CN115238549B - Method for monitoring safety coefficient under landslide rainfall condition by using ERT - Google Patents
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Abstract
The invention discloses a method for monitoring a safety coefficient under landslide rainfall conditions by using ERT, which comprises the following steps: an ERT monitoring device is deployed on the landslide, monitoring data are collected, and a geometric model of the landslide is built; establishing an inversion objective function applying prior model constraint, space smoothness constraint and regularization constraint, solving the minimum value of the regularization objective function by carrying out iterative update on regularization parameters and model increment, obtaining the rock-soil body resistivity at each moment according to the model vector at each moment obtained by solving, and synthesizing to obtain the resistivity space-time distribution; obtaining water space-time distribution according to the water-electricity relationship; and (3) analyzing and calculating the stress field of the landslide body by adopting a finite element according to the space-time distribution of the water, calculating the plastic potential function of the soil body, and calculating the safety coefficient of the landslide by using an intensity reduction method on the plastic potential function. The invention realizes more intuitively reflecting the safety coefficient evolution process of landslide under rainfall condition according to ERT monitoring data.
Description
Technical Field
The invention relates to the technical field of geophysical exploration, in particular to a method for monitoring a safety coefficient under landslide rainfall conditions by using ERT, which is a resistivity tomography technology.
Background
The topography of the south China is fluctuant, rainfall is abundant, a large number of landslide disasters can occur in rainy seasons each year, and great casualties and economic losses are caused. On one hand, after rainwater infiltrates into landslide soil, the weight of the soil is increased, and sliding force is increased; on the other hand, the effect of water makes the landslide soil body mechanics change, and the skid resistance reduces, once the skid resistance is greater than the skid resistance, the landslide can produce displacement or even destroy. The method is used for monitoring the space-time evolution process of the water in the landslide under the rainfall condition, and analyzing the influence of the space-time evolution process on the geotechnical engineering behavior is very important for the early warning of the landslide. At present, the monitoring of water in landslide is mainly realized by a water level gauge, an osmometer and other point-based sensors, and the sensors can continuously and accurately acquire hydrographic parameters such as pore water pressure, matrix suction and the like at the positions of the sensors, but the sensors have two defects: firstly, the rock and soil parameters including hydrologic parameters have space variability, the point-based sensor can only reflect the information of the surrounding positions of the sensor, and the information sensing capability of the position far from the sensor is limited; secondly, the sensors often need to drill holes on landslide bodies, the construction is complex, the cost is high, and the destructive behavior is likely to induce landslide.
Many studies have shown that the conductivity of soil is closely related to the water content of the soil. The rainfall can cause the water in the landslide to move and simultaneously cause the resistivity of the soil body to change. Based on this idea, resistivity tomography (ERT) techniques with resistivity as a core parameter can be used to characterize and analyze the spatial-temporal distribution of moisture inside landslide. More and more students in recent years have begun to utilize ERT to characterize and monitor landslide interiors with a number of very valuable and representative achievements. The researches explain how to utilize ERT technology to characterize and monitor the water movement in landslide by means of indoor experiments, actual case analysis, numerical simulation and the like, so as to qualitatively analyze the landslide damage process. However, the reflection of ERT data on landslide internal information is indirect, and is not intuitively related to landslide rock-soil behaviors, and how to use ERT time shift data to early warn landslide is a worthy research. The safety coefficient of the landslide is a more visual parameter for evaluating the stability of the landslide, and if the ERT monitoring data can be utilized to dynamically reflect the safety coefficient evolution process of the landslide under the rainfall condition, a more visual early warning effect can be achieved.
Disclosure of Invention
First, the technical problem to be solved
Based on the problems, the invention provides a method for monitoring the safety coefficient under the rainfall condition of the landslide by using ERT, which solves the problem of dynamically reflecting the safety coefficient evolution process of the landslide under the rainfall condition by using ERT monitoring data, so that the landslide stability is evaluated more intuitively, and a more intuitive early warning effect is achieved.
