Real-time monitoring and deep learning prediction modeling of rainfall infiltration effects in slope stability risk assessment

Slope stability has always been an important topic in geotechnical engineering, and the most important triggering factor for slope destabilization is rainfall infiltration. Rainfall infiltration is a complex process, including the top of the slope infiltration, slope surface infiltration, along the fissure infiltration, fissure to soil seepage and gravity conditions within the soil body seepage and other forms [1-4].

When the intensity of rainfall is less than the permeability coefficient of the slope soil, rainfall can easily seep into the deep saturated zone of the soil and directly recharge groundwater, while the shallow soil is difficult to reach a higher degree of saturation, and the slope is in a stable state [5-7]. When the intensity of rainfall is greater than the infiltration rate of the slope soil, on the one hand, the rainfall makes the shallow layer of the soil slope quickly reach saturation, and surface runoff is formed on the slope, causing scouring on the slope. On the other hand, rainwater infiltrates into the interior of the slope, causing changes in the seepage field, which increases the dynamic and hydrostatic loads acting on the soil body and reduces the shear strength of the soil body [8-11]. The water content of the slope soil body increases, and at the same time produces a certain amount of seepage force, so that the stability of the slope is reduced, resulting in slope sliding damage. Therefore, real-time monitoring of rainfall infiltration on slope stability has an important significance to show and take corresponding measures in time, and the construction of deep learning prediction model has an important role in this real-time monitoring process [12-15].

The aim of this study is to construct an implementation monitoring and deep learning prediction model to assess the impact of rainfall infiltration on slope stability. In the study, this paper first explores the mechanism of rainfall infiltration on slope stability, and analyzes the slope pore water pressure, slope displacement field and slope velocity field under rainfall conditions according to the influencing factors. After that, a stability prediction model and a 9-factor orthogonal test based on the Long Slope open pit mine were designed. On this basis, a neural network model for slope prediction was constructed by combining the alternating iterative global optimization algorithm, and the prediction effect of the model was analyzed.

2

Mechanisms of rainfall infiltration on slope stability

2.1

Saturated-unsaturated seepage theory

2.1.1

Darcy’s law for saturated-unsaturated soil water flow

Darcy’s law [16], which characterizes water movement in saturated soils, was obtained through infiltration tests. The formula is given below: (1) $q = v = - k_{s} \nabla h$

where “-” indicates that the water flow is in the direction of head reduction.

h represents the total head or total water potential, h = z + h_w, z represents the position potential, h_w represents the pressure potential; k_s represents the saturated permeability coefficient, which is taken as a constant for a particular saturated soil; v represents the flow velocity; and ∇h represents the hydraulic gradient vector. Darcy’s law for water flow in unsaturated soils can be expressed as: (2) $q = v = - k_{w} \nabla h$

The water content Θ_w can be expressed as a function of matrix suction, and thus the permeability coefficient function $k_{w (θ_{w})}$ can also be expressed as a function of matrix suction, denoted as K_w(u_a − u_w).

In summary, Darcy’s law for saturated-unsaturated seepage can be expressed uniformly as: (3) $v = - k_{s} k_{r} \nabla h$

Where: k_s represents the saturated permeability coefficient, k_r represents the relative permeability coefficient, and k_r = k_w/k_s, represents the ratio of the unsaturated permeability coefficient to the saturated permeability coefficient of the soil, i.e., 0 ≤ k_r ≤ 1.

2.1.2

Saturated-unsaturated seepage control equations

The motion and change of matter follow the law of conservation of mass, and the flow of fluid in porous media must satisfy Darcy’s law, and the continuity equation can be obtained by adopting the law of conservation of mass in the motion of fluid in porous media. By combining Darcy’s law and the continuity equation, the equation of motion of water in unsaturated soil can be introduced: (4) $\frac{\partial θ_{w}}{\partial t} = \frac{\partial}{\partial x} [k_{w x} \frac{\partial h}{\partial x}] + \frac{\partial}{\partial y} [k_{w y} (θ_{w}) \frac{\partial h}{\partial y}]$

When the soil is saturated, the soil pores are filled with water, at this time the water content Θ_w is the saturated water content θ_s, the permeability coefficient k_w is the saturated permeability coefficient k_s, if you ignore the compressibility of the water, $\frac{\partial θ_{w}}{\partial t} = 0$ , and thus the above equation becomes: (5) $\frac{\partial}{\partial x} [k_{s x} \frac{\partial h}{\partial x}] + \frac{\partial}{\partial y} [k_{s y} \frac{\partial h}{\partial y}] = 0$

The stress state variables (σ − u_a) and (u_a − u_w) are used to describe the stress state of unsaturated soils, and it is proposed that the change in volumetric water content Θ_w is related to normal stress (σ − u_a) and matrix suction (u_a − u_w) with the following relationship: (6) $d θ_{w} = - m_{1}^{w} d (σ - u_{a}) - m_{2}^{w} d (u_{a} - u_{w})$

where: u_a represents the pore gas pressure; u_w represents the negative pore water pressure; $m_{1}^{w}$ represents the coefficient of volume change of water with respect to a change in normal stress (o − u_a); and $m_{2}^{w}$ represents the coefficient of volume change of water with respect to a change in normal stress (u_a − u_w).

