Influence of Induced Variability of Unsaturated Soil Parameters on Seepage Stability of Ancient Riverbank

Abstract

In the restoration of ancient water engineering, the loss of fine soil particles from the ancient riverbank can easily cause seepage instability problems such as piping during the flood transient process. This paper explores the influence mechanism of flood fluctuation on soil seepage stability based on indoor experiments, field monitoring and saturated-unsaturated soil seepage theory. The paper obtains the soil-water characteristic curve of unsaturated soil using laboratory tests, builds the transient seepage finite element model of porous media and modifies parameters monitoring data to verify the numerical analysis results. The results showed that the groundwater level, pore water pressure and seepage hydraulic gradient had changed. The maximum pore water pressure between the ancient riverbank and antiseepage structure increased by 13.4%, the maximum hydraulic gradient at the toe of the riverbank increased by 49.3% and the instability of seepage significantly increased. Through the modified lime grouting between the ancient riverbank and the antiseepage structure, the structure of the soil mass was changed, and the maximum hydraulic gradient was reduced by 55.6%, which restrains piping damage. This study can be used in the restoration of ancient riverbanks to solve piping problems.

1. Introduction

The urbanization process in China has had a great impact on the urban water system structure. The cross integration of the urban flood control pattern optimization and historical water project protection based on flood control safety and landscape ecology is gradually becoming a research hotspot [1]. There are many ancient water conservancy projects in southern China, including ancient flood control levees, ancient weirs and dams, and ancient irrigation areas, which are mainly distributed in the tributaries of rivers in southern China. Historic water projects should be protected and restored from the perspective of increasing the water security elasticity of urban areas, improving the living environment, increasing biodiversity and other urban ecological comprehensive effects [2]. Historically, ancient riverbanks had the functions of flood control, navigation and military defense, such as those in Jingzhou in Hubei, Shouzhou in Anhui and Taizhou in Zhejiang [3,4,5,6]. Figure 1 shows the locations of representative ancient flood control dikes in southern China, which are distributed in cities and towns with relatively dense populations along rivers. The ancient riverbank and the old city form a whole, supporting the urban ecology, industry and space structure. With the increase in urbanization speed and scale in the south of China, on the one hand, the river section of the urban water network tends to be deep and narrow, which increases the water level difference inside and outside the riverbank; on the other hand, many ancient flood dikes have been damaged due to the space occupied by urban facilities. In view of the frequent piping, soil flow and other problems of ancient riverbanks, it is necessary to explore the seepage instability mechanism through in-depth theoretical analysis. In this paper, a numerical model of unsaturated soil parameter variation is proposed to study the seepage stability of bank slope soil, in order to obtain more practical results and provide a theoretical basis and methods for the repair of ancient riverbanks. The paper uses the Lanxi ancient riverbank as an example to illustrate the contents and methods of this study.

In recent years, with the improvement of flood control safety requirements and flood control standards, the protection and reinforcement of ancient riverbanks are facing many problems that need to be solved urgently. The conservation and repair of historical water project cultural relics require that the original appearance of the cultural relics must be maintained, and the repair materials must be raw materials. Hydrogeology and human settlements have an important impact on the safety of the ancient riverbank, especially the seasonal river water level fluctuation, and human settlements have a large impact on the seepage stability of the ancient riverbank. Many domestic and overseas scholars had carried out research on the influence of seepage characteristics on bank seepage stability. According to the relationship between the water content of unsaturated soil, matric suction and seepage coefficient, the seepage equation of saturated-unsaturated soil is proposed [7,8,9].