(II) technical scheme
Based on the technical problems, the invention provides a method for monitoring the safety coefficient under landslide rainfall conditions by using ERT, which comprises the following steps:
s1, deploying ERT monitoring equipment on a landslide, collecting monitoring data, collecting rock parameters and geological data on the landslide, and establishing a geometric model of the landslide through software;
s2, establishing an inversion objective function applying prior model constraint, space smoothness constraint and regularization constraint, solving the minimum value of the regularization objective function by carrying out iterative update on regularization parameter lambda and model increment delta m, obtaining the rock-soil body resistivity at each moment according to the model vector at each moment obtained by solving, and synthesizing to obtain the resistivity space-time distribution;
s3, obtaining water space-time distribution from the resistivity space-time distribution according to the hydropower relationship;
s4, analyzing and calculating a stress field of the landslide body by adopting a finite element according to the water space-time distribution, calculating a plastic potential function of a soil body according to the stress field of the landslide body, and calculating the safety coefficient of the landslide by using an intensity reduction method on the plastic potential function.
Further, the step S2 includes:
s21, establishing a regularized inversion objective function applying prior model constraint and space smoothness constraint:
in the above-mentioned method, the step of,for inverting the objective function +.>For data item->Is regularized model term, lambda is regularized parameter, D is observed data weight, W is model weight, A is positive algorithm, m apr For a reference model given from a priori information, d obs For observation data, m is a model vector to be solved;
s22, iteratively updating regularization parameters lambda and model increment delta m of the objective function, and solving the minimum value of the objective function;
s23, obtaining the resistivity rho of the rock-soil body according to the model vector m obtained by solving: m=lnρ;
s24, repeating the steps S21-S23 for the earth electric field response at each moment in the rainfall process to obtain the rock-soil body resistivity rho at each moment, and synthesizing to obtain a resistivity change curve, namely the resistivity space-time distribution.
Further, the D is calculated according to the following formula:
SD (d) obs ) Epsilon is the minimum trusted data value for the standard deviation of the observed data.
Further, the W is calculated according to the following formula:
r in the above ij K is the distance between the centers of two adjacent grid cells i The number of cells adjacent to the current cell.
Further, in step S22, the iterative update formula of the regularization parameter λ is:
where k is the current iteration number.
Further, in step S22, the iterative updating method of the model increment Δm includes:
A. and deriving the objective function, setting the objective function to be zero, and solving the model increment delta m through an incomplete Gaussian Newton method:
in the aboveFor jacobian matrix, g is the gradient of the objective function, and H is the approximated hessian matrix; and making the initial value of the search step alpha be 1;
B. judging whether the delta m meets the precision requirement, if so, entering a step D; if not, entering the step C;
C. calculating delta m according to the following formula, judging whether the following inequality is met, if yes, returning to the step B, otherwise, changing alpha to be half of the original one, and re-entering the step C;
m k+1 ＝m k +αΔm
m is in k For the model vector at the current iteration number k, phi is the objective function value,c is a constant;
D. and updating and iterating the objective function according to the current delta m.
Further, in step S3, the hydropower relationship is:
ρ＝KS -n
wherein, parameters K and n are obtained by fitting calculation to measured data.
Further, in step S4, the following steps are included:
s41, analyzing and calculating a stress field of the landslide body by adopting a finite element according to the water space-time distribution;
σ ij ＝σ′ ij +δ ij α eq p，
wherein f j X is the force to be applied ij Is vector in three directions, sigma ij As the total stress tensor, including the effective stress tensor sigma' ij And stress, delta, generated by water ij Is Kronecker symbol, alpha eq Equivalent pore water coefficient, p is pore water pressure:
in the case of a space-time distribution of unsaturated moisture,
in case of saturated moisture spatiotemporal distribution, p=ρ Water and its preparation method gH p
Wherein r and q are fitting parameters, have no practical meaning, ρ Water and its preparation method Where g is the density of water, the gravitational acceleration;
s42, calculating a plastic potential function of the soil body according to the stress field of the landslide body:
wherein Θ.E [ -pi/6, pi/6]Is the Rode angle, I 1 As the first invariant of stress, J 2 And J 3 The second and the third invariant of strain are respectively, C is cohesive force,is the internal friction angle theta and I 1 、J 2 、J 3 Initial value of C and->The initial value of (2) is obtained by finite element analysis according to the stress field of the landslide body;
s43, judging whether F presents a convergence state, if so, comparing the C with the C according to the following formulaAnd (4) reducing, returning to the step S42, otherwise, obtaining the current reduction coefficient which is the safety coefficient FOS:
c on right side of equal sign Upper part Andthe cohesion and internal friction angle obtained by the last reduction are respectively.
