Force Analysis of Anti-slip Pile Bodies on Soil Mudstone Slopes Under Heavy Rainfall

Abstract

The soil mudstone slope anti-slip piles are used as the object of study to analyse the pile forces under the action of heavy rainfall. Introduction to the project, description of the general topographic elevation of the area; extraction of seepage potential energy from soil mudstone, calculation of rainfall and rainfall infiltration, assumption of vertical wall backs and horizontal fill behind the wall, calculation of lateral pressure on the rock supported by anti-slip piles, analysis of its damage mode according to the morphology of the bedrock surface and the conditions of the rock outwash structural surface, and calculation of slope stability under the action of strong rainfall. Analysis of the results: setting the length of the anti-slip piles at 15.5–17.5 m is most reasonable under the effect of heavy rainfall.

1 Introduction

Slopes refer to all geological bodies on the surface of the earth’s crust that have a lateral protruding surface. With China’s infrastructure construction in full swing, various projects such as highway embankment filling and graben excavation, deep foundation excavation, earth and rock dam filling, mining excavation and other projects are also in full swing, and at the same time the number of slopes has also increased. The formation and development of landslides are not independently influenced by a single factor. The deformation and stability of earthy mudstone is a function of time. Just after construction, the deformation of the slope is not obvious. As one of the three major global geological hazards, the occurrence of landslides is often related to the success or failure of the entire project, accompanied by huge economic losses and, in serious cases, even casualties. Slopes are sensitive to rainfall factors and extreme rainfall factors can cause sudden changes in slope displacement [1, 2]. The stability analysis methods of slopes are all based on the geotechnical elastic-plasticity theory. When the slope is overstressed, the strength of the soil is insufficient to maintain the elastic phase and enters the plastic phase, at which time the deformation will continue to develop until destabilisation and damage, so the stability problem of the slope can be considered as a strength problem. However, the stability of slopes also has to consider internal and external factors. For a slope that has been excavated or is being excavated, the internal factors have already been determined, such as physical factors like gravity and water content. Not many studies have considered the combined effects of creep factors and extreme rainfall factors. The design of slope stabilisation measures in engineering is only calculated with short-term stability in mind, while the engineering geology and the performance of the support structure are subject to change during long-term use due to natural phenomena such as rainfall. Geometric factors such as slope height and slope gradient. The external factors such as load and boundary condition changes are also crucial for slope stability analysis, and the infiltration of water is one of the points that cannot be ignored. In slope engineering, the influence of water on slopes is mainly manifested in the infiltration of groundwater and rainfall infiltration, and most of the above-mentioned accidents occur after continuous strong rainfall, so it is also crucial to study the influence of seepage field on slope stability.

2 Project Overview

The soil-rock combination slope refers to the intrusion range of the underground function area including both soil and rock layers. The project is located in the southwest of S. Taking the S area as an example, through the regional geological boreholes included in the geological cloud platform developed under the auspices of the Geological Survey, it can be found that the distribution of strata in the area is dominated by rock formations, mainly sandstone and mudstone, and the nearby mountains show a long monopoly shape with a general northwest direction. The terrain is low and undulating, with an approximate elevation of 210–280 m. The alluvial ditches are mostly “V” shaped, mostly dendritic in development, and are Quaternary floodplain, alluvial, loess-like chalk and gravelly soils, with a grain size of 200 mm. The overlying soils are often fill, clay and sand, and the rock below the soils is strongly weathered for about 1 m, while the lower part of the rock is moderately weathered and weakly weathered in that order. The lithology is mostly shale, sandstone, mudstone and sandy mudstone, with shale, sandstone and mudstone being the main ones. The landslide of the new project is semi-circular in plan and bending in profile, with a maximum height difference of 60 m, a trailing edge width of 114 m and a leading edge width of 288 m, covering an area of 3.11 × 106 m², with an average thickness of 14 m and a volume of 33.64 × 106 m³. The rock type and distribution characteristics, mudstone interbedded structure, except for a group of slopes with parallel orientation and dip close to upright unloading fissures developed on the slopes of the two banks near the river, the rock is generally relatively intact. Three distinct fissures are visible at the back edge boundary, with the longest fissure 162.07 m and the deepest 44.3 m. As the leading edge of the landslide, the road at the site is severely deformed, with severe arching of the road surface and significant cracking, with the maximum crack width exceeding 22 cm. The left side boundary: the left side of the landslide is bounded by an alluvial ditch, the road is severely arched and obvious fissures can be seen, the fissures are about 6–12 cm wide, locally up to 17–22 cm. right side boundary: the right side of the landslide is bounded by a ridge, the right side of the mountain body is fractured and severely damaged, the maximum fissures can be 22–35 cm. according to the borehole, the stratigraphy of the slope body from top to bottom is: the Holocene landslide accumulation layer, the Upper Pleistocene of the Quaternary The slide body is mainly composed of the Middle Pleistocene Loess of the Quaternary, which is light brown in colour and hard in texture, with occasional calcareous nodules.

