Abstract
The rainfall often causes changes in the physical performance of the embankment, which leads to disasters such as embankment collapse and road surface settlement and cracking. Past research has tended to be limited to traditional embankment seepage models and is mostly based on the assumption that surface precipitation is uniform and rainfall intensity is constant. To adapt to the changes and development of the times, based on the water leakage mode of the flexibly assembled highway embankment, a new rainfall calculation model of the reinforced soil embankment is constructed and combined with the solid-fluid coupling physics theory, the sedimentation amount and slope stability of the embankment are analyzed at multiple levels, the mechanical properties of the new embankment under rainfall conditions are summarized, the factors affecting the settlement of the embankment and the stability of the slope are explored, and the reference model is provided for the construction of the new embankment, and the existing construction process is improved through multilevel cause analysis. We improve and develop the existing theoretical system to reduce the probability of road diseases, improve the efficiency of road construction, and reduce the cost of road maintenance.
1. Introduction
With the increasing load of vehicles and the requirements of special working conditions, ordinary embankments can no longer meet the needs of highway construction, and the new flexible prefabricated highways (Figure 1) bring a feasible solution. The difference between the new flexible prefabricated highway and the ordinary highway is as follows: (1) the roadbed is assembled and constructed by prefabricated concrete slabs, (2) the geogrid is buried in the embankment soil to form reinforced soil, and (3) The surface of the embankment slope is laid with a GRF surface layer, and the main role is to prevent the infiltration and erosion of rainwater. Compared with traditional highways, the new flexible prefabricated highways have the advantages of strong bearing capacity, fast construction speed, and strong ability to resist natural disasters, so they have a wide range of application prospects.
A large number of studies have shown that rainfall is an important cause of road diseases. Seepage of rainwater in the embankment soil, manifested as the wet front in the soil, for the rainwater in the embankment surface nonuniform penetration, due to the difference in the wet front propulsion and the interaction between them, will cause uneven settlement on the embankment surface, resulting in a series of diseases such as road cracking, while the change in soil moisture content will also affect the soil shear resistance, matrix suction and other mechanical properties, rainwater infiltration generated by the Darcy velocity field will also change the permeability of soil particles in the seepage field. As a result, the stability of the embankment slope body deteriorates, inducing serious consequences such as embankment collapse. Therefore, it is necessary to explore the mechanical properties of embankments under rainfall conditions.
In the past period, scholars at home and abroad have carried out a large number of model experiments [1–8] and numerical simulations [9–17] on the rainwater infiltration of embankment soil, most of which are based on the traditional research of uniform penetration of embankment soil surface and slope and constant rainfall intensity, studying the safety of embankment slope and the characteristics of rainwater seepage, and mainly focusing on preventing serious collapse accidents on embankments. However, the uneven settlement of the embankment caused by rainfall [18–24] is a more common form of destruction in the actual use process. Although this destruction will not directly lead to catastrophic consequences, it will lead to a series of diseases such as cracking and bulging of the road surface, affecting the normal use of the road, so the research and prevention of uneven settlement of the road surface are equally important. Moreover, with people's pursuit of safety and economy, the use of new flexible prefabricated highways in practical engineering is increasing, so many scholars have conducted systematic research on this [25–35], but the research content is mostly a single field calculation of the stress field, the impact of the seepage field in the absence of rainfall, and the mechanical properties of the embankment under the action of two-way fluid-structure interaction have important reference significance for analyzing the safety of the embankment under rainfall conditions, so we have conducted a series of studies on this.
The water leakage method of the flexible assembly highway embankment is very different from the previous embankment, which is embodied in the following. (1) The surface of the embankment soil is no longer the uniform infiltration of rainwater but concentrated in the slit. (2) Due to the protection of the GRF surface layer, the slope of the embankment has almost no rainwater infiltration. Therefore, based on the water leakage mode of flexible prefabricated highway embankment, this paper constructs a new rainfall calculation model for reinforced soil embankment and combines the solid-fluid coupling physics theory and rainfall intensity change theory to analyze the sedimentation amount and slope stability of the embankment at multiple levels, summarizes the mechanical performance of the new embankment under rainfall conditions, explores the factors affecting the settlement of the embankment and slope stability, provides a reference model for the construction of the new highway, and improves the existing construction process through cause analysis. Improve and develop the existing theoretical system.
2. A Flexible Prefabricated Highway Calculation Model That Considers the Effect of Bidirectional Fluid-Structure Interaction
2.1. Stress Field Calculation Method
2.1.1. Mechanical Equilibrium Equations
The expression for the equilibrium equation for soil mechanics of microunits in unsaturated soils [36, 37] is as follows:where is the total stress tensor of the soil, represents the total density of the soil medium and the liquid, andwhere is the porosity of the soil, is the effective saturation, is the density of the liquid phase, and is the density of the solid phase. We apply the principle of effective forces of Terraghi:where is the Biot-Willis coefficient, is the effective stress tensor, is the Kronecker Delta tensor, and when is satisfied, ; when , .
As can be seen from the theory of elastic mechanics, the constitutive equations of the soil skeleton are as follows:where is soil strain, is the Poisson ratio of soil, and is the modulus of soil elasticity. The geometric equations satisfy the strain and displacement under conditions assuming small deformations:where is the solid phase displacement.