The invention also discloses a system for monitoring the safety coefficient under the landslide rainfall condition by using ERT, which comprises:
at least one processor; and at least one memory communicatively coupled to the processor, wherein:
the memory stores program instructions executable by the processor to invoke the program instructions to perform the method of monitoring a safety factor in landslide rainfall conditions using ERT.
The invention also discloses a non-transitory computer readable storage medium storing computer instructions that cause the computer to perform the method of monitoring a safety factor under landslide rainfall conditions using ERT.
(III) beneficial effects
The technical scheme of the invention has the following advantages:
(1) According to the invention, a large amount of low-cost and wide-coverage ERT monitoring data are utilized, the inversion overall thought is utilized, the resistivity space-time distribution is calculated through incomplete Gaussian Newton inversion with multiple constraints, then the moisture space-time distribution is obtained according to the hydropower relation, and finally the safety coefficient of the landslide is calculated by utilizing the finite element strength folding and subtracting method, so that the safety coefficient evolution process of the landslide under the rainfall condition can be reflected more dynamically and intuitively, and the basis is improved for early warning or decision making;
(2) According to the invention, the specificity of landslide under rainfall condition is considered, multiple constraints such as prior model constraint, model smoothness constraint, regularization constraint and the like are carried out on the inversion process, so that the inversion accuracy, namely the accuracy of the calculated safety coefficient is improved;
(3) According to the invention, an imprecise incomplete Gaussian Newton method is adopted to calculate the search direction in the inversion process, a wolfe criterion is adopted to determine the iteration step length, a jacobian-free kryleov solving technology is adopted to avoid directly calculating the jacobian matrix, so that the inversion efficiency is improved, namely, the efficiency of calculating the safety coefficient is improved.
Drawings
The features and advantages of the present invention will be more clearly understood by reference to the accompanying drawings, which are illustrative and should not be construed as limiting the invention in any way, in which:
FIG. 1 is a flow chart of a method for monitoring safety factor under landslide rainfall condition using ERT according to an embodiment of the invention;
FIG. 2 is a schematic diagram of a landslide geometry model established in an embodiment of the invention;
FIG. 3 is a schematic diagram of saturation distribution and variation in rainfall process calculated according to an embodiment of the present invention;
fig. 4 is a diagram showing the comparison between the calculated safety factor and the theoretical safety factor in the embodiment of the present invention.
Detailed Description
The following describes in further detail the embodiments of the present invention with reference to the drawings and examples. The following examples are illustrative of the invention and are not intended to limit the scope of the invention.
As shown in fig. 1, the embodiment of the invention discloses a method for monitoring safety coefficient under landslide rainfall condition by using ERT, which comprises the following steps as shown in fig. 1:
s1, deploying ERT monitoring equipment on a landslide, collecting monitoring data, meanwhile, collecting rock parameters and geological data on the landslide, and establishing a geometrical model of the landslide through software, wherein basic parameters of the model are shown in the following table:
s2, establishing an inversion objective function applying prior model constraint, space smoothness constraint and regularization constraint, solving the minimum value of the regularization objective function by carrying out iterative update on regularization parameter lambda and model increment delta m, obtaining the rock-soil body resistivity at each moment according to the model vector at each moment obtained by solving, and synthesizing to obtain the resistivity space-time distribution;
the purpose of geophysical inversion is to reverse the spatial distribution of subsurface physical parameters from the observed data, however, the observed data is limited, so that the inverse problem solution has discomfort, and the inversion results often have unstable, non-unique and other problems. In order to reduce discomfort as much as possible, a regularized inversion method is adopted, and a regularized model constraint term is added in an inversion objective function to stabilize a model iteration process;
s21, establishing an inversion objective function applying prior model constraint, space smoothness constraint and regularization constraint as follows:
in the aboveFor inverting the objective function, mainly comprising the data item +.>And regularized model term->Two parts, lambda is regularization parameter, D is observation data weight, W is model weight, A is positive algorithm, m apr For a reference model given from a priori information, d obs For observation data, m is the model vector to be solved.