3 Force Analysis of Anti-slip Piles on Earthy Mudstone Slopes

3.1 Extraction of Seepage Potential Energy from Earthy Mudstone

When the soil is completely dry, it can be regarded as a soil-air two-phase body, and when the soil air is completely filled with fluid, then the object of analysis can be regarded as a soil–water two-phase body, and the flow of water between the pores is called saturated seepage. Under natural conditions, the lower part of the landslide is the slip-resisting section [3, 4]. Due to the action of various external forces making the leading edge of the slope the height of the prograde increases, the sliding resistance gradually decreases, resulting in the leading edge of the slope deformation and the slope surface cracks. For groundwater infiltration channels elongate deformation cracks, continuous rainfall formation of surface water can also be through the infiltration of deeper slopes, a combination of these unfavourable conditions lead to landslide body front edge deformation damage and landslide body front rear edge support weakened or even open, the front edge of the sliding body rear edge deformation caused by the weakening of sliding resistance. Rainfall infiltration is also a kind of vertical infiltration problem. The study of rainfall infiltration is mainly to investigate the relationship between rainfall and infiltration recharge, i.e. how much rainfall is converted into groundwater infiltration, especially in the seepage analysis of slope problems, due to the slope, it is more important to clarify the relationship between rainfall and groundwater infiltration, for which a rainfall infiltration model needs to be established. In this regard, the calculation of rainfall and rainfall infiltration is given by:

$$ L = \int\limits_{0}^{E} {\frac{{\left| {E - 1} \right|^{2} }}{\varepsilon }} $$

(1)

$$ H = \int\limits_{0}^{E} G \times \varepsilon $$

(2)

In Eqs. (1) and (2), $E$ represents the depth of accumulation of rainfall per unit area per unit time, $G$ represents the rate of infiltration and $\varepsilon$ represents the duration of rainfall. From Eqs. (1) and (2), it is possible to derive the depth of water accumulation per unit time, i.e. by subtracting the rainfall infiltration from the rainfall volume. In short, the steepness of the leading edge of the landslide eventually leads to a concentration of stresses located near the foot of the slope, and the slope produces an adjustment in the redistribution of stress internal forces due to the stress concentration phenomenon, resulting in the deformation of the slide and a weakening of the support for the middle section of the slide. Typical moisture content profiles are, from top to bottom: saturated zone, transitional zone, conductive zone, wet zone, the boundary of the wet zone is called the wetting front. And according to Darcy’s saturated seepage theory, the maximum infiltration rate in any direction for a slope soil of the same material can be found as follows:

$$ \beta_{\max } \left( \varepsilon \right) = - l\frac{{\mu \left( {1 + l} \right)^{2} }}{\varpi } $$

(3)

In Eq. (3), $l$ represents the saturated permeability, $\mu$ represents the pressure head and $\varpi$ represents the water content of the topsoil. The essence of seepage is the flow of liquids such as water in a pore medium. When the pore space is fully filled with water it is called saturated seepage and when water is only occupying part of the pore space it is called unsaturated seepage. According to the theory of soil water potential, the total potential energy of water in both saturated and unsaturated soils can be expressed by a formula:

$$ \eta = \eta_{1} + \eta_{2} + \eta_{3} $$

(4)