Under the effect of seepage force, the microstructure arrangement of soil particles has changed. The change rule of the permeability coefficient of unsaturated soil is studied through tests, the pore characteristics of soil are described by fractal function and the seepage development process is studied through coupling equations of computational fluid mechanics and discrete elements [10,11,12]. The coupling equation of seepage and erosion shows that the pore water pressure of unsaturated soil increases until the hydraulic gradient is greater than the critical hydraulic gradient, and the fine particle phase migrates, resulting in deformation and instability [13,14,15,16]. Based on the principle of “combination of prevention and drainage”, the curtain antiseepage and drainage technologies are applied in riverbank engineering, the antiseepage body is used to weaken the seepage of the riverbank groundwater, and the drainage facilities are used to reduce the groundwater, so as to improve the stability of the slope seepage [17,18,19,20]. By studying the water blocking effect of structures, the influence of underground structures on groundwater and surface subsidence is revealed, and the relationship between the depth of structures and the water blocking range is obtained [21,22]. Aiming at the dynamic development process of piping in multi-layer riverbank foundation structure, the distribution of seepage field inside the riverbank foundation at different stages of piping development is simulated by finite element analysis [23]. In order to reveal the influence rule and adverse factors of precipitation on the development of bank slope deformation, a three-dimensional fluid-solid coupling model of hierarchical precipitation for a suspended water stop curtain in deep permeable soil was established [24,25]. From the macro and micro scale, numerous studies on the relationship between the permeability coefficient and the seepage stability of the bank slope and prevention measures were performed [26,27,28,29]. However, existing knowledge on the process of the influence of unsteady seepage caused by water level transient on the stability of the riverbank is not sufficient. It is necessary to comprehensively apply saturated-unsaturated seepage theory and seepage constitutive model to explore the mechanism and law of piping caused by unsteady seepage.

Taking the seepage stability analysis of the Lanxi ancient riverbank as an example, this paper applies the saturated-unsaturated seepage theory of porous continuous media to establish the relationships among soil-water content, matric suction, pore water pressure and hydraulic gradient, studies the seepage law of the antiseepage curtain set up for ancient riverbanks, collects monitoring data, inverts the numerical model parameters of the ancient riverbank, reveals the seepage process and failure law of the ancient riverbank under standard flood and provides a theoretical basis and application case for similar research.

2. Saturated-Unsaturated Seepage Model

In recent years, the mathematical model based on saturated-unsaturated soil seepage provides a powerful means for studying transient unsaturated soil seepage. Due to the dynamic distribution of pore water pressure caused by the fluctuation of river water level, it is taken to be an important parameter to evaluate the induced seepage deformation of unsaturated soil. A large number of studies show that matric suction is the most important variable in unsaturated soil. Due to the complexity of its theory and application, its application scope is limited. Numerical analysis has proved to be an appropriate and effective tool to further consider the inherent variability of soil properties. In 1856, the French engineer Darcy proposed the linear seepage theory in saturated soil. In 1980, van Genuchten obtained the relationship between permeability and volume moisture content of unsaturated soil based on test statistics and established the van Genuchten model. This model expresses the characteristic parameters of water and soil through test data and incorporates the soil-water characteristic curve of unsaturated soil and seepage control differential equation into the mathematical model. In this paper, the medium is isothermal, and no chemical reactions were taken into account. It is assumed that the medium movement between the soil pores is single-phase flow, and the soil particles are filled with water and stagnant air.

The motion of water in soil can be described using a flow control equation. When the water level changes, the water transfer of unsaturated soil is different from that of saturated soil, and the permeability coefficient is no longer a constant. It changes constantly with the change in soil-water content or matric suction.

A generalized two-dimensional seepage differential equation based on Darcy’s law can describe the transient flow of water at any position in the soil under saturated-unsaturated conditions [30,31]. The following equation was derived by van Genuchten for predicting the relative hydraulic conductivity from knowledge of the soil-water characteristic curve [32]. The general expression of this equation can be written as:

$$\{\begin{array}{c}\frac{\partial }{\partial x}\left(k_{sx}\frac{\partial H}{\partial x}\right)+\frac{\partial }{\partial y}\left(k_{sy}\frac{\partial H}{\partial y}\right)+Q_w=\frac{\partial {\theta }_w}{\partial t} \left[(u_a-u_w\right)\le {\left(u_a-u_w\right)}_b]\\ k_w\left(\theta \right)={\left[\frac{{\left(u_a-u_w\right)}_{bo}{10}^{a\left(e-e_0\right)}}{u_a-u_w}\right]}^{\alpha } \left[(u_a-u_w\right)>{\left(u_a-u_w\right)}_b]\end{array}$$