Wherein the regularization parameter lambda is set to 0.05 early.
Wherein the observation data weight matrix D is calculated according to the following formula:
SD (d) obs ) Epsilon is the minimum trusted data value that prevents denominator terms from approaching 0 for the standard deviation of the observed data, typically 0.0125 is taken.
The matrix W is a model weight, and the existence of the matrix W can apply smooth constraint to the inversion process, so that the continuity of the inversion model in space is ensured.
R in the above ij K is the distance between the centers of two adjacent grid cells i As for the number of units adjacent to the current unit, it can be found from the above formula that if the distance between two units is closer, the weight is higher, the model is constrained by using W, and the smoothness of the inversion result in space is ensured; to further improve the accuracy of the inversion, a priori model m is used apr Constraints are placed on the inversion process. The prior model is constructed according to information obtained by means of drilling, exploration, test and the like of a research area, and the inversion solution can be ensured not to deviate from the real situation excessively through the constraint of the prior model.
S22, iteratively updating regularization parameters lambda and model increment delta m of the objective function, and solving the minimum value of the objective function;
after the initial value of the regularization parameter lambda is kept unchanged in two iterations, the following formula is adopted for self-adaptive dynamic calculation in the later period:
in the formula, k is the current iteration number, compared with the methods such as L-Curve, the calculation method can directly utilize the calculation result of the previous iteration, and the unnecessary forward modeling process is not needed, so that the calculation amount and time consumption are greatly reduced.
The model increment delta m is iteratively updated according to the following method:
to solve the minimum of the objective function described in equation (1), which is derived and set to 0, the model increment Δm can be solved by incomplete Gaussian Newton method, and the calculation formula is as follows
In the aboveFor the jacobian matrix, g is the gradient of the objective function and H is the approximated hessian matrix. Wherein the matrix J is an oversized compact matrix, and storage and calculation of the matrix J should be avoided as much as possible in the inversion process. The invention adopts the jacobian-free krylov subspace technology, and avoids the storage and solving of J by calculating the product of the jacobian matrix and a certain vector. The inversion efficiency can be effectively improved by quickly and efficiently solving the equation, the traditional Gaussian Newton method needs to solve the Heisen matrix H, but the solution is very time-consuming and unstable for the oversized problem, so the invention adopts the incomplete Gaussian Newton method to solve. In the method, a jacobian-free krylev subspace technology is adopted to calculate the product of a jacobian matrix and a vector, so that g is calculated to higher precision, and the correct solving direction is ensured.
And then adopting a precondition conjugate gradient method (quote) to calculate delta m to a certain precision within a limited iteration number. After obtaining the inaccurate Δm, the model can be iteratively updated by using the following formula:
m k+1 ＝m k +αΔm (6)
in the above formula, alpha is a search step length, and specific numerical values thereof need to meet Wolfe criterion:
where c is a small constant, in the present invention, is set to 0.0001, phi is the objective function value,is a field gradient operator. After calculationIn the process, the initial alpha is set to be 1, if the inequality is not established, the initial alpha is changed to be half of the original inequality until the inequality is established, and the updated model increment delta m can be obtained by calculating the equation (6) by utilizing the alpha at the moment and is used for iterative updating of the model.
Namely, the specific steps comprise:
A. the objective function is derived and set to be zero, and the model increment delta m is solved through an incomplete Gaussian Newton method, namely a formula (5);
B. judging whether the delta m meets the precision requirement, if so, entering a step D; if not, entering the step C;
C. calculating delta m according to the formula (6), judging whether inequality (7) is met, if yes, returning to the step B, otherwise, changing alpha to be half of the original value, and re-entering the step C;
D. and updating and iterating the objective function according to the current delta m.
S23, obtaining the resistivity rho of the rock-soil body according to the model vector m obtained by solving: m=ln ρ, ρ is the rock-soil body resistivity;
s24, repeating the steps S21-S23 for the earth electric field response at each moment in the rainfall process to obtain the rock-soil body resistivity rho at each moment, and synthesizing to obtain a resistivity change curve, namely the resistivity space-time distribution.