In Eq. (4), $\eta_{1}$ represents the gravitational potential, $\eta_{2}$ represents the pressure potential and $\eta_{3}$ represents the substrate potential. The matrix potential is the absorption of water by the porous medium thereby reducing the free energy of water, the magnitude of which is a negative value, which is mainly caused by the matrix suction (adsorption + curved lunar surface force). The matrix potential in saturated soils is generally 0. The surface tension in the void is created by the presence of unbalanced forces on both sides of the liquid surface. The central slip zone of a landslide is mostly a geologically existing soft zone (surface) that softens with water, decreases in strength and cannot withstand the thrusts generated by the sliding body at the trailing edge and deformation occurs. The middle section of the landslide moves downwards as the plastic zone expands, and the overall sliding of the landslide begins. Eventually the damage process of front traction, back loading, mid-slip zone shear connection and landslide sliding is formed. When the soil is not saturated, that is, when there is both air and water in the pore space, at this time the soil is a three-phase soil, water and gas, the study of the unsaturated soil seepage law is unsaturated seepage theory. Soil water infiltration can be broadly divided into vertical infiltration problems and lateral infiltration problems according to the direction of infiltration, lateral infiltration including embankment seepage problems, groundwater infiltration problems, vertical infiltration including rainfall infiltration, the earliest research on vertical infiltration problems is Klarman and Burdeman’s research on dry soil under waterlogging conditions, through the experiment to obtain the relationship between soil moisture content and soil depth. In addition, landslides often occur at the trailing edge of dangerous rock collapse and human activities (coal mining, construction, etc.) lead to the accumulation of the trailing edge of the landslide body, trailing edge tension cracks, the accumulation of load on the trailing edge of the landslide body gradually reaches and exceeds its ability to resist slippage, resulting in instability of the trailing slide at the initial stage, but the front of the landslide body produced a thrust, the slide body to the trailing edge deformation landslide centre compression deformation, is a gradual loading process, resulting in drum-shaped tension cracks.

3.2 Calculation of Lateral Pressure on Rock Supported by Anti-slip Piles

In the lateral pressure calculations for soil-rock combination slopes, the soil pressure is calculated according to the Coulomb or Rankine active earth pressure formulae and the rock pressure is calculated by converting the equivalent internal friction angle also according to the earth pressure formulae. As the cohesion of the soil is generated by the combined water and capillary pressure, its strength is very low and mutual slip can be generated between the soil particles, therefore the damage of the soil under the action of external forces is shear damage along the soft structural surface between the mineral particles, so it satisfies Moore a Coulomb’s theorem. If the shear strength of the anti-slip pile is inadequate, the pile is highly susceptible to cracking under landslide thrusts, and even gradually expanding into pile shear or fracture damage [5, 6]. This form of damage is permanent damage to the structure itself, indicating that the pile has lost its ability to resist the slope slide. Considering the lateral pressure generated by the soil layer when the soil layer will not slide along the soil-rock interface, the mathematical expression of the lateral pressure of the soil layer can be calculated according to the active earth pressure based on the flat section assumption, assuming that the back of the wall is vertical and the fill behind the wall is horizontal, the mathematical expression of the lateral pressure of the soil layer is specified as follows:

$$ V_{{\lambda_{1} }} = \frac{1}{2}\phi_{1} \sigma_{1} S_{{\lambda_{1} }} $$

(5)