2.1.2. Soil Plastic Yield Criteria
The criterion for soil destruction is the Drucker–Prager model. Drucker and Prager proposed a broad Mises yield and destruction criterion considering the effects of hydrostatic pressure in 1952, often referred to as the Drucker–Prager criterion or D-P criterion for short:where are constants related to the properties of clay materials, is the first invariant stress tensor, and is the second invariant of the stress partial tensor. The expressions for and are as follows:
For the constants and , they can be derived from the cohesion and the internal friction angle in the soil parameters , and the specific derivation formula is as follows:
2.1.3. Mechanical Analysis Model of Reinforcement-Soil Interaction
The material of geogrid is mostly glass fiber or polyester fiber, and the thickness of the geogrid buried in the soil is generally 2-3 mm, so when simulating the force of the geogrid in the soil and its impact on the surrounding soil, it is generally assumed that the grid is only affected by the pulling force, without considering its shear resistance [38]. Therefore, the truss tension unit is selected to simulate the force of the geogrid.
When considering the interaction of the reinforcement soil, the displacement generated by the soil near the geogrid is first calculated, which is generated by the global system under the action of the force, which is called the global strain. The global strain is then projected onto the axial strain of the geogrid using the edge tangent vector , the expression of which is as follows:
Global strain modeled using the Lagrange shape function, which specifies both the engineering strain and the green-Lagrangian strain to handle both small and large strains. The Grimm–Lagrange strain tensor for large displacements is defined as follows:
The engineering strain tensor for small displacements is defined as follows:
The unfolding formula of the axial strain is as follows:
The stress inside the geogrid where contribution to all additional stresses, is the elastic axial strain, is the total axial strain, and contributes to all inelastic strains, where the expressions and are as follows:where is the initial stress, is the external stress, is the initial strain, is the thermal strain, is the hygroscopic strain, and is the plastic strain. In this model, and . Therefore, the expression of the internal stress of the geogrid is as follows:
2.2. Calculation Formulas and Methods of the Seepage Field
2.2.1. Richards Model
Assuming that soil isotropy and liquids are incompressible, Richards' equation in three-dimensional states takes the following form:where pressure is the dependent variable. Wherein, represents specific water capacity, indicates effective saturation, represents the water storage coefficient, represents fluid density, represents gravitational acceleration, and are the fluid source (positive) or sink (negative).
And is the flux vector; the physical meaning is the velocity of the fluid through an infinitesimally small surface, and its expression is as follows:where represents the hydraulic permeability, represents the hydrodynamic viscosity, represents the relative permeability, represents the elevation, and the pressure is used here as the dependent variable to solve the Richards equation, but the boundary head can still be defined in the calculation, and the value of the dependent variable pressure is obtained by the transformation equation.
2.2.2. Soil Moisture Characteristic Curve
The matrix suction (or soil water suction) of soil water changes with the change of soil moisture content, and its relationship curve is called the soil moisture characteristic curve. This curve reflects the relationship between soil moisture energy and quantity and is an important parameter for studying the hydrodynamic properties of soil. There is a certain lag in the soil moisture characteristic curve; that is, the soil moisture content under the same suction force, and the water release state is larger than the water absorption state.
Many factors affect the soil moisture characteristic curve [39], and its main influencing factors are three. (1) Particle size: the smaller the particle size, the greater the slope of the curve, which is manifested as the greater the attraction ability to water. This is the most important factor affecting the soil moisture characteristic curve. (2) Structure: when the soil agglomeration is better, the number of agglomerates is larger, and the curve begins with a gentle rise and then turns into a rapid rise. The more agglomerate content, the lower the curve gentle rising section. When the soil is more dispersed, and the agglomerate content is relatively small, the curve rises quickly at the beginning, then undergoes a period of slow rise, and finally turns into a rapid rise, making the curve a typical “S” shape. (3) Bulk density: the slope of the curve, especially the slope close to saturated water content, increases when the bulk weight becomes larger. This is because when the bulk density increases, the soil pores, especially the larger pores, are compressed, the number of large pores is reduced, and the saturation moisture content is reduced.
Due to the complex composition of the subgrade soil, the soil moisture characteristic curve obtained by the experiment has more accidentality and is not universal, so the indirect inference method is used to obtain the soil moisture characteristic curve. Common soil moisture characteristic curve models include the van Genuchten model and Brooks-Corey model, and the van Genuchten model (VG model) is selected as the soil moisture characteristic curve equation.
The essence of the VG equation is a nonlinear equation, and the linear type is very similar to the actual measurement result. The disadvantage is that the equation has more parameters, and it is easy to encounter some problems where the parameters are negative or cannot be solved in the determination process. Its liquid volume fractional expression is as follows:where is the residual liquid volume fraction, is the saturated liquid volume fraction, is the effective saturation, and is the pressure head, where the expression of is as follows:
The expression for than water capacity is as follows:
The expression for the relative permeability is as follows:where are all constitutive relation parameters of the retention model, where . According to the experimental measurement and related data in this paper, , , and , and the water and soil characteristic curve of the effective saturation with respect to the piezometric head is obtained as shown in Figure 2.