(1)

where k_w and k_s are the permeability coefficients of unsaturated and saturated soil, respectively, in cm/s; k_sx and k_sy are the permeability coefficients in x and y directions, respectively, in cm/s; H represents the total head, in m; Q_w is the unit volume flow applied on the boundary, represented as 1/s; t refers to time, in seconds; ${\left(u_a-u_w\right)}_b$ indicates the generalized limit value of suction between saturated and unsaturated regions; e is the pore ratio, when e =$e_0,\left(u_a-u_w\right){ }_b=\left(u_a-u_w\right){ }_{b0}$; where a and $\mathsf{\alpha }$ are the parameters related to the intake value, in 1/kPa, given here as Equations (2) and (3), respectively:

$$a=\mathsf{\Delta }\lg \left(u_a-u_w\right){ }_{b0}/\mathsf{\Delta }e$$

(2)

$$\mathsf{\alpha }={\eta }_0+d\left(e-e_0\right)$$

(3)

where $u_a$, u_w are the pore pressure and pore water pressure, in kPa; when e = e₀, $\eta ={\eta }_0$, and d = $\Delta \eta /\mathsf{\Delta }e$; θ_w represents the water content per unit volume of soil, in a percentage. Its value is calculated by Equation (4) [33]:

$${\theta }_w={\theta }_r+\frac{{\theta }_s-{\theta }_r}{{\left[1+{\left(\frac{\Psi }{a}\right)}^n\right]}^m}$$

(4)

where ${\theta }_s$ and ${\theta }_r$ indicate saturated and residual volume water content, respectively, in percentages; $\Psi$ is the matric suction, in kPa; n and m are the fitting parameters of the soil-water characteristic curve, $m=1-1/n$.

When calculating the seepage of saturated-unsaturated soil, it is necessary to obtain the soil-water characteristic curve measured by the clay plate pressure test, and then use the van Genuchten model to fit the relationship curve between the water content of saturated-unsaturated soil, matric suction and permeability coefficient. The expression is [34]:

$$k_r\left(\theta \right)=\frac{k_w}{k_s}={\Theta }^i\frac{{{\displaystyle \int }}_0^{{\theta }_w}\frac{d{\theta }_w}{{\Psi }^j}}{{{\displaystyle \int }}_0^{{\theta }_s}\frac{d{\theta }_w}{{\Psi }^j}}$$

(5)

where $\Theta$ is the relative degree of saturation; i and j are constants, i = j = 2. Equation (6) can be obtained after Equation (5) is derived:

$$k_w=k_s\frac{{\left[1-\left(a{\Psi }^{n-1}\right)\left(1+{\left(a{\Psi }^n\right)}^{-m}\right)\right]}^2}{{\left(1+a\Psi \right)}^{nm/2}}$$

(6)

Compared with saturated soil, the permeability coefficient of unsaturated soil is no longer a constant but a function varying with soil saturation and is obtained from its soil-water characteristic curve function.

Firstly, the relationship between the volume moisture content and the matric suction was obtained using the pressure test of the ceramic plate. Then, using the linear fitting function “Newfunction” in Origin 2018, the fitting parameters of the models of the soil–water characteristic curve were obtained. Figure 2a shows that, with decreasing water content, the matric suction of the loess soil increased gradually. The lower the soil moisture content, the greater the increase in matric suction. The reason for this is that, with decreasing water content and less free water in the soil pores, water remains only in the smaller pores between the soil particles. At this time, the transmission of pore water pressure depends mainly on the water–air interface in the smaller pores, namely the shrink film. Smaller pores provide shrink films with a smaller radius of curvature, thereby allowing the shrink films to withstand larger pore air pressure and transmit smaller pore water pressure. Therefore, the difference between pore air pressure and pore water pressure is greater when the soil-water content is lower, and the lower the water content, the greater the matric suction of unsaturated soil. The relationship curve between the permeability coefficient of saturated-unsaturated soil and the matric suction, as calculated by Equation (6), is shown in Figure 2a.

As can be seen in Figure 2b, when the matric suction is less than the air inlet pressure, the soil permeability coefficient is close to the constant value; when the matric suction is close to the air inlet pressure, the soil permeability coefficient starts to change; when the matric suction is greater than the air inlet pressure, the soil permeability coefficient decreases rapidly. When the soil is saturated, the matric suction is equal to zero and the pore pressure is equal to the value of pore water pressure. The relationship curve between the permeability coefficient and volume water content exhibits a negative correlation.