In Eq. (5), $\phi_{1}$ represents the soil weight, $\sigma_{1}$ represents the height of the soil part of the retaining wall and $S$ represents the active earth pressure coefficient. However, in the case of rock, although it has the same three-phase nature as soil, the mineral particles form a strong polymerisation through crystalline and cemented connections, so that the rock is much stronger than the soil and is in an unplastic state. This damage may be due to a misjudgement of the slip surface, resulting in a low slip resistance due to insufficient anchorage depth, or due to an unreasonable design of the anti-slip pile cross-section and reinforcement, resulting in a pile with insufficient bending and shear resistance. If the anti-slip pile is placed in a poorly anchored soil stratum, the pile will be susceptible to tilting or tipping under landslide thrust before damage occurs but the anchorage is insufficient to cause the overall instability of the anti-slip pile. In terms of rock microstructure, rocks are composed of a variety of mineral grains, pores and cements [7, 8]. It has the same three-phase nature as soil and therefore borrows many of the theories of soil mechanics for the study of rock mechanics. However, the strength of the rock is considerably higher than that of the soil due to the strong polymerisation of the mineral particles through crystalline and cemented joints. The formula for the active earth pressure ensemble for a standard combination of loads is:

$$ R = \frac{{\left| {1 - k} \right|^{2} }}{{\delta^{2} }} \times \sqrt {\left\| {k + n} \right\|} $$

(6)

In Eq. (6), $k$ represents the cohesion of the soil, $\delta$ represents the standard value of the mean surface load and $n$ represents the angle of internal friction of the soil. In this case, the pile body is usually not structurally damaged, and the anchorage capacity of the strata can be improved by means of grouting or adding anchor cables to limit the deformation of the pile top to achieve the purpose of secondary reinforcement. If the shear strength of the soil between the piles is low and the soil flows out from between the piles, then the anti-slip piles are intact but the stability of the slope is reduced and the anti-slip piles fail. If there is an outwardly inclined hard structural surface, the calculation can be made according to the active rock pressure formula, in which the soil layer should be considered as the surface uniform load, the specific expression formula for the inclination of the outwardly inclined structural surface of the side slope is as follows:

$$ V = 1 + \frac{2g\sin \theta \cos \gamma }{{\phi_{1} \sigma_{1} \sin \left( {\theta + \gamma } \right)}} $$

(7)

In Eq. (7), $g$ represents the cohesive force on the surface of the outwardly dipping structure, $\theta$ represents the angle of internal friction on the surface of the outwardly dipping structure and $\gamma$ represents the angle of friction between the rock and the back of the retaining wall. As the excavation area of the slope is a shallow stratum, the rock layer is assumed to be in a linearly elastic natural stress field without consideration of tectonic stresses. The residual sliding force of the soil layer is calculated as follows:

$$ \varphi_{z} = W_{z - 1} \xi_{z - 1} + C_{z} - \frac{{U_{z} }}{Q} $$

(8)

In Eq. (8), $W$ represents the slip force per unit width of the $z - 1$ th calculation bar due to gravity and other external forces, and $\xi$ represents the slip force per unit width of the $z$ th calculation bar due to gravity and other external forces, $C$ indicates the transfer coefficient of calculation strip $z - 1$ to calculation strip $z$, $Q$ indicates the angle of internal friction between the rock slope and the fill, and 3 indicates the length of the sliding zone at the bedrock face. Normally, the piles are not damaged at this point and the original anti-slip piles can continue to be used when appropriate measures are taken to manage the newly formed landslide. Anti-slip piles have a significant effect on slope management and are widely used in slope engineering, but their structural design parameters largely determine the reinforcement effect of the slope. Therefore, the rock excavation unloading is in the elastic recovery stage, and the corresponding rock pressure acting on the support structure is the elastic deformation pressure. For the soil-rock combination slope supported by anti-slip piles, as the piles are applied first and then the rock and soil in front of the piles are excavated, the elastic deformation of the rock between the piles is completed soon after excavation, but as the anti-slip piles limit the elastic deformation of the rock afterwards, there is a residual elastic deformation pressure acting on the anti-slip piles.