2.3. Bidirectional Fluid-Structure Interaction Calculation Method
Formulas (21) and (22) in Section 2.2.1 show that
to the right of the equation is the fluid source-sink term, again
Therefore,where is the volumetric strain of the matrix material and is the volumetric strain rate of the matrix material. The right side of the equation can be understood as the rate of expansion of the pore space, and as increases, the volume fraction available to the fluid also increases, causing the liquid to sink, hence the minus sign in .
The coupling of the stress field and the seepage field involves two constitutive relationships. One is related to stress, strain, and pore pressure. That is, considering the influence of water on the soil, pore water pressure will help the soil to bear a part of the pressure:where is the Gauchy stress tensor, is the strain tensor, is the fluid pore pressure, and is the elastic matrix obtained by measuring the strain caused by the change of stress under constant pore pressure under drainage conditions. The coupling of the volume portion is expressed as follows:where in the volume modulus of the empty matrix. is the average pressure calculated from the stress tensor , and the expression is as follows:
Another constitutive relation relates to the increase in fluid content with volumetric strain and pore pressure increase. That is, considering the effect of soil on water, the deformation of soil will lead to changes in water content. Fluid pore pressure is proportional to the expansion of the porous matrix and changes in fluid content:wherein the Biot–Willis modulus is the reciprocal of the water storage coefficient , which can be defined as the change in fluid content due to changes in pore pressure under constant volume strain:
The water storage coefficient can be measured experimentally or calculated from the properties of the matrix material:where is the porosity, is the volume modulus of the fluid, and is the volume modulus of the solid volume, that is, the volume modulus of the homogeneous block of the solid material constituting the porous matrix. The Biot-Willis coefficient can be measured experimentally and can also be defined according to the volume modulus of porous materials and the volume modulus of solids:
The volume modulus of a porous material is always smaller than the volume modulus of a solid (a solid block is harder than a porous block made of the same material), so is always bounded .
Since the volume modulus of solids is not convenient for direct measurement in experiments, we can combine (31)and(32)to eliminate :
3. Study
3.1. Model Dimensions
In this paper, a new two-way six-lane flexible assembled highway is used as the research object. The pavement surface layer is permeable asphalt, the pavement base layer is a precast concrete slab, and the embankment slope is paved with a GRF surface layer. The total width of the road surface is 26 meters, of which the width of each lane is 3.75 meters according to the highway construction standard, the total width of the six lanes is 22.5 meters, the width of the central divider is 2 meters, and the buffer zone of 0.75 meters is set aside on each side of the road. The prefabricated roadbed is divided into four pieces, each with a width of 6.2 meters, and during assembly, 0.5 meters of water supply and drainage facilities are set aside on both sides of the pavement, and the thickness of each concrete slab layer is 0.8 meters, and the spacing is 0.05 meters as a construction joint and expansion joint. The cross-sectional view of the embankment of the roadbed is shown in Figure 3.
3.2. Computational Model Building
The surface material of the highway pavement is permeable asphalt, which does not consider the blocking effect of the road facing the rainwater and only considers the obstruction of the rainwater by the concrete slab layer of the subgrade. The subgrade is simplified to four concrete slabs, and the self-weight of the surface material and the vehicle load is added to the upper surface of the concrete slab as a uniform load and then transferred to the reinforced Earth embankment below. The surface boundary conditions of the four concrete slabs are uniformly loaded, the lower surface is in contact with the embankment, and the elastic deformation and plastic deformation of the concrete slab are considered.
The calculated thickness of the reinforced Earth embankment is 5 meters, and the geogrid is arranged from 0.5 meters below the pavement, with a spacing of 0.4 meters, and a total of 9 floors are arranged. The material of the geogrid is high-strength glass fiber. Its shear resistance is negligible, and the material is mainly subject to tensile force, simplifying it to a truss model. That is, only tensile stress exists in the geogrid. The reinforcement mechanism of reinforced soil is mainly through the mutual bite and bonding between the geogrid and the soil to achieve the result of common force. To be able to better simulate the interaction between the geogrid and the soil, it is achieved by generalized stretching. The specific implementation method is to establish a correspondence between the strain of the soil part near the geogrid and the coordinates of the global material and then project the global strain to the axial strain of the geogrid through the edge tangent vector of the geogrid surface, to achieve the effect of simulating the interaction between the tendons and soils.
The main function of the slope laying GRF surface layer is to prevent the infiltration and erosion of rainwater, and only the boundary condition of the embankment slope body is changed in the model to no rainwater infiltration, which does not directly affect the stress distribution of the slope and the entire embankment, so it is not indicated in the schematic diagram.
The yield model of embankment soil was chosen to match the Drucker-Prager model of the Moore–Coulomb theory. The boundary condition at the cross-section of the embankment is set to roller support, that is, the constraint of zero normal displacements, the bottom boundary condition of the embankment is set to a fixed constraint, and the hydraulic model of the embankment selects Richards' equation. The final model and boundary conditions are shown in Figure 4.