Saturated soil has high volume moisture content and low matric suction, and its permeability obeys Darcy’s law. The calculation formulas of head loss and hydraulic gradient in saturated soil follow Darcy’s law, and the permeability coefficient is a stable value, as shown in Equation (7). Calculation of the hydraulic gradient value was performed using Equation (8). As the volume water content of unsaturated soil decreases, the matric suction increases rapidly, and the pore water transport resistance between soil particles increases. According to the test results, a formula is fitted to describe the value of the hydraulic gradient, as shown in Equation (9).

$$k_s=k_i[(u_a-u_w)\le {\left(u_a-u_w\right)}_b$$

(7)

$$\mathsf{\Delta }{u}_i=u_t-u_{t-1}$$

(8)

$$i_i=\frac{h_{fi}}{l_i}=\frac{\mathsf{\Delta }{u}_i}{{\gamma }_w{l}_i}$$

(9)

where h_fi is the head loss at a point in saturated soil, in kPa; $\Delta u_i$ is the permeability pressure difference at a point, in kPa; u_t and $u_{t-1}$ is the permeability pressure at time t and t − 1, in kPa; l_i is the seepage path, in m; i_i is the hydraulic gradient; and ${\gamma }_w$ is the unit weight, in kN/m³.

In order to facilitate the engineering application, this paper simplifies the water and soil characteristic curve of unsaturated soil and generalizes the relationship between the suction and permeability coefficients of unsaturated soil into a linear relationship, as shown in Equation (10).

$$k_w=k_i-c[\Psi -{\left(u_a-u_w\right)}_b\left]\right[(u_a-u_w)>{\left(u_a-u_w\right)}_b$$

(10)

where c is the fitting coefficient of the equation.

The head loss in unsaturated soil can be calculated according to Equation (11):

$$h_{fi}^{\prime }=\frac{\mathsf{\Delta }{u}_i}{{\gamma }_w}-\Psi$$

(11)

where $h_{fi}^{´}$ is the head loss at a point in unsaturated soil, in kPa.

Equation (12) is obtained using the simultaneous solutions of Equations (10) and (11).

$$i_i=\frac{\mathsf{\Delta }{u}_i}{{\gamma }_w{l}_i}-\frac{\Psi }{l_i}=\frac{\Delta u_i}{{\gamma }_w{l}_i}-\frac{k_i-k_w}{c{l}_i}-\frac{{(u_a-u_w)}_b}{l_i}$$

(12)

Equations (10)–(12) above take into account the matric suction on unsaturated soil, which means that the seepage stability of unsaturated soil is affected by the variation of pore water pressure and the permeability coefficient.

3. Reference Case Study

3.1. Tests and Physical Parameters

Taking the Lanxi ancient riverbank as an example, this paper studies the influence of matric suction of saturated-unsaturated soil on soil seepage deformation, and then proposes measures to protect the ancient riverbank from seepage piping. The ancient riverbank is located at the downstream of the intersection of Qujiang River and Jinhua River in Zhejiang Province. On the right bank of Lanjiang River, it is a provincial cultural relic. Its geographical location and the appearance of the ancient riverbank are shown in Figure 3. In the rainy season, Qujiang River and Jinhua River converge on the Lanjiang River, which often causes flood disasters. Due to the large fluctuation of water level and the impact of rainfall and human settlements, safety problems such as collapse, wall deformation, leakage and piping occur frequently. In order to protect the original structure of cultural relics and minimize the impact of repair on adjacent buildings, an antiseepage wall is set at the back of the ancient riverbank to prevent the escape of fine soil particles due to seepage pressure.

The Lanxi ancient riverbank is a vertical retaining wall structure with rubble masonry external protection and internal filling. The maximum wall height is about 6 m and the bottom width is about 1.5 m. The buildings behind the wall are close, with the nearest distance of 2.0 m. The top of the ancient riverbank is a 1.15 m high black brick crenel, with a gap of about 1 m. The soil behind the wall is loose-filling, poor-uniformity and high water permeability, and the initial permeability coefficient was 3.6 × 10⁻²~5.1 × 10⁻³ cm/s.

The geology of the typical section can be divided into three formations from top to bottom: LayerⅠ₁ is the artificial fill surface layer, with a thickness of 2.20~9.00 m, mainly composed of rubble, a small amount of gravelly sand and a small amount of cohesive soil, with poor homogeneity. There are sewage pipes, residential power cables and other underground pipe networks near the residential area. LayerI₂ is plain fill with a thickness of 2.50~4.40 m. It is mainly composed of sand and gravel and sand, with general uniformity. Layer II is a sandy gravel, mainly composed of volcanic rock gravel, with gravel, silt and clay between the gravels, with a thickness of 5.40~10.70 m. Layer III is the pelitic siltstone with complete lithology. The geological cross section is shown in Figure 4, and the physical and mechanical parameters of each soil layer are shown in

Table 1. Physical and mechanical indexes of soil layer in the typical section.