At a particular time step, the coefficients $m_{1}^{w}$ and $m_{2}^{w}$ can be taken as constants, and the above equation can be changed to: (7) $\frac{\partial θ_{w}}{\partial t} = - m_{1}^{W} \frac{\partial (σ - u_{a})}{\partial t} - m_{2}^{W} \frac{\partial (u_{s} - u_{w})}{\partial t}$

Another form of expression for the seepage control equation for unsaturated soils: (8) $\frac{\partial}{\partial x} (k_{w x} \frac{\partial h}{\partial x}) + \frac{\partial}{\partial y} (k_{w y} \frac{\partial h}{\partial y}) = - m_{1}^{W} \frac{\partial (σ - u_{a})}{\partial t} - m_{2}^{W} \frac{\partial (u_{s} - u_{w})}{\partial t}$

Assuming that no external load is applied to the soil in the description of the transient seepage process in the above equation and that the gas phase is continuous in the saturated zone: (9) $\frac{\partial σ}{\partial t} = 0, \frac{\partial u_{a}}{\partial t} = 0$

That is, Eq. (8) can be simplified as: (10) $\frac{\partial}{\partial x} (k_{w x} \frac{\partial h}{\partial x}) + \frac{\partial}{\partial y} (k_{w y} \frac{\partial h}{\partial y}) = - m_{2}^{W} \frac{\partial (u_{a} - u_{w})}{\partial t}$

Where, $m_{2}^{w} = - \frac{\partial θ_{w}}{\partial (u_{a} - u_{w})}$ , i.e., the absolute value of the slope of the soil-water characteristic curve.

Is obtained from $h_{w} = z + u_{w} / γ_{w}, \frac{\partial σ}{\partial t} = 0, \frac{\partial u_{a}}{\partial t} = 0$ and replacing u_w in the above equation with total head h: (11) $\frac{\partial}{\partial x} (k_{w x} \frac{\partial h}{\partial x}) + \frac{\partial}{\partial y} (k_{w y} \frac{\partial h}{\partial y}) = ρ_{w} g m_{2}^{w} \frac{\partial h}{\partial t}$

When the soil is saturated, the soil-water characteristic curve changes less and $m_{2}^{w}$ is close to zero, thus the above equation can be used to describe the continuous flow of water in saturated-unsaturated soil: (12) $k_{w x} (θ_{w}) = k_{w y} (θ_{w}) = k_{w z} (θ_{w})$

Then the above equation is: (13) $\frac{\partial}{\partial x} (k_{w} \frac{\partial h}{\partial x}) + \frac{\partial}{\partial y} (k_{w} \frac{\partial h}{\partial y}) = ρ_{w} g m_{2}^{w} \frac{\partial h}{\partial t}$

In summary, the controlling equation for saturated-unsaturated seepage is:

Steady-state flow: (14) $\frac{\partial}{\partial x} (k_{w} \frac{\partial h}{\partial x}) + \frac{\partial}{\partial y} (k_{w} \frac{\partial h}{\partial y}) = 0$

Unsteady-state flow: (15) $\frac{\partial}{\partial x} (k_{w} \frac{\partial h}{\partial x}) + \frac{\partial}{\partial y} (k_{w} \frac{\partial h}{\partial y}) = ρ_{w} g m_{2}^{w} \frac{\partial h}{\partial t}$

2.1.3

Determination of unsaturated seepage coefficients

In the process of practical application, if the relationship between volumetric water content Θ_w and pressure head h_c and unsaturated permeability coefficient k is derived by test, the volumetric water content and permeability coefficient corresponding to pressure head can be derived by interpolation through Eq. (14), and if the measured data are insufficient, Θ_w and k must be calculated by fitting the model of the soil-water characteristic curve.

Based on the parameter fitting method proposed by Mualem’s theory [17], an equation for predicting the relative permeability coefficient of the soil k_r was derived: (16) $k_{r} = S_{e} {[\int_{0}^{S_{e}} \frac{1}{h_{c} (x)} d x / \int_{0}^{1} \frac{1}{h_{c} (x)} d x]}^{2}$

where h_c represents the pressure head and S_e represents the effective saturation, i.e. the state of water in the pore space: (17) $S_{e} = \frac{θ - θ_{r}}{θ_{s} - θ_{r}}$

where θ_s represents the saturated volumetric water content and θ_r represents the residual volumetric water content.

Where the relationship between effective saturation and pressure head is: (18) $S_{e} = {[\frac{1}{1 + {(a h_{c})}^{n}}]}^{m}$

where m = 1 − 1/n, n, a are soil properties parameters, and Eqs. (17) and (18) together form an expression for the soil-water characteristic curve.