3.3. Model Conditions and Parameters
The parameter source of the soil in this paper is the embankment soil at the Jiuliguan of the Beijing-Hong Kong-Macao Expressway and the soil is obtained by layered compaction of improved soil, and the compaction degree is greater than 95%. The design speed is 100 km/h, and the design bending and sinking value is 125 (0.01 mm). It can be seen from the road design code that the uniform distribution force of the road surface weight and vehicle load on the concrete panel of the subgrade is 260。
The thickness of the concrete slab layer is 80 cm, according to the highway design code, and the material is C35 concrete. The specific parameters of the mechanical properties of each material are shown in Tables 1–3.
The specific hydraulic parameters of the improved soil of the embankment are shown in Table 4.
The three constitutive relational constants in the calculation-time formula are all taken at default values, , and .
3.4. Grid Partition
To ensure the accuracy of the simulation results, different division methods are selected for different parts of the meshing, and the minimum length unit of the geogrid is 0.01 meters, and the maximum length unit is 0.04 meters. The mesh division of the embankment soil adopts the method of mapping, and the more refined quadrilateral grid elements are divided into cross-sections of the embankment, of which the smallest grid element has a side length of 0.2 m, and the largest grid element has a side length of 2.75 m, and then the mesh division is projected to the entire embankment soil part using the mapping. The meshing of concrete slabs is consistent with that of embankments, and the mesh network is divided into quadrilaterals in a mapped manner. Finally, the soil near the geogrid refines the mesh again using local encryption. After the meshing is complete, it is shown in Figure 5.
4. Calculation Results and Analysis
According to the classification of rainfall levels, the amount of rainfall per hour in the range of 2.6 mm–8.0 mm is moderate rain. This paper selects rain as the rainfall condition, the proposed maximum rainfall is 7 mm/h, considering that when rainwater infiltration happens due to the presence of concrete slabs, rainwater will be concentrated in the joints between concrete slabs, and the influence of the ratio of pavement drainage facilities and concrete slab width to slit width is considered, and the maximum infiltration speed of rainwater in the slit between the concrete slabs is 60 mm/h. By consulting the relevant literature [40], it can be seen that, during a complete rainfall process, the rainfall intensity will change with time. For moderate-scale rainfall that lasts for several days, the rainfall rate will first remain stable, then gradually increase, and finally slow down until it stops. We approximate this process using a modified Chicago hydrograph [41]. On the first day, which is the initial stage, the rainfall rate is basically maintained at 30% of the maximum rate. Days 2–4 were the main stages of rainfall, and the rainfall rate reached the maximum value of this rainfall process and remained stable. Day 5 is the final stage, and the rainfall rate gradually decreases to zero. At the same time, in order to prevent a large sudden change in the calculation process, the change process of the infiltration speed was simplified, and the curve was made smoother. The curve of infiltration rate versus time is shown in Figure 6 (where the longitudinal axis peak 1 represents the maximum penetration rate of the study, 60 mm/h).
To comprehensively explore the changes in the mechanical properties of the reinforced Earth embankment under rainfall, this paper compares the effective saturation, road settlement, and slope stability of the reinforced Earth embankment and the unreinforced embankment under rainfall, comprehensively analyzes the difference between the mechanical properties of the two embankments, analyzes the variation of soil thickness at different depths of the reinforced soil embankment, and conducts an in-depth study of the change characteristics of the reinforced Earth embankment under rainfall, and finally draws conclusions and seeks solutions.
4.1. Changes in the Effective Saturation of Embankment Soil
According to the Chicago rainfall hydrograph model, the rate of rainwater infiltration at the slit is defined as a function of time pw2(t), the maximum rate of rainfall infiltration is 60 mm/h, the infiltration rate , where is a function of the y-axis coordinate value to concentrate the infiltration of rainwater in the slits, and there is no inlet for seepage of rainwater under the concrete slab. We select the cross-section at x = 25 m in the middle of the road section to obtain a shadow map of the effective saturation of the embankment soil with time. Below is the effective saturation shadow plot of d = 0, d = 2, d = 4, and d = 6 for reinforced and unreinforced embankments.
As can be seen from Figures 7 and 8, the change law of the effective saturation of the soil body is almost the same under the same rainwater infiltration conditions of the two embankments, and the geogrid does not affect the seepage of rainwater in the embankment. The change of the effective saturation of the soil is centered on the infiltration of the slit to spread around and is affected by the permeability of the soil, the change of the effective saturation of the soil has a certain lag, and the higher the hydraulic conductivity, the better the permeability of the soil, the faster the seepage velocity, the less obvious the hysteresis. At the same time, it can be seen that there is an area under the concrete slab, and the effective saturation of the soil in this area has hardly changed, calling this area an uninviting area. A more in-depth study can find that only increases the duration of rainfall; for example, extending the duration of the peak infiltration rate from 1 day to 3 days in this study does not change significantly in the area of the uninvited area, and as the duration of rainfall increases, the area of the uninvited area decreases more and more slowly until it does not change. However, when the width of the slit is changed, the area of the uninvited area is significantly reduced, and the size of the unapproached area is also significantly changed when the hydraulic conductivity of the soil is changed. When the hydraulic conductivity of the soil increases, that is, the better the water permeability of the soil, the smaller the area of the uninvited area. Changing the infiltration rate of inlet rainwater can also affect the area of the uninvited area, and the faster the infiltration rate, the smaller the area of the uninvited area.