The model is continuously iterated and updated by adopting the method until the termination condition is met, and the inverted model is output. The whole inversion process adopts the modes of self-adaptive regularization, prior model constraint, space smoothness constraint and the like, so that the stability of inversion is improved, and the multi-solution property of knowledge is reduced. The jacobian-free krylov subspace technology is adopted to avoid the storage and solving of a large compact matrix J, and incomplete Gaussian Newton solving equation sets are adopted, so that the calculation speed is increased, and the calculation time is reduced. Inversion is carried out on the earth electric field response at each moment in the rainfall process, so that the slope resistivity change at each moment can be obtained, then the distribution of water is calculated through the resistivity space-time distribution, and the evolution of the safety coefficient is calculated.
S3, obtaining water space-time distribution from the resistivity space-time distribution according to the hydropower relationship, as shown in figure 3;
the correlation of the soil resistivity and the water content is the basis for reflecting the space-time evolution of the water content in the landslide by using ERT monitoring data. The relationship of porous media is given in this section Archie:
rho in the above is the resistivity of the rock-soil body;is porosity; m becomes the cementation index; ρ w For the pore water resistivity, S is the saturation, n is the saturation index, and S is calculated from the obtained ρ. For the same rock-soil body, the pore structure and the physical property of pore water are not changed in the seepage process, and the Archie formula can be simplified as follows under the condition of only considering the saturation change:
ρ＝KS -n (9)
the relation between the saturation and the resistivity can be obtained by fitting the calculated parameters K and n to the measured data. Equation (9) simplifies the relation between the resistivity of the landslide body under the rainfall condition and water, and uncertainty exists in the actual situation, so that noise with different degrees is respectively added when the resistivity data of the rock-soil body are synthesized, and the influence of the uncertainty on the calculation of the safety coefficient is overcome.
S4, analyzing and calculating a stress field of the landslide body by adopting a finite element according to the water space-time distribution, calculating a plastic potential function of a soil body according to the stress field of the landslide body, and calculating a safety coefficient of the landslide by using an intensity reduction method on the plastic potential function;
after the water space-time distribution is obtained through inversion, the stress field of the landslide body can be further calculated by adopting finite element analysis, and then the safety coefficient of the landslide is calculated by adopting finite element strength folding and Subtracting (SRM).
S41, analyzing and calculating a stress field of the landslide body by adopting a finite element according to the water space-time distribution;
the stress balance equation considering the unsaturated moisture space-time distribution condition is:
in the above, sigma ij X is the total stress tensor ij Is a vector in three directions, f j For the forces to be applied, the total stress is the sum of the effective stress and the stress generated by water, according to the effective stress principle:
σ ij ＝σ′ ij +δ ij α eq p (11)
sigma 'in the above' ij Delta as effective stress tensor ij Is Kronecker symbol, alpha eq The equivalent pore water coefficient, p, is the pore water pressure, and under the condition of unsaturated water space-time distribution, the relationship between the saturation and the pressure water head given by the van Genuchten model can be solved.
In the above formula, r and q are fitting parameters, have no practical meaning and are ρ Water and its preparation method Where g is the density of water, the gravitational acceleration.
In the case of a saturated moisture space-time distribution, the gap water pressure p and the pressure water head Hp have the following relationship:
p＝ρ water and its preparation method gH p (13)
S42, calculating a plastic potential function of the soil body according to the stress field of the landslide body;
the soil body is a complex elastoplastic material, whether yield occurs or not is judged by plastic potential, the invention adopts Mohr-Coulomb (M-C) criterion to judge, and the plastic potential function is as follows:
in the above formula, Θ.e [ -pi/6,]is the Rode angle, I 1 As the first invariant of stress, J 2 And J 3 The second and the third invariant of strain are respectively, C is cohesive force,is the internal friction angle theta and I 1 、J 2 、J 3 Initial value of C and->And (3) carrying out finite element analysis according to the stress field of the landslide body to obtain the initial value of (2).