Combining the soil-water characteristic curves and the Mualem model, the V-G model for the unsaturated permeability coefficient [18] was obtained: (19) $k_{r} (S_{e}) = S_{e}^{1 / 2} {[1 - {(1 - S_{e}^{1 / m})}^{m}]}^{2}$ (20) $k_{r} (h_{c}) = \frac{{1 - {(a h_{c})}^{n - 1} {[1 + {(a h_{c})}^{m}]}^{- m}}^{2}}{{[1 + {(a h_{c})}^{n}]}^{m / 2}}$

where the significance of a, n, m is the same as described before, and can be estimated by fitting a soil-water characteristic curve, where the best estimation point is at the midpoint between the saturated volumetric water content Θ_s and the residual volumetric water content Θ_r, and the slope of the curve between (Θ_r, Θ_s) can be estimated by the following equation S_p: (21) $S_{p} = \frac{1}{θ_{s} - θ_{r}} | \frac{d θ_{p}}{d (l o g ψ_{p})} |$

Then parameter m, a can be estimated: (22) $m = 1 - \exp (- 0.8 S_{p}) (0 \leq S_{p} \leq 1)$ (23) $m = 1 - \frac{0.5755}{s_{p}} + \frac{0.1}{s_{p}^{2}} + \frac{0.025}{s_{p}^{3}} (S_{p} > 1)$ (24) $a = \frac{1}{ψ} {(2^{1 / m} - 1)}^{(1 - m)}$

where θ_p denotes the volumetric water content at the best estimate point, ψ_p denotes the substrate suction value at the best estimate point, and can also be expressed as a pressure head h_c.

2.2

Mechanisms of rainfall-induced slope instability

1)

The role of matrix suction

In the process of rainfall, the seepage inside the slope is increasing, the negative pore water pressure is enhanced, and the shear strength, cohesion, and angle of internal friction of the rock and soil body are decreasing, which causes the slope to be damaged, and the infiltration of rainfall makes the matrix suction inside the slope decrease, which makes the slope slope occur.

2)

Groundwater seepage from rainwater infiltration

Rainwater infiltration makes the water in the slope body increase, the slope body produces dynamic water pressure, under the action of which, the slope body is constantly subjected to scouring, scour resistance decreases constantly, the water is constantly taken away from the soil body.

3)

Rainwater infiltration makes the slope rock and soil body softening effect occurs

Slope in the rainfall process, rainwater infiltration makes the slope strength will be significantly reduced, thus making the slope destabilization damage.

4)

The erosion effect of rainwater on the slope surface

In the rainfall process, the runoff formed on the surface of the slope will continue to wash the surface of the slope soil face soil damage, in the process of rainfall and rainfall after the formation of the slope runoff makes the surface of the slope soil by the strong scouring effect, so that the surface of the slope soil transport.

2.3

Schematic diagram of rainfall infiltration

A schematic diagram of the zoning of the typical water content distribution profile is shown in Figure 1. When accumulated water infiltrates from the surface of homogeneous soil body, the distribution of typical water content can be divided into four zones from top to bottom: saturated zone, transition zone, conduction zone and wetting zone. Among them, the leading edge of the wet zone is called the wetting front.

3

Slope stability analysis

In this study, we analyzed the stability of the rock body on the slope of a long-slope open-pit mine, and made a comprehensive analysis of the stability of the slope by taking into account the multi-field coupling environment of the rock body (seepage field, velocity field, displacement field and stress field) under rainfall conditions.

3.1

Pore water pressure analysis of slopes under rainfall conditions

Rainfall infiltration is one of the main causes of slope instability in a long slope open pit mine, and according to the actual sliding situation of large slopes in long slope open pit mines in the past, slope instability usually occurs under strong rainfall conditions. In order to study the change rule of slope pore water pressure under different rainfall duration conditions, six groups of rainfall conditions (4h, 8h, 12h, 16h, 20h, 24h) were set up in this simulation.

In order to understand more intuitively the change rule of slope pore water pressure during continuous rainfall, 9 monitoring points were selected from the pore water pressure monitoring points on the slope water level surface to be analyzed, and the change of pore water pressure under different rainfall time is shown in Figure 2. In the early stage of rainfall slope geotechnical body is in the unsaturated state, the volume expansion of the gas phase part of the geotechnical body, resulting in the loss of balance in the air pressure in the soil to produce negative pore water pressure, when the air pressure reaches the equilibrium of the negative pore water pressure gradually dissipate, at this time, the pore water pressure of 0, and the early stage of rainfall pore water pressure grows very fast, mainly due to the early stage of rainfall geotechnical body water content is mainly combined with the water, at this time of matrix suction is very large, the rainfall is easy to be absorbed by the slope geotechnical body. The main reason is that the water content of geotechnical body in the early stage of rainfall is mainly bound water, at this time, the matrix suction force is very large, and rainfall is easily absorbed by the slope geotechnical body. With the growth of rainfall time, the water content of the geotechnical body increases rapidly to reach the matrix suction and then weakened, after the saturation of the slope rock body infiltration capacity is weakened and then the pore water pressure growth slows down and eventually tends to stabilize.