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The generation of unmerged areas is mainly related to the microscopic mechanism of water seepage in the soil, and the seepage of water in the soil is mainly affected by gravity, capillary gravity, water molecular gravity, molecular gravity on the surface of soil particles, etc. These forces will change with the movement mode of water and the effective saturation of the soil, and this phenomenon occurs under the ever-changing interaction of these forces. The presence of unmerged areas leads to a large difference in effective saturation at different locations at the same height in some soils, inducing uneven settlement of the road surface. Therefore, reducing the area of unmerged areas is an important way to prevent uneven settlement of the road surface.
4.2. Settlement of the Upper Surface of the Embankment
Nonuniform settlement of the upper surface of the embankment is the direct cause of uneven settlement of the road surface. Due to the large elastic modulus of concrete subgrade panels, the corresponding variables are small, and the pavement itself hardly has shear resistance. The settlement on the surface of the embankment soil can be directly regarded as the settlement of the pavement. The upper half of the embankment model was sliced, the cross-section parallel to the XY plane was selected for slicing, and the upper surface of the embankment soil was obtained. The z-axis displacement of the upper surface of the reinforced Earth embankment and the unreinforced Earth embankment at each moment is shown in Figures 9-10.
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A positive displacement in Figure 10 indicates that the soil on the surface of the embankment is displaced upwards (uplift), and a negative value indicates that the displacement of the soil on the surface of the embankment is downward (subsidence). Comparing Figures 9 and 10, it can be seen that the displacement change of the road surface between the reinforced Earth embankment and the unreinforced embankment during rainfall is consistent, and both of them have different degrees of uplift on the road surface within 1–5 days with the increase of the infiltration rate of rainwater, and the location of the maximum uplift is also the same. However, the degree of uneven settlement on the surface of the two embankments is quite different. The difference between the maximum and minimum displacement of the reinforced Earth embankment is about 3 mm and the maximum displacement value is about 4.5 mm on the fifth day, while the difference between the maximum and minimum displacement of the unreinforced embankment is 4 mm on the fifth day, and the maximum displacement value is about 11 mm. The maximum displacement difference of the reinforced Earth embankment was reduced by 25%, and the maximum displacement value was reduced by 59.1% compared with the unreinforced embankment.
From Figure 10, we can see that the whole reinforced Earth embankment has undergone different degrees of uplift. With the infiltration of rainwater, in the abscissa direction, the z-axis direction displacement at both ends of the embankment did not change significantly, while the z-axis direction displacement of the middle part increased by 1.5 mm in 1–5 days, from 9.5 mm on the first day to 11 mm on the fifth day, and a certain degree of reduction occurred in 5–7 days, falling to about 10 mm. In the direction of the ordinate, there is a clear layering, which is divided into 5 layers along the ordinate from bottom to top and is symmetrically distributed with a centerline (Figure 9(a)). The z-axis displacement of the 1,5 areas on the upper and lower sides is the smallest, which is due to a certain degree of slippage of the embankment slope, which reduces the impact of soil expansion caused by the increase in the effective saturation of the soil; the 2,4 areas are exactly located at the two slits, and the displacement is the largest; the middle 3 areas, although also located in the slits, are slightly less than the displacement of the 2,4 areas due to the distribution and permeability of the soil stress.
To more intuitively see the displacement of the surface on the reinforced soil embankment, the schematic diagram of the cross-sectional height change of the embankment can be combined with the schematic diagram of the surface height change on the embankment, as shown in Figures 11 and 12.
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As can be seen from Figure 11, as the rain sweeps in, the cross-sectional height of the embankment undergoes a process of first rising and then descending a certain distance. However, this process is not uniform for the points on the cross-section, and it can also be seen in Figure 12 that there is a significant layering of the height change of the embankment surface in the y-axis direction, which reflects the uneven settlement of the embankment soil on the cross-section. In addition, in Figure 12, it can also be found that as rainwater infiltration, in addition to the layering in the y-axis direction, the phenomenon of squeezing uplift at both ends of the embankment in the x-axis direction towards the middle occurs, which reflects the uneven settlement on the longitudinal section of the embankment soil. As the rate of rainwater infiltration increases, the degree of uplift of the intermediate soil is higher and higher compared to the two ends, and the degree of uneven settlement of the longitudinal section of the embankment increases. After the rainwater infiltration rate is reduced to zero, the uplift part of the middle soil gradually decreases, and the degree of uneven settlement of the longitudinal section decreases.
Combined with the real shot of the road surface in Figure 13, it can be seen that the model analysis results are consistent with the actual road surface settlement.
4.3. Soil Settlement at Different Heights of Embankments
The uneven settlement of the upper surface of the embankment is the result of the accumulation of soil settlement below, so the settlement of each high soil layer does not reflect the contribution value to the final settlement of the surface on the embankment. To this end, the soil of the embankment can be divided into soil layers of equal thickness, and the sedimentation of the upper surface of each soil layer is subtracted from the sedimentation of the lower surface of the soil layer to obtain the thickness change of each soil layer, to explore the contribution of different heights of soil layers to the surface settlement value of the reinforced soil embankment.
To take into account the analysis accuracy and the amount of calculation, the embankment soil is divided into ten soil layers on average, and the thickness of each soil layer is 50 cm. A schematic diagram and numbering of soil layers is shown in Figure 14.
