T is temp centigrade.

The calibration equation of Eq. 11 is only applicable in the range of 10–100 kPa matrix suction. Beyond this range, the sensor automatically uses linear extrapolation to determine matrix suction, resulting in calculation error. In addition, the calibration equation is proposed for Owyhee silt loam soil, and the characteristics of granite residual soil in this work are quite different, so the calibration equation itself may have a deviation. It is known that if the value of the matrix suction signal from the WATERMARK sensor is directly used as the final experimental result, it may result in large error. To reduce the experimental error and modify the calibration equation so that it can be applied to the soil sample in this test, the calibration test is carried out in the laboratory. The matrix suction measured by the filter paper method is used as the reference value in the calibration test. Six calibration points are selected, which are at 5.7, 10.9, 49.3, 96.2, 148.8 and 197.6 kPa, respectively. The matrix suction signal values at different calibration points are measured for the same batch of soil samples. The test results are shown in Figure 12.

The calibration point of Figure 12 is fitted by linear equation and the calibration curve of the WATERMARK matrix suction sensor is obtained as follows: ψ = 4.121 ψ x − 7.259   ,   R 2 = 0.978 (12)

The data collected by the WATERMARK matrix suction sensor and the data calculated by the prediction model are presented together in Figure 13. The former is the measured value and the latter is the predicted value.

In the moisture absorption stage, the relative error of the initial value is -5.83–2.67%. When the matrix suction begins to decline rapidly, the prediction model shows a high agreement. In the dehumidification stage, it can be found that the prediction model for matrix suction recovery is advanced. Compared with the measured values, the predicted matrix suction recovered earlier and the matrix suction at the same time point is larger. There may exist an hysteresis effect in the process of moisture absorption and dehumidification of unsaturated soil, which results in two kinds of soil-water characteristic curves (wetting curve and drying curve), and it shows that this model cannot reflect the hysteresis of suction recovery. However, as the dehumidification process continues, the matrix suction increases, the error caused by hysteresis decreases gradually, and the relative error can still be controlled within 10% in the late dehumidification stage. Overall, the relative error of the prediction model is controllable and the accuracy is good. The field test further proves the feasibility of indirectly measuring the matrix suction of unsaturated soil by the composite structure parameters of electrical conductivity.

During the simulated rainfall, the flow rate at the outlet of the runoff gathering pit was measured with a measuring cylinder. Testing was done every 10 min before the occurrence of slope runoff and every 30 min after the occurrence of slope runoff. Based on the inverse calculation of the infiltration rate, the calculated results are plotted as the infiltration rate time-history curve, as shown in Figure 14.

Figure 14 indicates that during the first 20 min of rainfall, all the rainwater seeped into the soil, and the infiltration rate is equal to the rainfall intensity. With the development of rainfall, the rainfall cannot penetrate the slope completely because of the effect of rainwater dripping and the vegetation barrier, and part of it remains on the slope temporarily and cannot form runoff. At t = 1.32 h, the field observation found that stranded runoff started to appear on the slope. After that, the infiltration rate gradually decreased with the duration of rainfall. When t > 4h, the change of infiltration rate gradually slowed down and finally stabilized at about 3.26 mm/h, which is slightly larger than the permeability coefficient K _s = 7.2 × 10⁻⁵ cm/s = 2.592 mm/h.

The central measurement line was selected as the main measurement line for this monitoring and the time variation curves of infiltration response of saturation, structural parameters, and matrix suction on the main measurement line are plotted sequentially in Figure 15.

Figure 15A shows that the horizontal electric conductivity increases rapidly with the wetting front after rainfall. It illustrates that there is a positive correlation between the horizontal electric conductivity and saturation. Moreover, a similar trend of the vertical electric conductivity is shown in Figure 15B. The magnitude of the vertical electric conductivity is slightly larger than that of the horizontal electric conductivity. The penetrated channel in the vertical direction caused by rainwater during the rainfall may lead to the increase in the electric conductivity. Figure 15C is the time-history curve of the conductivity of pore water. It indicates that there is no consistent trend for the change of the conductivity of pore water. The conductivity of pore water fluctuated sharply in z < 1.5 m while is fluctuated slightly at z = 2.0 m.