3.2

Analysis of slope displacement field under rainfall conditions

3.2.1

Analysis of the X-direction displacement field of the slope

Based on the monitoring points set up on the slope in the previous period to monitor the deformation of the slope in the X-direction, the monitoring results of seven key monitoring locations selected from the monitoring points were analyzed. The changes of X-direction displacement under different rainfall times are shown in Figure 3. From the figure, it can be seen that the X-direction deformation of the slope is very small at the beginning of rainfall when the displacement grows slowly, after a period of time, the displacement of the slope grows rapidly, and the slope is saturated in the whole after 15 hours of continuous rainfall, and surface runoff formed by the rainfall is no longer infiltrated, and then the X-direction displacement of the slope no longer increases, and basically tends to be stabilized. Although the overall trend of X-direction displacement and deformation of the slope under different rainfall times is basically the same, due to the different locations of the monitoring points, there are still some differences between the monitoring points. Monitoring point 16 is located at the top of the slope, relative to other locations, the displacement at the top of the slope is not large, and it is the smallest displacement among all the monitoring points; monitoring point 22 is located in the middle of the whole slope, which is the monitoring point with the largest displacement, and it can be found that this point is located in the area with the largest displacement, and the displacement at other locations spreads from the center of the body of the slope to the surroundings, and the smaller the displacement is away from the center of the body of the slide, and the more the displacement at the The displacement of the monitoring points at the same elevation is basically the same.

3.2.2

Analysis of Z-direction displacement field of slope

According to the deformation characteristics of the slope, a total of eight monitoring points were selected from the top of the slope to the foot of the slope to monitor the displacement changes in the Z direction under different rainfall times, so as to more intuitively analyze the relationship between slope settlement or bottom bulge with rainfall time. The Z-direction displacements under different rainfall times are shown in Fig. 4. Monitoring points 12 and 16 are the monitoring points located at the back edge of the slope, and basically there is no displacement change in the Z-direction in this area. Monitoring points 2 and 4 are located at the bottom of the slope, and the displacement in the Z direction of monitoring point 2 is the largest and reaches about 18 cm, while the displacement of monitoring point 4 decreases relative to that of monitoring point 2 but is larger than that of monitoring point 12, which is located in the middle of the slope. Monitoring points 19, 20, and 24 are located at the top of the slope, and the Z-direction displacement of the slope in this area is negative, mainly due to the settlement at the top of the sloping haulage slope and the bottom drum at the foot of the slope.

3.3

Slope velocity field analysis under rainfall conditions

3.3.1

Analysis of the velocity field in the x-direction of the slope

The X-direction deformation velocity under different rainfall times is shown in Figure 5. Different rainfall time under the slope X direction deformation velocity cloud map, in the slope selected 8 monitoring points to monitor the deformation velocity of the slope, monitoring point 12, 13, 18, 25, 30 mainly monitor the deformation velocity of the slope waist, the deformation velocity of the slope in this area shows a strong non-convergence in the early part of the deformation velocity, and the overall trend of the curve is basically the same. 5 monitoring point is located at the bottom of the slope, the point of non-convergence at the beginning of the rainfall, the main reason is that the strength of the rock and soil body at the bottom of the long time rainfall weakens and the resistance to shear decreases. The non-convergence is weaker in the early stage of rainfall, and the non-convergence is enhanced in the later stage, which is mainly due to the prolonged rainfall, and the weakened shear strength of geotechnical body at the bottom of the slope is reduced. After 15 hours of rainfall, all the monitoring points basically converge and the deformation rate of the slope basically tends to stabilize.

3.3.2

Analysis of the velocity field in the z-direction of the slope

Eight monitoring points were selected from the Z direction to make an analysis of the overall deformation velocity of the slope. The deformation velocity of the Z-direction position under different rainfall times is shown in Figure 6. At the beginning of rainfall, the top of the slope has negative deformation speed, which is actually reflected as the top of the slope sinking. At the bottom of the pit, the bottom drum occurs, and the deformation speed is positive, and the change rule is consistent with the change rule of displacement. After 15 hours of rainfall, the overall deformation rate of the slope began to stabilize. During 0-15 hours of rainfall, the rainfall time and deformation rate of the slope show a strong phenomenon of non-convergence, at this time, the slope may be damaged, and after 15 hours of rainfall, the deformation rate converges and stabilizes.

4

Stability prediction of slopes

4.1

Stability prediction modeling

Still taking a typical expansion and contraction fissured soil slope-expansive soil slope as an example, the main factors affecting the stability of expansive soil slope are rainfall, slope height, slope ratio, fissure depth of weathering layer, soil gravity, cohesion, angle of internal friction, saturated permeability coefficient and saturated water content. Thirty-two groups of test schemes were established as training samples through orthogonal tests, and any eight groups of test schemes were selected as prediction samples from the total test groups by removing the remaining 32 groups. The safety coefficients predicted by the neural network were compared with the stabilization safety coefficients calculated by Geostudio software to reveal whether the neural network prediction is feasible. The parameters of the Long Slope open pit mine used for the stability analysis are shown in Table 1.

Table 1.