Number	Name	Thickness /m	Natural Density /(kN·m−3)	Volume Water Content /%	Void Ratio	Initial Permeability Coefficient /(cm·s−1)	Cu 1	Cc 2
Ⅰ1	Artificial fill-1	4.8	15.1	44.2	1.01	8.9 × 10−3	7.9	1.4
Ⅰ2	Artificial fill-2	4.5	16.9	41.7	0.97	4.8 × 10−3	7.1	1.5
Ⅱ	Sandy gravel	7.3	17.6	38.3	1.12	3.7 × 10−3	9.5	1.7
Ⅲ	Pelitic siltstone	>7	20.3	/	/	/	/	/

¹ Cu: coefficient of uniformity; ² Cc: Curvature coefficient.

.

At the site of the ancient riverbank, soil samples Ⅰ₁, Ⅰ₂ and Ⅱ were taken along the depth for the soil property test. According to the standard for the geotechnical testing method (GB/T50123-2019), the engineering classification of soil was determined through the fine particle gradation analysis test. Then, the relationship between the volume moisture content, permeability coefficient and matric suction of the soil sample was obtained by using the porous clay plate test, which provides parameters for the finite element numerical analysis. At the same time, the microscopic images of soil samples were obtained by means of an electron microscope scanning test to analyze the structural changes of soil samples under the effect of matric suction. The test process is shown in Figure 5.

Artificial fill soil samples were taken along the section height at the ancient riverbank for soil test, and soil samples with a particle size of less than 2 mm for particle analysis were taken after screening. The grain grading curves of layers I and II soil samples less than 2 mm are shown in Figure 6. The mass of the soil samples in layers I and II with particle size greater than 0.075 mm should not exceed 50% of the total mass, the liquid limit was 44%, the plastic limit was 27%, the plastic index was 17, and the filling type was silty clay.

The porous clay plate test was used to measure the pore water pressure of the saturated-unsaturated soil mass of I₁, I₂ and II, as shown in Figure 6. The relationship between the water content and the matric suction was made available by fitting the test data. The relationship curve between the permeability coefficient and the matric suction was obtained using the van Genuchten model, as shown in Figure 7.

Figure 7b shows the relationships between the permeability coefficient and matric suction in the Ⅰ₁, Ⅰ₂ and Ⅱ soil samples. The permeability coefficients of saturated soil are constants, and the relationship between the permeability coefficient and suction of unsaturated soil is generalized as a linear relationship, as shown by the dotted lines 1, 2 and 3 in Figure 7b, and Equation (10) are their expressions. The hydraulic gradient of the saturated soil is calculated with Equation (9), and the hydraulic gradient of unsaturated soil is calculated with Equation (12). The relevant parameters and calculation formulas are shown in

Table 2. Soil unsaturated parameters and hydraulic gradient calculation formula of three soils.

Soil Layer	ki /(cm·s−1)	${\left({\mathit{u}}_{\mathit{a}}-{\mathit{u}}_{\mathit{w}}\right)}_{\mathit{b}0}$/kPa	n	m	c	ii
Ⅰ1	8.9 × 10−3	13	2.06	0.515	1.714	$i_{i1}=\frac{\Delta u_i}{10l_i}-\frac{k_i-k_w}{1.714l_i}-\frac{13}{l_i}$
Ⅰ2	4.8 × 10−3	24	2.75	0.636	1.908	$i_{i2}=\frac{\Delta u_i}{10l_i}-\frac{k_i-k_w}{1.908l_i}-\frac{24}{l_i}$
Ⅱ	3.7 × 10−3	27	7.12	0.860	1.917	$i_{i3}=\frac{\Delta u_i}{10l_i}-\frac{k_i-k_w}{1.917l_i}-\frac{27}{l_i}$

.

The soil samples before and after the porous clay plate test were taken, dried and then subjected to the scanning electron microscope test. After being magnified 500 times, the soil microstructure under the action of matric suction of 0 and 1000 kPa was obtained, as shown in Figure 8. It can be seen that the pores of soil particles were filled with fine particles after the matric suction of 1000 kPa, and the particles were closely arranged. It shows that the soil particles have undergone seepage deformation. Under the action of seepage pressure, the hydraulic gradient increases to a certain value, and the soil particles migrate in the pores, thus changing the soil microstructure.

