Near-fault earthquake pile-anchor slope stability analysis method based on energy balance

Abstract

The invention relates to a geotechnical engineering seismic strengthening technology, in particular to a near-fault earthquake pile-anchor slope stability analysis method based on energy balance. The problem that in the prior art, the stability condition of the side slope under the earthquake action is not easy to analyze is solved. According to the method, a three-dimensional slope calculation model is constructed; a pile-anchor combination collaborative reinforcement mechanism is constructed; a pile-anchor combined failure mode is constructed; and according to the function relation of the limit analysis upper bound method, the safety coefficient of the slope in the combined pile anchor reinforcing state is solved. Aiming at the specific pulse effect and the like of near-fault earthquakes, a state equation is established based on a limit analysis method, and by constructing a pile-anchor reinforcing structure and an energy dissipation balance model, the slope safety coefficient and the change rule of a three-dimensional slip crack surface under different slopes and reinforcing structures under different earthquake effects are rapidly obtained; stability analysis of three-dimensional slope reinforcement is enriched, reference is provided for actual slope engineering, and the actual three-dimensional slope stability can be evaluated more accurately.

Description

Technical Field

[0001] The present invention relates to the seismic reinforcement technology of geotechnical engineering, in particular to a method for analyzing the stability of pile-anchor slopes under near-fault earthquakes based on energy balance. Background Art

[0002] Under the current situation of densely distributed deep and large active fault zones in the southwestern region, with the westward trend of China's major strategies, transportation lines inevitably approach the fault zone areas. Due to the short duration and high pulse characteristics of ground motion in the near-fault area, it has relatively large energy, and a single combined reinforcement structure is difficult to meet the needs of earthquake landslide prevention and mitigation. The cable-stayed anti-slide pile reinforcement structure is an engineering structure that combines the advantages of prestressed cables and anti-slide piles:

[0003] The prestressed cable acts together with the anti-slide pile to resist the sliding of the soil mass and the disturbance of external loads, reducing the lateral deformation of the anti-slide pile structure and effectively enhancing the lateral stiffness of the anti-slide pile structure;

[0004] The internal and external force distributions of the anti-slide pile tend to be uniform, which is conducive to giving full play to the mechanical properties of the anti-slide pile. The synergistic effect of the two can effectively improve the slope stability. However, the existing slope stability reinforcement fails to fully consider the three-dimensional characteristics of the actual slope and the action mechanism of pile-anchor synergistic reinforcement, and fails to fully consider the stability of the slope under earthquake action.

[0005] Numerical simulation can better obtain the stress and strain conditions of the slope, but it takes too much time to establish the model and calculate;

[0006] Experimental simulation can more realistically obtain the actual slope conditions, but it is costly and time-consuming.

[0007] There is an urgent need for a reinforcement analysis method that can solve the above problems. Summary of the Invention

[0008] The present invention provides a method for analyzing the stability of pile-anchor slopes under near-fault earthquakes based on energy balance, which solves the problem that it is difficult to analyze the stability of slopes under earthquake action in the prior art.

[0009] The technical solution of the present invention is realized as follows:

[0010] A method for analyzing the stability of pile-anchor slopes under near-fault earthquakes based on energy balance includes the following steps:

[0011] S1. Construct a three-dimensional slope calculation model: Input the slope geometric dimensions, slope strength parameters, anti-slide pile geometric parameters, cable inclination angle α, anti-slide pile spacing D1, and the position x of the pile-anchor combined reinforcement F / L E ;

[0012] S2. Constructing a synergistic reinforcement mechanism of pile-anchor combination: According to the limit analysis method and Ito plastic deformation theory, the corresponding anchor cable tension T at the critical failure state of the slope after the pile body is deformed is obtained. i ; Effective height of pile row h i ; The deflection y of the anti-slide pile and the anchor cable tension T i ;

[0013] S3. Construct the failure mode of pile-anchor combination: According to the principle of virtual work, the internal energy consumption is equal to the external power, and the energy consumption relationship is obtained;

[0014] S4. According to the functional relationship of the upper limit method of limit analysis, solve the safety factor of the slope under the combined pile-anchor reinforcement state; optimize and solve the minimum stability coefficient of the slope.

[0015] A further technical solution is that the effective height h of the pile row in step S2 is i and anchor cable tension T i Specific calculation: S21, the distribution of effective earth pressure on the critical pile side is:

[0016] p(z′)=k1-k2z′(0.33);

[0017] Among them, k1 and k2 are the calculation constants of effective earth pressure on the pile side, and the height of the anti-sliding pile from the top to point E is z;

[0018] The foundation reaction force under the sliding surface is calculated based on the elastic foundation beam K method:

[0019] p=ky(0.34)

[0020] Obtain the differential equation for deflection based on structural mechanics:

[0021]

[0022] Among them, y1 and y2 are the deflections above and below the sliding surface of the anti-slide pile respectively; E P is the deflection of the anti-slide pile; I P is the moment of inertia of the anti-sliding pile; E S is the soil deformation modulus; h i is the effective height of the pile row;

[0023] The deflections y1 and y2 above and below the sliding surface of the anti-slide pile are obtained:

[0024]

[0025] According to the connection conditions of the anchor cable at the anti-sliding pile head, the above formulas can be combined to obtain the anchor cable tension T i Integration constant A i , B i The expression is:

[0026]

[0027] According to the anti-slide pile pile head displacement limit condition, the anchor cable tension T can be obtained. i Expression:

[0028]

[0029] The further technical solution is that the external power and the internal power are respectively:

[0030] S31. For the external power, it is divided into three parts: the self-weight power of the soil mass, the seismic force power, and the anchor cable power;

[0031] S32. For the internal power, it is divided into two parts: the energy consumption at the velocity discontinuity surface and the energy consumption of the anti-slide pile;