The long slope open-dew parameters used in the analysis of stability

Severity (kN/m³)	Cohesion (kPa)	Interior friction Angle	Saturation coefficient(m/hr)	Saturated volume moisture content(%)
Same as the weathering layer	16.73	21.64	1.9×10^-4	Same as the weathering layer

4.2

Orthogonal experimental design

The orthogonal test is an economical and efficient test method because it can greatly reduce the number of tests compared to the full factorial test and does not lose important test information and does not reduce the credibility of the test. A total of nine test factors were selected, including daily rainfall, slope height, slope ratio, fissure depth of weathered layer, soil gravity, cohesion, angle of internal friction, saturated permeability coefficient and saturated water content, and four levels were taken for each factor. The orthogonal design factors and levels used for the stability analysis are shown in Table 2.

Table 2.

The orthogonal design factors and levels of the stability analysis are used

Influencing factor	Level
Influencing factor	1	2	3	4
Solar rainfall (mm)	100	200	300	400
Heavy (kN/m³)	17.31	19.04	19.62	20.18
Cohesive (kPa)	7	10	13	16
Internal friction Angle	15	18	20	22
Saturation coefficient(m/hr)	0.007	0.014	0.018	0.022
Saturated volume moisture content(%)	32	36	42	46
Crack depth (m)	0.5	1	1.5	2
POE high (m)	15	30	45	60
Slope ratio	1:1.2	1:1.6	1:1.8	1:2

5

Neural network prediction study of slopes

5.1

Optimization of BP Neural Networks

5.1.1

BP Neural Network Model Structure

The basic structure of a BP network consists of three layers i.e. input layer, hidden layer and output layer each layer is fully connected to each other. The working principle of a BP network is to make the output of the network as close as possible to the desired output through the nonlinear approximation ability of the BP network. This is mainly achieved by constantly adjusting the connection weights and thresholds of each neuron. The method of adjusting the connection weights and thresholds of each neuron is also called a learning rule the commonly used learning rule is the least squares learning rule also known as the linear correction rule.

5.1.2

Disadvantages and Improvements of BP Neural Networks

Since the essence of the BP algorithm is an unconstrained optimization computational method, many optimization algorithms can be used for the learning process of BP networks. Global optimization computational methods and evolutionary optimization computational methods can be used for optimization. In the backpropagation algorithm, it is a forward and backward computation for each sample to find the correction value for the connection weight vector W and then for W. The global optimization algorithm is to use the information of all the samples to find the correction value of w and correct for w. Various evolutionary computation methods have also emerged in recent years, and in this paper we use the alternating iteration algorithm.

5.2

Fundamentals of Alternate Iterative Global Optimization Algorithms

In this paper, the alternating iteration global optimization algorithm [19] is used, and the principle and computational steps of the method are described below. Let the node input of the input layer of the network be x_j,ip(j = 1, …, r; ip = 1, …, q; r is the number of nodes in the input layer, q is the total number of samples), and the excitation function of the hidden layer is: (25) $f (x) = \frac{1.0}{1.0 + e^{(- x)}}$

Then passing the input signal to the implicit layer node aI_i,p (i = 1, …, s1,s1 is the number of nodes in the implicit layer), then: (26) $a 1_{i, i p} = f (\sum_{j = 1}^{r} w 1_{i j} x_{j, i p} + b 1_{i})$

where w1_ij is the weight coefficient between node j and node i, and b1_i is the deviation of node i; then the output information of the implicit layer is passed to the output node a2_kip (k = 1, …, n, n is the number of output nodes), then the final output is: (27) ${a2}_{k, ip} = \sum_{i = 1}^{s 1} w 2_{k i} a 1_{i, i p} + b 2_{k}$

where w2_ki is the weight coefficient between node i and node k and b2_k is the deviation of node k.

It can be seen that: the output a2 of the neurons in the output layer of the network is a linear combination of the outputs a1 and W2 = {w2, b2} of the neurons in the hidden layer, while the deviation b1 of the neurons in the hidden layer and the connection weight w1 of the neurons in the hidden layer to the input neurons are nonlinear parameters (W1 = {w1, b1}), then alternating iteration algorithms can be devised to determine all of the connection weights W and deviations B.

Assuming that W1 is known, then the output of the hidden layer neurons in the network corresponding to the learning sample (x_j,ip, t_j,ip), (j = 1, …, r, k = 1, …, n, ip = 1, …q) can be derived a1_i,ip(i = 1, …, s1, ip = 1, …, q). Based on the method of least squares for numerical approximation of linear functions, the system of equations A*W2 = B for calculating the connection weights w2 can be derived, and then the elements of the matrix A in the system of equations are: (28) $a ((m - 1) * (s 1 + m m) + i, (m - 1) * (s 1 + m m) + j) = \sum_{p = 1}^{q} a 1 (i, i p) * a 1 (j, i p)$

where m = 1, …, n, j = 1, …, s1 + mm, i = 1, …, s1 + mm, mm = 0 means that the effect of the deviation b2 is not taken into account and mm = 1 means that the effect of the deviation b2 is taken into account;

The elements in the right column vector B are: (29) $b ((i - 1) * (s 1 + m m) + j) = \sum_{i p = 1}^{q} t (i, i p) * a 1 (j, i p)$

Where i = 1, …, n, j = 1, …, s1 + mm, mm = 0 means that the influence of deviation b2 is not considered, and mm = 1 means that the influence of deviation b2 is considered; thus the value of connection right W2 can be found by solving the system of equations.