S43, judging whether F presents a convergence state, if so, comparing the C with the C according to the following formulaReducing, returning to the step S42, otherwise, obtaining the current reduction coefficient as the safety coefficient FOS;
in the SRM method, the two parameters are continuously reduced according to the following formula until the calculation result no longer presents a convergence state, and the current reduction coefficient at this time is the safety coefficient FOS:
c on the right side of the equal sign Upper part Andthe cohesive force and the internal friction angle obtained by the last reduction are respectively C and +.>The current cohesion and internal friction angle, respectively.
F in the plastic potential function of the soil body is in a stable convergence state, and C in the plastic potential function are required to be continuously matchedPerforming reduction to obtain C and +.>The critical point of the safety factor FOS is obtained, and the safety factor and theoretical safety factor pair calculated by the invention is shown in fig. 4, and basically accords with the change rule of the theoretical safety factor.
Finally, it should be noted that the above-mentioned method may be converted into software program instructions, which may be implemented by a system including a processor and a memory, or by computer instructions stored in a non-transitory computer readable storage medium. The integrated units implemented in the form of software functional units described above may be stored in a computer readable storage medium. The software functional unit is stored in a storage medium, and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) or a processor (processor) to perform part of the steps of the methods according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
In summary, the method for monitoring the safety coefficient under the landslide rainfall condition by using ERT has the following beneficial effects:
(1) According to the invention, a large amount of low-cost and wide-coverage ERT monitoring data are utilized, the inversion overall thought is utilized, the resistivity space-time distribution is calculated through incomplete Gaussian Newton inversion with multiple constraints, then the moisture space-time distribution is obtained according to the hydropower relation, and finally the safety coefficient of the landslide is calculated by utilizing the finite element strength folding and subtracting method, so that the safety coefficient evolution process of the landslide under the rainfall condition can be reflected more dynamically and intuitively, and the basis is improved for early warning or decision making;
(2) According to the invention, the specificity of landslide under rainfall condition is considered, multiple constraints such as prior model constraint, model smoothness constraint, regularization constraint and the like are carried out on the inversion process, so that the inversion accuracy, namely the accuracy of the calculated safety coefficient is improved;
(3) According to the invention, an imprecise incomplete Gaussian Newton method is adopted to calculate the search direction in the inversion process, a wolfe criterion is adopted to determine the iteration step length, a jacobian-free kryleov solving technology is adopted to avoid directly calculating the jacobian matrix, so that the inversion efficiency is improved, namely, the efficiency of calculating the safety coefficient is improved.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although embodiments of the present invention have been described in connection with the accompanying drawings, various modifications and variations may be made by those skilled in the art without departing from the spirit and scope of the invention, and such modifications and variations fall within the scope of the invention as defined by the appended claims.
Claims (6)
1. A method for monitoring a safety factor in landslide rainfall conditions using ERT, comprising the steps of:
s1, deploying ERT monitoring equipment on a landslide, collecting monitoring data, collecting rock parameters and geological data on the landslide, and establishing a geometric model of the landslide through software;
s2, establishing an inversion objective function applying prior model constraint, space smoothness constraint and regularization constraint, solving the minimum value of the objective function by carrying out iterative update on regularization parameter lambda and model increment delta m, obtaining the rock-soil body resistivity at each moment according to the model vector at each moment obtained by solving, and synthesizing to obtain the resistivity space-time distribution;
s21, establishing a regularized inversion objective function applying prior model constraint and space smoothness constraint:
in the above-mentioned method, the step of,for inverting the objective function +.>For data item->Is regularized model term, lambda is regularized parameter, D is observed data weight, W is model weight, A is positive algorithm, m apr For a reference model given from a priori information, d obs For observation data, m is a model vector to be solved;
the D is calculated according to the following formula:
the W is calculated according to the following formula:
the iterative updating formula of the regularization parameter lambda after the initial value is kept unchanged in two iterations is as follows:
in the formula, SD (do bs ) For the standard deviation of the observed data, ε is the minimum trusted data value, r ij K is the distance between the centers of two adjacent grid cells i K is the current iteration number, which is the number of adjacent units of the current unit;
s22, iteratively updating regularization parameters lambda and model increment delta m of the objective function, and solving the minimum value of the objective function;
s23, obtaining the resistivity rho of the rock-soil body according to the model vector m obtained by solving: m=lnρ;
s24, repeating the steps S21-S23 for the earth electric field response at each moment in the rainfall process to obtain the rock-soil body resistivity rho at each moment, and synthesizing to obtain a resistivity change curve, namely the resistivity space-time distribution;
s3, obtaining water space-time distribution from the resistivity space-time distribution according to the hydropower relationship;
s4, analyzing and calculating a stress field of the landslide body by adopting a finite element according to the water space-time distribution, calculating a plastic potential function of a soil body according to the stress field of the landslide body, and calculating the safety coefficient of the landslide by using an intensity reduction method on the plastic potential function.