3.3 Calculation of Slope Stability Under the Effect of Heavy Rainfall

The infiltration of rainfall is a dynamic process, the infiltration of water will change the moisture content of the soil, the moisture content of the soil changes with height, the surface soil is the first to reach saturation, when the moisture content of the soil increases, first of all the soil capacity increases, the increased mass can be seen as an additional load may cause significant changes in the force of the slope. The soil-rock combination slope is composed of the upper soil layer and the lower rock layer with different properties. The damage mode should be analysed according to the morphology of the bedrock surface and the conditions of the outwardly inclined structural surface of the rock layer, which mainly includes possible damage modes such as internal circular sliding damage of the soil layer, sliding damage along the soil-rock interface, flat sliding of the rock layer and composite damage of the rock and soil layer [9, 10]. Secondly, the shear parameter of the soil decreases significantly with changes in water content, and the reduction in shear strength causes slope damage to occur in a less stressed state, a phenomenon that can also be explained by the extended Moore Coulomb strength criterion, i.e. the presence of pore water pressure in the water-bearing soil leads to a reduction in inter-skeleton stress in the pore medium and a consequent reduction in shear strength, which occurs when rainfall reaches a certain level of damage. The structural relationship between the soil body and the rock layer is shown in Fig. 1.

Fig. 1

Structural relationship between soil and rock layers

Due to the low strength of the soil, the slope stability of the soil layer can be calculated using the circular sliding method. When the bedrock face dips outwards, the soil layer may also produce sliding damage along the bedrock face, when the transmission coefficient method can be used to calculate the stability of the soil layer. Usually when the safety factor for such landslides is greater than 1.25, the soil slope can be judged to be in a stable state. If, under special circumstances, the coefficient of safety of a landslide is greater than 1.15, the soil slope can be judged to be in a stable state. If the cohesion of the slope is equal to zero, the coefficient of safety of the landslide can be expressed as:

$$ A = \frac{\tan m}{{\tan n}} $$

(9)

In Eq. (9), $m$ indicates the inclination of the sliding surface and $n$ indicates the slope angle. With the continuation of rainfall, especially the continuous heavy rainfall weather that occurs in the southern rainy season, the road surface becomes waterlogged and the groundwater level can be too high, which is the initial condition for seepage field analysis, so it is also essential to study the coupled analysis of seepage stress under different groundwater level conditions. After the end of rainfall, the water accumulated in the slope will continue to seep out and the water table will fall with time. At this time, different bedrock inclination angles will affect the rate of dissipation of residual water, so the stability of the slope flow-solid coupling under different bedrock angles should also be considered. Then the calculation formula for the sliding force is:

$$ P = x\frac{\tan m}{{\tan n}}\sum {\left( {\psi - u} \right)^{2} } $$

(10)

In Eq. (10), $x$ represents the dip angle in the direction of the slide infiltration pressure, $\psi$ represents the structural correction factor and $u$ represents the single wide infiltration pressure of block $u$. When there is an outward sloping structural surface of the rock layer, the wedge-shaped rock block is prone to sliding damage along the outward sloping structural surface, and at the same time drives the upper overburden layer to deform outward. The thickness of the upper soil layer is 8.2 m and the bedrock face is gently sloping and slightly inclined inwards, so the soil layer will not produce sliding damage along the bedrock face. When rainfall occurs, as the rainfall continues, the water content of the upper layer of the soil gradually increases, and the negative pore water pressure gradually dissipates. 8 days after the strong rainfall occurs, the pore water pressure within the more moist soil of the surface layer has increased to between −50 and −20 kN/m². In calculating the stability of slopes, the linear rupture surface method is often used in order to visualise and simplify the analysis of such slope planes. Usually a slope containing permeable gravel, sand, gravel or sandy soils will form a linear rupture surface when it breaks. In this case, the equation for the shear strength of the soil is as follows:

$$ d = \alpha + r\sum {\frac{{\left( {1 - \alpha } \right)}}{{r^{2} }}} + D $$

(11)

In Eq. (11), $\alpha$ represents the effective stress factor, $r$ represents the pore water pressure and $D$ represents the material strength. The maximum negative pore water pressure inside the slope also rose to −277 kN/m², and the eight days of rainfall caused the negative void is pressure within the slope to drop by 20% as a percentage and 30% as a peak. As the permeability coefficient of the lower mud layer of the slope is much smaller than the permeability coefficient of the soil above the rock and the intensity of the rainfall, the negative pore water pressure of the mud rock above the water table does not change much as seen from the cloud map. Rainwater collects at the toe of the slope causing the water content at the toe to rise gradually and the soil to become saturated until the precipitation is connected to groundwater, at which point a large saturated seepage zone appears on the slope. The criteria for slope instability damage include excessive displacement change, in order to analyse the change in slope displacement field after the end of rainfall.