3.2. Numerical Model and Field Monitoring

3.2.1. Numerical Model

In the process of water level fluctuation, piping often occurs in the original ancient riverbank of Lanxi, endangering the stability and safety of the ancient riverbank. In order to retain the original ancient dike, an antiseepage wall was set behind the dike, which changes the seepage characteristics of the structure. By establishing a two-dimensional finite element numerical model of saturated-unsaturated seepage in porous continuous media, the influence of antiseepage wall on the groundwater level, pore water pressure and hydraulic gradient of the ancient riverbank were studied.

The average water level height of the Lanjiang River in winter is 23.14 m, and the water level of the Lanjiang River fluctuates sharply in rainy season. The typical flood fluctuation period and the corresponding hydrostatic pressure of the groundwater at the back side of the ancient dike were taken as the boundary conditions of the numerical model, as shown in Figure 9. The water level of Lanjiang River rose sharply from June 30, 2021, reached its highest point of 29.53 m at 6:00 on July 2, and dropped to 22.95 m at 18:00 on July 5, with a drop of 6.58 m, as shown in line 1 of Figure 9. The antiseepage wall is set behind the dike. The monitoring data shows that the peak value of the groundwater level behind the ancient dike decreases significantly, and its change with time is shown in line 2 of Figure 9.

The impervious core at the back water side of the ancient dike has a diameter of 1.60 m and a depth of 6.61 m. The upper part of the antiseepage wall is a concrete wall, and its bottom is located on the Sanhe soil foundation. The lower part of the concrete wall uses cement grouting to form a curtain to prevent seepage. The project implementation process is shown in Figure 10. The permeability coefficient of concrete cutoff wall is 2.5 × 10⁻¹¹ cm/s and the permeability coefficient of cement grouting curtain is 1.6 × 10⁻⁸ cm/s.

When establishing the numerical model, several oblique broken lines were used to simplify the slope surface of the ancient riverbank slope. The top elevation of the ancient riverbank is 33.05 m, the toe elevation is 26.88 m, the foundation elevation of the ancient dike is 24.80 m. The upper vertical section is 6.17 m high and 0.22 m wide at the top. The bottom of the upstream slope is 19.05 m high, and the slope gradient is 22° and 43°, respectively, from bottom to top. The ancient dike is close to the building, the building foundation is deep foundation, and the upper load directly acts on the bearing layer, so its effect on the ancient dike could be ignored. The antiseepage wall is composed of concrete wall and a cement grouting curtain. The curtain penetrates the sand gravel layer and reaches the pelitic siltstone. The numerical model adopts a quadrilateral finite element with a side length of 0.5 m and generates 7023 nodes and 2584 elements. The numerical model of the ancient dike with antiseepage wall is shown in Figure 11.

3.2.2. Field Monitoring

A water level logger was buried between the antiseepage wall and the house foundation to measure the change in the groundwater level. The water level logger is located 6.5 m from the top of the ancient dike, and the depth is 12.46 m below the ground. It monitored the change of groundwater level behind the ancient dike. The groundwater level data was extracted from June to July 2021 and is shown in line 2 of Figure 9. The buried water level logger and the extracted water level data are shown in Figure 12. In order to get the seepage stability of the ancient dike under the action of the transient water level, the typical locations A₁ and A₂ of the numerical model were taken to study. Points A₁ and A₂ are located on both sides of the impervious core. Point A₁ is located 1.1 m above the foundation behind the ancient dike, that is, at 25.90 m elevation. And point A₂ is 2.2 m horizontally away from point A₁, with the same elevation at point A₁.

4. Discussion

4.1. Permeability Characteristics and Pore Water Pressure Distribution of Ancient Riverbank

When the flood peak passes through, the water level of the Lanjiang River changes rapidly. The relationship between the permeability coefficient of the ancient riverbank and the pore water pressure follows the saturated-unsaturated seepage model. The groundwater level monitoring value of A₂ pore and the volumetric water content result calculated by the numerical model during flood peak fluctuation are shown in Figure 13. When the groundwater level monitoring value of A₂ point is 25.9 m higher than the elevation of the A₂ point, the calculated volumetric water content of the A₂ point reaches 0.41, that is, the A₂ point saturation is 100%. When the groundwater level monitoring value of the A₂ point is lower than 25.9 m, the volumetric water content of the A₂ point will decrease accordingly. The numerical calculation results of the A₂ point are in good agreement with the measured values of the groundwater level, which verifies that the numerical model parameters and boundary conditions are reasonable and the numerical model results are reliable.