When the value of W2 is determined, W1 can be corrected and calculated according to the GAUSS-NEWTON method in the global optimization algorithm, which is calculated as follows: the hidden layer neuron can be denoted as a1 = f(X, W1), and it is assumed that the initial value of W1 is W1(0), and such that w₁ = W₁(0) + ΔW₁, (ΔW₁ is the increment of w₁). In the neighborhood of w₁(0), a Taylor series expansion is made for f(X, W) and the higher terms of ΔW1 are omitted.

When X = X_P, there is $f (X, W 1) = f_{0} (X_{B} W 1) + \frac{\partial f_{0} (X_{p}, W 1)}{\partial W 1} Δ W 1$ , where $(f_{0} (X_{R}, W 1) = f [X_{P}, W 1 (0)], \frac{\partial f_{o} (X_{p}, W 1)}{\partial W 1} = \frac{\partial f (X_{p}, W 1)}{\partial W 1} | w_{1 = W 1 (0)})$ . mark ΔW1 = (Δw1, Δb1)^T, then: (30) $f (X_{P}, W 1) = f_{0} (X_{P}, W 1) + \frac{\partial f_{0} (X_{P}, W)}{\partial w 1} Δ w 1 + \frac{\partial f_{0} (X_{P}, W)}{\partial b 1} Δ b 1$

The energy function is still used for training the network: $E = 0.5 \sum_{p = 1}^{q} \sum_{k = 1}^{n} {(t_{k, j p} - a 2_{k, i p})}^{2}$ . The learning objective of the network is still to determine the weights and deviations to minimize the E-value. According to the principle of multivariate function extremum should be: (31) $\frac{\partial E}{\partial W 1} = 0$

Then the specific expression for the components of $\frac{\partial E}{\partial W 1} = 0$ is derived as $\frac{\partial}{E} \partial w 1 = 0, \frac{\partial E}{\partial b 1} = 0$ . Organizing the above obtained equations yields the system of equations A11*ΔW1 = B11, A11 is a symmetric matrix, then the elements in A11, B11 are determined as follows:

Let $x x 1 (k, r * (i - 1) + j) = \frac{\partial f}{\partial w 1_{i j}}$ , then: (32) $x x 1 (k, s 1 * r + i) = \frac{\partial f}{\partial b 1_{i}} (k = 1, \dots, n, i = 1, \dots, s 1, j = 1, \dots, r)$

Then the elements in A: (33) $a (i, j) = \sum_{i p = 1}^{q} x x 1 (k, i) * x x 1 (k, j)$

For an element in B, let: (34) $d p (m m 1, i p) = t (m m 1, i p) - a 2 (m m 1, i p)$

t(mm1, ip) for the desired output value (mm1 = 1, …, n), then: (35) $b (i) = \sum_{i p = 1}^{q} d p (k, i p) * x x 1 (k, i)$

where k = 1, …, n; i = 1, …, (r + mm)*s1; j = 1, …, (r + mm)*s1, mm = 0 means that the effect of deviation b1 is not taken into account and mm = 1 means that the effect of deviation b1 is taken into account; then solving the system of equations gives the value of ΔW1, which can be corrected for m.

5.3

BP neural network model based on slope prediction

5.3.1

Determination of factors affecting slope stability

In practice, the pore water pressure ratio r_u is commonly used to reflect the effect of pore water pressure, which is defined as follows: (36) $r_{u} = \frac{u}{γ \cdot h}$

Eq:

u - pore water pressure at a point in the soil slope section;

γ - the capacitive weight of the soil;

h - the height of the soil bar.

Generally speaking, τ_u is not a constant in the whole soil slope section, and the average value is often taken for calculation in design.

In summary, there are many factors affecting the slope, which are not only random, but also fuzzy, and are the result of the combined effect of many factors. From the various influencing factors to select the main factors, ignoring the secondary factors, according to this principle to select the slope profile factors: slope height (H), slope ratio (θ); slope soil properties: weathering layer fissure depth (γ), cohesion (c), angle of internal friction (φ); water pressure: saturated permeability coefficient (r_u), etc., a total of eight representative indicators as the input neurons of artificial neural network. The output of the network is the safety coefficient or whether the slope occurs or not.

5.3.2

Neural network models for slope prediction

1)

Determination of the number of neurons in the input and output layers

The number of neurons in the input and output layers of the network is designed completely according to the requirements of the user. It has been mentioned earlier that a total of 8 influencing factors are identified so that 8 neurons are identified for the input layer. The output data is the safety factor output layer can determine 1 neuron.

2)

Determination of the number of hidden layers and the number of hidden layer neurons

The neural network evaluation model constructed in this paper is an input layer, a single hidden layer, an output layer, which has a total of 8 neurons in the input layer, a total of 13 neurons in the hidden layer, and a total of 1 neuron in the output layer. The excitation function of the neuron is generally selected as the sigmoid activation function $f (x) = \frac{1}{1 + e^{- x}}$ , and the hidden layer to the output layer also uses the tangent sigmoid function.