2. The method of claim 1, wherein in step S22, the iterative updating method of the model increment Δm is as follows:
A. and deriving the objective function, setting the objective function to be zero, and solving the model increment delta m through an incomplete Gaussian Newton method:
in the aboveFor jacobian matrix, g is the gradient of the objective function, and H is the approximated hessian matrix; and making the initial value of the search step alpha be 1;
B. judging whether the delta m meets the precision requirement, if so, entering a step D; if not, entering the step C;
C. according to m k+1 ＝m k +αΔm calculates Δm, and determines whether the inequality is satisfiedIf yes, returning to the step B, otherwise, changing alpha to be half of the original alpha, and re-entering the step C;
m is in k For the model vector at the current iteration number k, phi is the objective function value,c is a constant;
D. and updating and iterating the objective function according to the current delta m.
3. The method for monitoring safety coefficient under landslide rainfall condition using ERT of claim 1, wherein in step S3, the hydropower relationship is:
ρ＝KS -n
wherein S is saturation, and parameters K and n are obtained by fitting calculation to measured data.
4. The method for monitoring safety coefficient under landslide rainfall condition of claim 3 wherein step S4 comprises the steps of:
s41, analyzing and calculating a stress field of the landslide body by adopting a finite element according to the water space-time distribution;
σ ij ＝σ′ ij +δ ij α eq p，
wherein f j X is the force to be applied ij Is vector in three directions, sigma ij As the total stress tensor, including the effective stress tensor sigma' ij And stress, delta, generated by water ij Is Kronecker symbol, alpha eq Equivalent pore water coefficient, p is pore water pressure:
in the case of a space-time distribution of unsaturated moisture,
in case of saturated moisture spatiotemporal distribution, p=ρ Water and its preparation method gH p
Wherein r and q are fitting parameters, have no practical meaning, ρ Water and its preparation method The density of water, g here is the gravity accelerationDegree, alpha is pore water coefficient, H p Is a pressure water head;
s42, calculating a plastic potential function of the soil body according to the stress field of the landslide body:
wherein Θ.E [ -pi/6, pi/6]Is the Rode angle, I 1 As the first invariant of stress, J 2 And J 3 The second and the third invariant of strain are respectively, C is cohesive force,is the internal friction angle theta and I 1 、J 2 、J 3 Initial value of C and->The initial value of (2) is obtained by finite element analysis according to the stress field of the landslide body;
s43, judging whether F presents a convergence state, if so, comparing the C with the C according to the following formulaAnd (4) reducing, returning to the step S42, otherwise, obtaining the current reduction coefficient which is the safety coefficient FOS:
c on right side of equal sign Upper part Andthe cohesion and internal friction angle obtained by the last reduction are respectively.
5. A system for monitoring a safety factor in landslide rainfall conditions using ERT, comprising:
at least one processor; and at least one memory communicatively coupled to the processor, wherein:
the memory stores program instructions executable by the processor to invoke the program instructions capable of performing the method of monitoring a safety factor in landslide rainfall conditions using ERT of any of claims 1-4.
6. A non-transitory computer-readable storage medium storing computer instructions that cause the computer to perform the method of monitoring a safety factor under landslide rainfall conditions using ERT of any of claims 1-4.
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