When the ancient riverbank is not equipped with the antiseepage wall, the pore water pressure of the soil mass changes with the flood water level during the flood fluctuation process, showing the characteristics of consistent change law. At point A₁ of the original structure of the ancient riverbank, when the flood reaches the peak, the pore water pressure reaches the maximum value of 36.4 kPa. With the flood passing through the peak, the pore water pressure decreases accordingly. Figure 13 shows the transient values of pore water pressure at points A₁ and A₂ on both sides of the antiseepage wall of the ancient riverbank. In the process of flood fluctuation, the pore water pressure change rule of A₁ between the ancient dike and the antiseepage wall is consistent with the flood fluctuation. When the flood reaches the peak value of 29.53 m, the pore water pressure at the A₁ point reaches 41.28 kPa. In the process of flood fluctuation, the pore water pressure decreases synchronously, and the fluctuation rate is characterized by rapid change first and then slow down. The variation law is similar to that of the original A₁ point of the ancient riverbank, but the peak value increases by 13.4%. As the flood peak of the Lanjiang River began to fall, the water level dropped by 11.9% and the pore water pressure droppe by 79.3% within 16 hours, then the water level dropped slowly, and the water level dropped by 13.6% and the pore water pressure dropped by 53.6% within 69 hours. The pore water pressure at the A₂ position between the antiseepage wall and the road changes slightly and tends to be gentle. It is less affected by the water level change of the Lanjiang River. The maximum pore water pressure is about −5.5 kPa, 66.7% less than the maximum pore water pressure at A₁ point, and the minimum value is close to the A₁ point. It can be seen that the pore water pressure between the antiseepage wall and the road rises and falls gently during the flood fluctuation due to the seepage resistance of the impervious curtain.

When the flood reaches the peak value, the peak value of the groundwater level of A₂ is 24.57 m, 3.38 m lower than the peak water level, that is, 11.40% lower than the flood level, with a time lag of about 6 hours. After the flood peak passes, the groundwater level slowly decreases. The numerical calculation results are consistent with the monitoring values. The numerical model analysis method is effective, and the parameters are reasonable. It can be seen from the comparison that the permeability coefficient decreases after the antiseepage wall is set on the ancient riverbank, the pore water pressure between the antiseepage wall and the road changes gently, and the change time lags behind.

It can be seen from the above results that for the original ancient riverbank with strong water permeability, the change in pore water pressure of soil mass is synchronous with the change in water level of the Lanjiang River. After the antiseepage wall was set, the seepage path of water was greatly increased and the pore water pressure was greatly reduced and lagged behind the water level fluctuation.

4.2. Variation Characteristics of Hydraulic Gradient of Ancient Riverbank

The transient water pressure difference was calculated using a saturated-unsaturated seepage model. The change curve of permeability pressure difference at points A₁ and A₂ under the transient water level after the antiseepage wall is shown in lines 1 and 2 of Figure 14, which is basically consistent with the results of finite element analysis. The transient change trend of the permeability pressure difference at the toe of the ancient dike was basically the same before and after the antiseepage wall was set, but the difference between the transient permeability pressure difference at A₁ and A₂ points on both sides of the antiseepage wall was large, about 2000 times. The maximum value of the permeability pressure difference at the A₁ point is 3.17 kPa, the minimum value is −2.54 kPa, and the maximum permeability pressure difference at the A₂ point is 11.68 Pa. The seepage prevention effect of the antiseepage wall is obvious, which greatly reduces the water pressure at the back side. The finite element numerical calculation results are consistent with the monitoring data.

The hydraulic gradient is calculated using Equation (12) and Table 2, and the relationship curve between hydraulic gradient and time is obtained, which is compared with the results of the finite element calculation. The hydraulic gradient of the ancient riverbank changes with the rise and fall of the flood peak of the Lanjiang River. At the maximum water pressure change rate, the hydraulic gradient reaches the maximum. Figure 15 shows the gradient distribution. The maximum hydraulic gradient A₁ of the ancient dike at this time is taken, and the change rule of the hydraulic gradient with water level is shown in Figure 16. When the water level change rate continues to increase, the hydraulic gradient at point A₁ increases rapidly. When the water level is 27.58 m, the water level change rate reaches the maximum, and the hydraulic gradient at point A₁ reaches the maximum of 0.62. When the water level change rate decreases, the hydraulic gradient starts to decrease. As the water level of the Lanjiang River slows down, the hydraulic gradient at point A₁ decreases gradually. When the flood peak decreases rapidly, the hydraulic gradient decreases rapidly. When the water level changes slowly, the hydraulic gradient changes steadily, as shown in Figure 16.