3)

Determination of the end standard of the learning process

In this paper, 0.002 is selected as the allowable learning error. In addition, the number of learning times can be used as the criterion for the end of the learning process.

6

Neural network prediction results for slope stability

6.1

Training of Neural Networks

Based on the means of on-site field tests and indoor experiments to obtain the values of the factors affecting the stability of slopes, respectively, the values of the factors affecting the stability of slopes are daily rainfall, gravity, cohesion, internal friction, saturated permeability coefficient, saturated volumetric water content, depth of fissure, slope height, and slope ratio of the nine key factors were selected out. The group of example data as training samples for the network is shown in Table 3.

Table 3.

Training sample

Serial number	Solar rainfall (mm)	Heavy (kN/m³)	Cohesive (kPa)	Internal friction Angle	Saturation coefficient (m/hr)	Saturated volume moisture content (%)	Crack depth (m)	POE high (m)
1	90.2	17.49	8	19.51	0.0197	39.49	1.12	12.38
2	129.98	18.24	7.35	12.42	0.0151	35.44	0.84	27.72
3	82.6	19.58	9.75	17.27	0.0178	38.99	1.24	28.85
4	116.97	19.25	7.77	7.25	0.0222	38.31	1.13	11.39
5	86.01	15.87	8.59	21.07	0.0155	36.07	1.32	29.78
6	97.59	17.5	8.74	14.55	0.016	38.94	1.18	32.94
7	97.47	20.42	8.73	16.85	0.0112	29.64	1.41	29.97
8	100.16	22.07	8.41	10.73	0.0159	37.48	1.14	25.69
9	106.46	21.97	9.45	14.98	0.0048	34.92	1.39	24.22
10	66.79	16.76	9.44	14.51	0.0131	34.14	1.42	28.87
11	108.81	15.53	7.78	15.5	0.0144	38.53	1.19	22.37
12	112.55	14.54	9.55	13.91	0.0117	30.55	1.49	8.59
13	74.15	14.66	6.61	18.85	0.0125	32.1	1	24.29
14	118.54	13.84	8.87	15.93	0.0123	35.94	1.4	12.48
15	126.51	16.78	9.33	17.18	0.0111	39.56	1.16	21.68
16	85.62	19.62	7.83	15.85	0.0122	33.49	1.33	25.66
17	103.12	17.27	11.42	15.72	0.0137	34.36	1.39	37.05
18	93.1	16.85	7.31	19.34	0.023	37.04	1.32	20.32
19	104.98	16.62	7.9	16	0.0119	36.74	1.22	19.32
20	90.94	20.59	7.49	16.06	0.0173	40.67	1.42	26.07
21	97.5	14.73	5.25	17.06	0.0168	41.39	1.29	29.27
22	112.17	15.97	8.9	17.62	0.0219	33.95	1.4	24.37
23	108.86	17.46	8.92	14.16	0.0132	34.26	1.12	33.65
24	93.44	19.02	9.92	18.15	0.0164	37.54	1.45	17.35
25	104.8	17.32	7.58	16.95	0.0184	36.09	1.21	15.36
26	84.1	16.72	9.21	11.24	0.015	37.37	1.32	36.66
27	120.65	15.51	10.29	14.99	0.0136	40.14	0.94	27.44
28	118.06	19.82	5.87	20.39	0.0141	35.17	1.15	22.84
29	108.23	18.02	9.4	15.31	0.0121	39.23	1.06	27.27
30	113.38	20.08	10.84	13.75	0.0128	26.09	1.25	16.44
31	101.19	15.93	7.03	13.41	0.017	35.65	1.34	33.17
32	102.99	16.42	7.61	15.28	0.0049	34.91	1.23	10.22

The convergence plots of the three parallel network training are shown in Fig. 7. The results show that the accuracy of parallel networks 1, 2 and 3 reaches 0.9997, 0.9960 and 0.9908, respectively, which shows that the accuracy of the model is greater than 0.99 in the test results under the three parallel networks, with very small differences. It can be seen that using the trained neural network, the evaluation of slope stability can be realized according to the nine key factors affecting the slope stability factors, and the prediction effect of the model is good.

6.2

Neural Network Testing

The network model can well meet the application needs of slope engineering. The prediction results of the model in the steady state are shown in Table 4; the test results of the model in the test bank and in the example calculation are shown in Table 5 and Table 6, respectively. The results can be seen, the test value and the actual value of the same example of the slope were analyzed, according to the rainfall influence of the unsaturated long-slope open pit mine water absorption rate in different rainfall calendar conditions under the change rule of the study, and at the same time consider the slope height, slope, cohesion, angle of internal friction, the natural capacity of the weight of a variety of factors affecting the stability of slopes with the change in the absorption rate of the stability of the slope was evaluated and compared.

Table 4.