In the reinforced Earth embankment, the distribution height of the geogrid is 1.3 m–4.5 m, so the soil layer numbered 3–9 is the reinforced soil layer, and the No. 1, 2, 10 is the unreinforced soil layer. Since the moisture content on the left and right sides of the embankment is symmetrical with the settlement, only one side of the embankment soil body is analyzed. The maximum uplift x = 25 m and y = 26.5 m (Point A), and the center of the embankment x = 25 and y = 20.5 m (Point B) were selected for analysis. The variation in the thickness of each soil layer at point A of the reinforced Earth embankment is shown in Figure 15.
In Figure 15, a positive change in thickness indicates that the thickness of the soil layer increases. That is, a bulge occurs, and if it is negative, it means that the thickness of the soil layer decreases. That is, subsidence occurs. As can be seen from the figure for the soil layer numbered 8, 9, 10 on the upper level of the embankment, the thickness change that occurs in different periods is almost the same, and the change with the change in the rate of rainwater infiltration is not obvious. However, for the No. 1–7 soil layer in the lower part of the embankment, the thickness change that occurs in different periods varies greatly, and the trend of the soil layer changing more obviously is the deeper soil layer. There are two reasons for the change of soil thickness, namely, the change in the mechanical properties of the soil layer and the change of the overlying load. The change in the moisture content of the deeper soil layer is small, and the change in mechanical properties is not obvious, but due to the change in the moisture content of other soil layers on the toppling, the pressure on itself changes greatly, so the change in soil weight caused by the change in water content is the main reason for the change in the thickness of the lower soil layer.
In different periods, the most obvious change in soil thickness was in Soil No. 4, which reached a maximum thickness change of 1.43 mm on Day 5, and the soil layer with the smallest change in thickness was Soil Layer No. 5, with a thickness change of only 0.76 mm on day one. It can be observed that although Soil Layers No. 4 and 5 are adjacent to each other, the amount of thickness change is very different, respectively, the maximum value and the minimum value. Combined with the change in the effective saturation of the soil body of the reinforced soil embankment in Figure 7, it can be found that soil layer No. 4 and 5 is located at the junction of saturated soil and unsaturated soil, and it can be learned from the water and soil characteristic curve of the VG model that when the soil is close to full saturation, the matric suction of the soil will drop sharply to zero, resulting in a huge change in the shear resistance of the soil and other mechanical properties, and there is also a difference in the permeability of saturated soil and unsaturated soil in the seepage field.
Synthesizing the four curves at different times, it can be found that the difference in the temporal distribution of soil thickness changes is less than the difference in spatial distribution, that is, as the rainwater infiltration rate changes, the thickness of the same soil layer changes in different periods, and the latter changes more than the difference in thickness changes of different soil layers at the same time. Therefore, the effect of rainwater infiltration rate on the amount of soil thickness change is not intuitively seen in Figure 15. For this purpose, a representative soil layer of 4, 8, 9, 10 was selected and a curve of the thickness of the soil layer was plotted over time, as shown in Figure 16.
As can be seen from Figure 16, the amount of change in the thickness of the soil layer has undergone a process of change that first increases and then decreases over time, but the details of the changes are not the same. Combined with the rainwater infiltration rate change curve of Figure 6, it can be found that all four curves have similarities with the curve of Figure 6. The moisture content of the four soil layers changes regularly with the infiltration of rainwater. First, with the increase of rainwater infiltration rate, the water absorption of the soil layer expands. Then, with the cessation of rainwater infiltration, the pore water continues to move downward under the action of gravity, the moisture content of the soil layer decreases, and the increase in the thickness of the soil layer gradually decreases, but finally, due to the existence of residual pore water, the moisture content of the soil layer has increased compared with the beginning; so compared with the beginning, the soil layer has undergone a certain degree of expansion.
Through observation, it can be seen that there is a certain difference in the peak time point of the thickness change of the four soil layers, the peak of the No. 10 soil layer in the uppermost part of the embankment soil body appears at the earliest time, reaching the maximum value of the thickness change on the third day, while the three soil layers of 3, 8 and 9 reach the peak of the thickness change on the fourth day, and there are two reasons for this phenomenon: First, it is affected by the distance from the rainwater infiltration point. No. 10 soil layer is at the top of the embankment, closest to the rainwater infiltration point, and the lag phenomenon is not obvious. The time for the peak of the thickness change is earlier, as other soil bodies gradually approach the bottom of the embankment, the lag phenomenon is more obvious, and the time for the peak of the thickness change is more backward; the second is that the interaction between the tendons and soil hinders the displacement of the soil. No. 10 soil layer does not have a geogrid buried, while No. 3–9 soil layer is buried with a geogrid, and the interaction between the geogrid and the soil constrains the displacement and deformation of the soil, so it is more hysterical than the change of soil thickness without the geogrid.
The variation in the thickness of the different numbered soil layers at x = 25 m and y = 20.5 m (Point B) in the center of the embankment is shown in Figure 17.