After the antiseepage wall was set, the hydraulic gradient distribution of the ancient riverbank has changed. Between the ancient dike and antiseepage wall, the hydraulic gradient contour is densely distributed, reaching the maximum value of 1.16 at the toe of the dike, as shown in Figure 17.

In order to improve the cohesion of the soil mass between the ancient dike and the antiseepage wall, the modified lime grouting measures are adopted to treat the defects of the internal soil mass, improve the compactness and integrity of the soil mass and avoid the secondary damage to the ancient buildings caused by the shortcomings such as excessive cement strength and high soluble salt content. The implementation process is shown in Figure 18. The ratio of modified lime slurry is hydrated lime: mineral powder = 2:3, water binder ratio is 0.43, with adhesive additives, bonding additives and ordinary water reducing agent added, and the grouting and mixing machine is used for grouting. The flexural strength value of the modified lime slurry can reach above 1.5 MPa, and the compressive strength value can reach above 15 MPa.

After the modified lime grouting treatment, the hydraulic gradient distribution of the ancient riverbank changes. When the water level of the Lanjiang River rapidly increases to 27.92 m, the maximum hydraulic gradient at point A₁ is 0.42, which is 57.0% lower than that without lime grouting treatment. At this time, the hydraulic gradient distribution is shown in Figure 19. Then, the water level of the Lanjiang River rises and slows down, and the hydraulic gradient at point A₁ decreases gradually. When the flood peak decreases rapidly, the hydraulic gradient increases rapidly and then decreases gradually to stabilize, as shown in Figure 20.

From the above results, it can be seen that the pore water pressure and hydraulic gradient have changed after the ancient riverbank was set with antiseepage wall, and the maximum hydraulic gradient appears at the toe of the dike, where the hydraulic gradient changes instantaneously with the water level. The modified lime grouting between the ancient dike and the antiseepage wall can effectively reduce the hydraulic gradient value, control the seepage deformation and avoid piping and soil flow.

5. Conclusions

In this paper, the saturated-unsaturated transient seepage numerical model of continuous media is established to solve the seepage instability problem, such as piping caused by the loss of fine soil particles in ancient riverbanks. Through laboratory tests, on-site monitoring data and saturated-unsaturated soil seepage theory, the mechanism of the impact of flood transient changes on soil seepage stability is studied, and the prevention measures of piping soil flow caused by flood fluctuation in ancient riverbanks are studied.

On the basis of saturated-unsaturated seepage theory, this paper derives the calculation formula of the permeability coefficient and hydraulic gradient of saturated-unsaturated soil and applies it to the ancient riverbank repair project. The comprehensive comparison between the monitoring data and numerical analysis results shows that the theoretical formula has good adaptability to the transient saturated-unsaturated seepage stability analysis.

The ancient riverbank is located in a relatively densely populated town, and the impact of flood, human settlement environment, cultural relics protection and other factors should be comprehensively considered in its repair. The monitoring data and numerical simulation results show that, compared with the original structure with good water permeability, the extreme value of pore water pressure behind the toe of the ancient flood control embankment is increased by 13.4%, the maximum value of hydraulic gradient is increased by 55.6%, and the pore water pressure and hydraulic gradient behind the antiseepage wall are greatly reduced. The results show that the seepage resistance of the soil can be effectively reduced by setting antiseepage wall in the ancient riverbank without changing the cultural relics, but the local seepage gradient behind the ancient dike increases, so the modified lime grouting measures must be taken to improve the cohesive force of soil particles to prevent piping. The analysis results show that the maximum hydraulic gradient of the ancient riverbank is reduced by 57.0% after the ancient riverbank is repaired with an antiseepage wall and modified lime grouting, which effectively prevents seepage deformation. This paper provides a theoretical method for the seepage stability analysis of saturated-unsaturated soil, an application case for the repair measures of ancient riverbanks, and a reference and theoretical basis for the repair of similar historical water projects.