4 Case Studies

4.1 Construction Preparation

TJ-22 earth pressure gauges (range 0–0.1 MPa, diameter 8 cm) were buried behind the wall and placed on the centreline of the anti-slip piles and baffles at distances of 2 m, 4 m, 6 m, 8.5 m and 11.5 m respectively from the top line of the wall. The maximum height of the excavated slope is 25 m, and the maximum slope technology is grade 3. The slope of this section is a typical overburden bedrock type slope, the upper layer of soil is a thicker gravel-bearing miscellaneous fill with a thickness ranging from 3–30 m, which varies greatly, and the lower bedrock is a sandy mudstone layer, and the dip of the rock layer at the project site is 10–30°. All three levels of slope slopes are cut at a rate of 1:1 and the slope reinforcement scheme is proposed to use anchor frame beam protection. The reinforcement gauge is a GXR series vibrating string type reinforcement gauge corresponding to the main reinforcement. The rebar meter is connected to the main reinforcement cut into sections and tied together with the main reinforcement using sleeves and other strengths, and the test leads are carefully led to the top of the pile and protected.

4.2 Force Analysis

Controlling the length of the anti-slip pile within a reasonable range can effectively enhance the safety factor of the construction, therefore, this force analysis on the anti-slip pile body of the soil mudstone slope, based on and a series of changes in the pile displacement and pile shear stress parameters, the optimum pile body length was selected. The variables were set to three types: anti-slip pile length 13.5–15.5 m, anti-slip pile length 15.5–17.5 m, and anti-slip pile length 17.5 m and above. The specific results are shown in Figs. 2 and 3.

Fig. 2

Variation in pile displacement (m)

Fig. 3

Variation in pile shear stress (KPa)

As can be seen from Figs. 2 and 3, the pile displacement is minimum and the pile shear stress is maximum when the length of the anti-slip pile is 15.5–17.5 m. For the upper part of the pile, the shear stress is positive under the action of the landslide, for the lower part of the pile, the passive soil pressure in front of the pile is greater than the active soil pressure behind the pile and the shear stress is negative. When the pile length is short, the absolute value of shear stress in the upper part of the pile is larger than the absolute value of shear stress in the lower part, while when the pile length is long, the absolute maximum value of shear stress in the upper part of the pile and the absolute maximum value of shear stress in the lower part are almost equal. With the increase in the length of anti-slip piles, the displacement of each point of the pile roughly shows a gradually decreasing trend, in the local range with the increase in the length of anti-slip piles the displacement of each point of the pile has a slight increase, indicating that too long anti-slip piles do not have a significant effect on increasing the stability of the landslide body. Therefore, under the effect of heavy rainfall, the length of anti-slip piles should be set at 15.5–17.5 m, which is the most reasonable.

5 Conclusion

After rainfall occurs, the water content of the soil within a certain range of the slope surface layer increases. The increase of water in the pore space increases the soil weight on the one hand, and on the other hand, the increase of pore water pressure leads to the decrease of matrix suction of the pore medium eventually reduces the shear strength of the soil, so the increase of soil weight and the decrease of effective stress of the slope are the main reasons for the damage of unsaturated soil slopes under rainfall infiltration conditions. The long-term stability state of anti-slip pile slopes under different strong rainfall types shows different response laws. The displacement of the slope, which gradually stabilises under conventional creep, does not change abruptly due to rainfall under low intensity long duration rainfall conditions, but the rate of change of the slope displacement under heavy rainfall is much greater than that under conventional creep, and the displacement of the monitoring point changes more significantly due to heavy rainfall. Due to the constraints of the study, the reinforcement effect and soil arch effect under the double-row and multi-row arrangement were not analysed in this study, which can be further explored in the future.