It can be seen from Figure 17 that the thickness of the soil layer numbered 7–10 changes with time is small, while the thickness change of the soil layer 1–6 varies greatly in time. Overall, the difference in the temporal distribution of soil thickness changes is less than in spatial distribution. The thickness change of all soil layers is greater than zero, indicating that all soil layers have undergone different degrees of expansion, and the maximum thickness change at different times occurs in the No. 1 soil layer, and the maximum thickness change is about 1.42 mm; the smallest thickness change at different times occurs in the No. 7 soil layer, and the minimum thickness change is about 0.55 mm.
At the same time, it can be seen from the figure that the thickness change of different soil layers is reciprocating, which is caused by the uneven distribution of effective saturation in the embankment soil. As can be seen from the change of the effective saturation in Figure 7, the effective saturation of the soil body is centered on the seepage inlet and is fan-shaped layer by layer. With the diffusion of the wet front, different water content layers are formed, and there is a constant pressure head below the embankment, which forms a bottom-up water content layering phenomenon, and under the joint action of the two, this reciprocating oscillation-like soil thickness change curve is produced. We compare Figure 17 at point B with Figure 12 at point A to find that the curve at point B oscillates more, and it can be found from the effective saturation change plot of Figure 7, which is due to the interaction of several seepage inlets at point B, and the layering of effective saturation is denser.
To more intuitively see the law of the change in the thickness of the same soil layer with time, the most representative soil layers of 4, 8, 9, and 10 were also selected to plot the time-course curve of the change in soil thickness, as shown in Figure 18.
As can be seen from Figure 18, the thickness change of the soil layer at point B is very similar to the thickness change trend at point A, all of which are the soil body first undergoes a certain expansion and rise, but the values of soil expansion are different, but the essence is the same, and there is a certain lag relative to the rainwater infiltration speed change curve, and the lag is more and more obvious with the increase of depth. At the same time, although the trend of change between the two positions is very similar, the amount of change is much different. At point A, the peak thickness increase of the four soil layers was 1.42 mm, 0.95 mm, 1.07 mm, and 1.17 mm, respectively. At point B, the peak thickness increase of the four soil layers was 0.77 mm, 1.05 mm, 0.61 mm, and 1 mm, respectively, and compared with the two, the increase in peak thickness of the soil layer at point B was generally less than at point A. Observing the Darcy velocity field of the soil of the reinforced Earth embankment (Figure 19), it can be found that the Darcy seepage velocity at point B is higher than at point A, which causes the soil layer at point A to receive less permeability than at point B, so the thickness of the soil layer at point A is higher than that at point B.
4.4. Embankment Slope Stability
In the process of rainfall, in addition to considering the uneven settlement of the embankment soil, it is also necessary to consider the decline in the stability of the embankment slope due to the change in the effective saturation of the soil. The slope safety factor can well reflect the stability of the embankment slope and can also intuitively see the potential of the slope to continue to bear loads. This paper uses the strength reduction method to calculate the safety factor of the embankment slope, and the strength reduction method refers to the use of the reduction factor to continuously reduce the cohesion and the internal friction angle of the soil, thereby reducing the strength of the soil until the slope plastic damage occurs; the reduction coefficient value at this time is the safety factor of the embankment slope in this condition.
First, through the compilation and calculation equation to calculate a series of strength reductions after the value, and then the value from large to small into the calculation, until the embankment slope plastic damage occurs, a group of before the destruction, the strength reduction factor corresponding to the value is the safety factor under this working condition. The strength reduction method is calculated as follows:where are the original cohesion force (Pa) and internal friction angle (rad) of the soil, is the strength reduction coefficient, and and are the cohesion force (Pa) and internal friction angle (rad) after strength reduction, respectively.
To explore the change of the safety coefficient of the embankment slope at different times with the change of the rainwater infiltration rate, this paper calculates the safety coefficient of the embankment at each moment and obtains the curve of the change of the safety coefficient of the reinforced soil embankment and the unreinforced embankment with time, as shown in Figure 20.
As can be seen from Figure 20, the safety factor of the slope of the reinforced Earth embankment continues to decline until the sixth day, of which the safety factor of the slope changes most sharply in the process of 2-3 days. From 3.14 on the second day to 2.73 on the third day, combined with the change of rainwater infiltration rate in Figure 6 and the effective saturation distribution map of the embankment of reinforced soil in Figure 7, it can be seen that from day 1.5 to day 3 is the stage when the rainwater infiltration rate rises rapidly to reach the peak, and the wet front spreads to the edge of the embankment slope body around the second day, resulting in a change in the mechanical properties of the embankment slope body, and due to the change of the seepage field where the slope soil is located, the penetration force of the slope soil in the horizontal direction increases, which aggravates the instability and destruction of the slope soil.
Observing the two curves, it can be found that the safety factor of the two embankments is the same, but the safety factor of the reinforced Earth embankment is higher than that of the unrestrained embankment. And after the wet front spread to the embankment slope, the safety factor of the unreinforced embankment decreased by 0.76, while the safety factor of the reinforced Earth embankment decreased by only 0.41, which was 46.1% lower than that of the unrestrained embankment. The initial safety factor of the reinforced Earth embankment was 3.26, which was 20.3% higher than the 2.71 of the unrestrained embankment. The safety factor on the slope of the reinforced Earth embankment on the seventh day after the rain was 2.61, which was 56.3% higher than the 1.67 of the unreinforced embankment. Therefore, it shows that reinforced Earth embankments can significantly improve the stability of the embankment slopes under rainfall.