Figure 15D illustrates that: (1) The initial saturation of soil shows an upward trend from top to bottom, which is 59.81, 52.57, 65.31 and 70.14%, respectively. At z = 0.5 m, the soil saturation is slightly higher. This may be attributed to the root reinforcement near the surface, which results in a higher water-holding capacity of the soil at this location. (2) Soil infiltration response has a lag that lasts longer at a larger depth. The response time of the wetting front from top to bottom is 1.74, 3.92, 5.68 and 9.50 h, respectively. At z = 2.0 m, the response is the slowest, the rising rate is the slowest, and the range of saturation is the smallest. A similar pattern is observed during the period of natural dehumidification after the rain stopped. (3) During 24 h < t < 36 h, the decrease trend of saturation is accelerated, and the trend is the most obvious at 0.5 m. This is because during daytime the temperature of slope surface rises under the sunlight and the evaporation rate speeds up, which leads to a larger water loss.

Figure 15E shows that the change trend of comprehensive structural parameter (R _e ) is opposite to the change trend of saturation (S). The R _e decreases rapidly during the simulated rainfall period but increases slowly during the natural drying period. As can be seen from Figure 15F: (1) The initial matrix suction decreases from top to bottom, the shallow depth makes the suction larger, and the deep depth makes the suction smaller, which is 171.64, 163.95, 86.15 and 45.82 kPa, respectively. Combined with the analysis of Figure 15D, it can be concluded that in the initial stage, with the increase of depth, the soil saturation gradually increases, and the matrix suction gradually decreases. (2) The response time of matrix suction is synchronized with the hydrological response. When the wetting front reaches the corresponding depth, the matrix suction decreases rapidly to zero. The time to reach zero suction is 3.83, 5.16, 6.5 and 11.83 h, respectively, and the duration in the zero suction state is 5.33, 7.67, 7.00 and 8.33 h, respectively. (3) There is no significant correlation between the recovery rate of matrix suction and depth during natural drying period. During 24 h < t < 36 h, the recovery rate of matrix suction increased significantly at z = 0.5 m, which is related to the decrease of soil saturation. During the rest of the dehumidification period, the recovery rates are similar. At the end state (t = 48 h), the matrix suction distribution is the same as the original state, but the corresponding values have been decreased to 60.66, 44.17, 29.10 and 14.79 kPa, respectively. Compared with the monitoring results of the saturation in Figure 15D at the same time, the results show that although the saturation is almost the same as the initial state, the matrix suction decreases greatly. This indicates that the recovery of matrix suction has a greater lag than the saturation. Namely, the recovery time of matrix suction to the initial state is longer than that of saturation.

To analyze the distribution of substrate suction on the artificially cut slope more intuitively, the monitoring data at typical moments on the three measurement lines are selected and plotted as a substrate suction contour map (Figure 16). The data between the actual points are generated by interpolation of the cubic spline curve and extrapolated at the boundary to a range of 20 cm.

Figure 16 shows that at the initial state (t = 0 h), the overall matrix suction force on the slope is large on the top and small on the bottom, the suction force on the left side of the profile above 1.2 m is slightly larger than that on the right side, the suction force on the profile below 1.2 m is roughly distributed in horizontal layers, and the suction force value decreases layer by layer. At t = 6 h (when the simulated rainfall stops), the wetting front reaches about z = 1.1 m due to the lag of rainfall infiltration, and the depth range (z ≤ 1.1) is saturated, which shows the matrix suction ψ = 0 kPa. The remaining unsaturated area (1.2 m < z < 2.2 m) has a matrix suction roughly distributed between 20 and 60 kPa, with a higher suction area (>60 kPa) at the foot of the left slope. At t = 12 h, the rainfall has been fully infiltrated and most of the area within the slope has reached saturation, which shows that the matrix suction is 0 kPa. Since the left slope top has entered the drying state, the matrix suction has slightly recovered. At t = 24 h, the upper and middle part of the slope (z < 1.5 m) gradually dried and the matrix suction began to recover. The recovery rate on the center line is smaller and that on the left and right sides are larger. The lower part of the slope (z > 1.5 m) is still in the saturated zone and the matrix suction remained ψ = 0 kPa. At t = 36 h and t = 48 h, the matrix suction on the slope has started to rise gradually. The contour shape is a parabola with a downward opening and the contour shape is restored to 10–90 kPa, which is 27–35% of the initial state.