The prediction of the model in a stable state

Serial number	Solar rainfall (mm)	Heavy (kN/m³)	Cohesive (kPa)	Internal friction Angle	Saturation coefficient (m/hr)	Saturated volume moisture content (%)	Crack depth (m)	POE high (m)
1	90.453	18.822	8.609	19.818	0.01984	40.866	1.1408	13.0754
2	130.233	19.572	7.959	12.728	0.01524	36.816	0.8608	28.4154
3	82.853	20.912	10.359	17.578	0.01794	40.366	1.2608	29.5454
4	117.223	20.582	8.379	7.558	0.02234	39.686	1.1508	12.0854
5	86.263	17.202	9.199	21.378	0.01564	37.446	1.3408	30.4754

Table 5.

The results of the model in the test library

Serial number	Solar rainfall (mm)	Heavy (kN/m³)	Cohesive (kPa)	Internal friction Angle	Saturation coefficient (m/hr)	Saturated volume moisture content (%)	Crack depth (m)	POE high (m)
1	90.43	18.61	8.59	19.79	0.01982	40.75	1.138	13.0742
2	130.21	19.36	7.94	12.7	0.01522	36.7	0.858	28.4142
3	82.83	20.7	10.34	17.55	0.01792	40.25	1.258	29.5442
4	117.2	20.37	8.36	7.53	0.02232	39.57	1.148	12.0842
5	86.24	16.99	9.18	21.35	0.01562	37.33	1.338	30.4742

Table 6.

The experimental results in the calculation of the model

Serial number	Rainfall duration(h)	Lift up	grade	Cohesive force	Internal friction	Saturated volume moisture content(%)	Crack depth (m)	POE high (m)
0	0	20	40	10.04	15.26	35.21	1.418	25.064
1	8	20	40	10.03	14.79	35.52	1.138	34.344
2	16	20	40	10.37	15.78	38.8	1.468	18.412
3	24	20	40	10.14	14.19	37.35	1.228	16.232

According to the calculation results, it can be seen that under the conditions of various factors affecting the stability of the Long Slope open pit mine selected in this paper, the test values are basically consistent with the conclusions obtained from the actual values. In addition, the working state corresponding to the solution of the limit equilibrium method is virtual, and the internal force between the soil blocks and the reaction force at the bottom of the slip surface cannot represent the real existing force of the soil body in the generation of slip deformation, according to which it is not possible to analyze the occurrence and development process of the stabilization damage, and it is not possible to take into account the effect of deformation on the stability of the soil body.

At the same time, the ability of neural network promotion is not only related to its own network performance, but also related to the number and representativeness of the training samples. Therefore, in the case of insufficient samples, only with the deepening of the understanding of the intrinsic mechanism of slope stability, as well as the accumulation of engineering practice experience, it is possible to establish a neural network with better promotional ability. With the continuous accumulation of the number of slope stability samples and the increasing scale, the neural network will be more likely to reflect its applicability.

7

Conclusion

In this paper, we mainly consider the influence of various factors on the slope stability of Changpo open pit mine under rainfall infiltration conditions, and explore the influence of each factor on the slope stability of Changpo open pit mine through real-time monitoring and BP neural network prediction model. The results show that: 1)

The groundwater level of the slope geotechnical body rises with the growth of rainfall time, the slope geotechnical body reaches the saturated state, and the infiltration rate of rainfall decreases. The X-direction displacement field of the slope increases with the growth of rainfall time, and finally tends to stabilize. At the beginning of rainfall, the settlement phenomenon begins to appear at the top of the slope at the back edge of the slope, and with the growth of rainfall time, the settlement area does not expand, and finally passes through. At the early stage of rainfall, the deformation velocity in the X direction and the deformation velocity in the Y direction show a strong non-convergence phenomenon, but the convergence tends to be stabilized when the rainfall reaches 15 hours.

2)

Under the conditions of the nine factors selected in this paper to affect the stability of yellow slopes, such as “daily rainfall, gravity, cohesion, internal friction and so on”, the test values are highly consistent with the conclusions of the actual value. However, if there are more influencing factors to be considered or the environment of the long slope open pit mine, the evaluation results and comparison between the test values and the actual values need to be further considered.

Język:: Angielski

Częstotliwość wydawania:: 1 razy w roku
Dziedziny czasopisma:: Nauki biologiczne, Nauki biologiczne, inne, Matematyka, Matematyka stosowana, Matematyka ogólna, Fizyka, Fizyka, inne

Kanał RSS czasopisma

Real-time monitoring and deep learning prediction modeling of rainfall infiltration effects in slope stability risk assessment

Guopeng Qu

Kan Wu

Data publikacji: 26 wrz 2025

Otrzymano: 19 sty 2025

Przyjęty: 08 maj 2025

DOI: https://doi.org/10.2478/amns-2025-1042

Słowa kluczoweRainfall infiltration, Slope stability, Orthogonal experiment, BP neural network, Alternate iteration algorithm

© 2025 Guopeng Qu and Kan Wu, published by Sciendo.

This work is licensed under the Creative Commons Attribution 4.0 International License.

Słowa kluczowe
Rainfall infiltration, Slope stability, Orthogonal experiment, BP neural network, Alternate iteration algorithm