To explore the failure form of the embankment slope at different times, this paper selects the embankment conditions at four moments of d = 1, d = 3, d = 5, and d = 7, and plots the effective plastic strain that occurs when the embankment soil is destroyed, as shown in Figure 21.
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As can be seen from Figure 21, in the first three days, as the strength of the reinforced Earth embankment continues to decrease, a penetrating plastic sliding surface is formed at about 1 m below the top of the embankment. The sliding surface is located at the top of the slope on both sides, and the plastic damage area is smaller, mainly located in the unreinforced area of the embankment, and the damage to the road surface is concentrated in the range of two meters on each side of the road surface. At the same time, it can be found that on the left and right sides of the road surface, about 5 m away from the edge, there is a hidden potential sliding surface that is gradually forming, and it is becoming more and more obvious with the infiltration of rainwater. On the fifth day, the plastic sliding surface of the reinforced Earth embankment changed significantly, the area of the plastic destruction area increased significantly, and the potential sliding surface was fully revealed. Then, as the rate of rainwater infiltration gradually decreases until it stops, on the seventh day, the plastic sliding surface of the embankment returns to its prerain position and scale, but it is clear that the embankment at this time has a more obvious and larger potential sliding surface than before the rainfall.
From Figure 22, we can see that, with the change of effective saturation of the soil, the plastic sliding surface during the destruction of the unreinforced embankment has not changed significantly. Compared with the destruction form of the reinforced Earth embankment, the plastic damage area of the unreinforced embankment is larger, forming a sliding surface from the bottom of the slope to the upper surface of the embankment, and the impact area on the road surface is larger, and the road surface damage area caused by the slope collapse is the range of 5m between the edges on both sides of the road surface, which is 150% more than that of the reinforced earth embankment.
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5. Conclusion
Through the calculation and analysis of the effective saturation, pavement settlement, soil thickness variation, slope safety factor, and failure form of the reinforced soil embankment, combined with the effective saturation of the unreinforced embankment, the safety factor of the slope, and the form of destruction, the following main conclusions are drawn:(1)The diffusion of the wet front in the soil is centered and divergent, and the geogrid does not significantly change the change process of the effective saturation of the soil. In the process of rainwater infiltration, there is an infiltrated area. Its area is only related to the width of the slit, the water permeability of the soil, and the rainwater infiltration rate but has nothing to do with the rainfall duration. The presence of unmerged areas is an important cause of uneven settlement of the embankment, and the uneven settlement of the road surface can be reduced by replacing the upper part of the embankment with more permeable soil. The area of the uncovered area can be reduced.(2)Rainfall will lead to the uplift of the embankment surface, the distribution of uneven settlement on the embankment surface on the cross-section has obvious layering characteristics, and reinforced Earth embankments can significantly reduce the overall vertical displacement and vertical uneven displacement of the embankment under rainfall.(3)The difference in the temporal distribution of the soil thickness change of the reinforced soil embankment is less than the difference in the spatial distribution. The amount of change in the thickness of the soil layer at different depths is large, and the thickness change of the bottom to the upper soil layer is distributed in a jagged manner, and the largest mutation occurs at the junction of saturated soil and unsaturated soil. The amount of soil thickness change of the embankment increases with the depth of the soil layer, and the lag is more obvious.(4)The safety factor of the embankment slope is related to the diffusion of the wet front surface in the slope, and when the wet front surface spreads to the embankment slope, the safety factor of the embankment falls off a cliff. There are two main reasons for this phenomenon: one is that the change of effective saturation leads to changes in the mechanical properties of the soil, such as matrix suction and shear resistance; the other is that the infiltration of rainwater changes the Darcy velocity field of the seepage flow, increasing the horizontal directional permeability of the soil particles on the slope. The time it takes for the wet front to reach the embankment slope is related to changes in rainfall intensity and soil permeability.(5)With the acceleration of the rainwater infiltration rate, the area of the plastic sliding surface will increase, and the maximum area will be reached about two days after reaching the peak infiltration speed. At the same time, attention should be paid to the development of the potential sliding surface of the embankment, and the potential sliding surface has changed greatly after the rainfall has stopped, and the phenomenon of secondary collapse is prone to occur after the slope collapse of the embankment, causing greater damage.(6)Reinforced Earth embankment can effectively improve the safety factor of the embankment slope and reduce the impact of rainfall on slope stability. At the same time, the geogrid can effectively limit the development of the plastic sliding surface, reduce the area of the plastic damage area, and reduce the loss caused by the collapse of the embankment.
Data Availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Authors’ Contributions
Liang Huang developed software, carried out formal analysis, wrote the original draft, and visualized the study. Wenbo Ma conceptualized the study, developed the methodology, supervised the study, carried out funding acquisition, wrote the original draft, and reviewed and edited the manuscript. Haotian Li developed the methodology, administrated the project, and reviewed and edited the manuscript. Shizhan Xu developed the methodology, carried out funding acquisition, and reviewed and edited the manuscript. Zebin Song developed the methodology and reviewed and edited the manuscript. Yujie Hou administrated the project and reviewed and edited the manuscript.
Acknowledgments
The authors gratefully acknowledge funding from the National Natural Science Foundation of China.