[0032] Further, the external power and the internal power are respectively: Specifically, step S31 is: S311. The self-weight power of the three-dimensional sliding block soil mass can be expressed as:

[0033]

[0034] The self-weight power of the plane inserted block soil mass can be expressed as:

[0035]

[0036] The self-weight power of the three-dimensional composite failure mechanism soil mass is:

[0037]

[0038] Among them, θ0 is the initial rotation angle, θ is the rotation angle, ω is the angular velocity of the rotation center, H is the slope height, β is the slope angle, R is the radius of the circular cross-section of the curved cone, r m is the average radius of the upper and lower two logarithmic spirals, and its trajectory is the position of the center of the circular cross-section of the curved cone. a and d are respectively the distances between the slope surface and the center line of the curved cone. The above variables can all be obtained from the geometric relationship:

[0039] R = (r - r') / 2 (0.44);

[0040] r m = (r + r') / 2 (0.45);

[0041]

[0042] b = B - B max (0.50);

[0043] S312. The seismic power of the three-dimensional sliding block can be expressed as:

[0044]

[0045] The seismic power of the plane-inserted block soil mass can be expressed as:

[0046]

[0047] The seismic power of the three-dimensional composite failure mechanism is:

[0048]

[0049] S313, the tensile force T of k prestressed anchor cables i The work done is:

[0050] W Ti = T i ·v E ·sin(θ E -α)(0.54);

[0051] W T = ∑W Ti (0.55).

[0052] Furthermore, the specific step S32 is:

[0053] S321. The energy consumption of the three-dimensional sliding surface velocity can be expressed as:

[0054]

[0055] The energy consumption of the plane-inserted block sliding surface velocity can be expressed as:

[0056]

[0057] The energy consumption of the three-dimensional composite failure mechanism sliding surface velocity is:

[0058]

[0059] S322. The energy consumption of the lateral force of the anti-slide pile for the three-dimensional sliding body is:

[0060]

[0061] The energy consumption of the lateral force of the anti-slide pile for the plane-inserted block is:

[0062]

[0063] The energy consumption of the lateral force of the anti-slide pile for the three-dimensional composite failure mechanism is:

[0064]

[0065] A further technical solution is that, based on step S3, according to the functional relationship of the upper bound method of limit analysis, the safety factor of the slope in the state of combined pile-anchor reinforcement is solved. Specifically:

[0066] S41. In the constructed pile-anchor combined failure mode, according to the principle of virtual work, the internal energy consumption is equal to the external power:

[0067]

[0068] Based on the upper bound theorem of limit analysis and combined with the strength reduction method, the implicit function expression of the safety factor Fs of the reinforced slope is calculated as follows:

[0069]

[0070] The optimization variables related to Fs satisfy the following constraints:

[0071]

[0072] For a further technical solution, the effective height h of the row piles in step S2 i Specifically: S22. The effective height h of the row piles i is derived based on Ito's plastic deformation theory, the K method of elastic foundation beams, and structural mechanics knowledge. It is realized by establishing equations and combining boundary conditions for solution. The specific reverse deduction process first determines the earth pressure and foundation reaction force according to (1.1)(1.2), establishes the deflection differential equation according to (1.3) and solves the general solution of the deflection according to (1.4). According to the continuity conditions (1.3.1)(1.3.2)(1.3.3)(1.3.4) of the deflection curve of the anti-slide pile at the sliding surface, the integral constants a0, a1, a2, and a3 can be determined. After determining all the integral constants A and B (1.5), according to the differential equation of the elastic curve of the anti-slide pile, the deflection y of the anti-slide pile and the cable anchor tension T are obtained by continuous integration i ; Since in the established equation system, the effective height h of the row piles i is correlated with other parameters. After knowing other parameters and the relevant data determined through the above steps, the effective height h of the row piles can be deduced inversely i ;

[0073]

[0074] A pile-anchor slope stability analysis method under near-fault earthquakes based on energy balance disclosed by the present invention, aiming at the pulse effect unique to near-fault earthquakes, etc., establishes a state equation based on the limit analysis method, and through constructing a pile-anchor reinforcement structure and an energy dissipation balance model, has the following specific beneficial effects:

[0075] 1. By quickly obtaining different slope parameters (height, slope angle, internal friction angle, cohesion) and reinforcement structure parameters (reinforcement position, pile spacing, cable anchor tension T) under different seismic actions i)Under certain conditions, the variation laws of the slope safety factor and the three-dimensional slip surface; enrich the stability analysis of three-dimensional slope reinforcement, provide reference for actual slope engineering, so as to more accurately evaluate the stability of actual three-dimensional slopes;

[0076] 2. Explore the influence of different pile-anchor combination reinforcement parameters on slope stability, and provide a scientific basis for the design and reinforcement of slope engineering;

[0077] 3. The present invention is a theoretical analysis method based on programming languages, which can quickly and accurately analyze the stability of slopes under earthquake action, obtain the stability of slopes under different reinforcement measures, and quickly evaluate the reinforcement effects of different slope reinforcement measures in the early stage of the project, providing technical support and guidance for project implementation. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0079] Figure 1 : Schematic flow chart of the present invention;

[0080] Figure 2 : Schematic diagram of physical quantity representation in the three-dimensional slope reinforced by pile-anchor combination;

[0081] Figure 3 : Schematic diagram of the calculation model of the three-dimensional slope reinforced by pile-anchor combination. DETAILED DESCRIPTION OF THE INVENTION

[0082] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the protection scope of the present invention. DETAILED DESCRIPTION OF THE INVENTION I

[0084] Combined with Figure 1 As shown in the schematic flow chart of the present invention, the specific implementation of the present invention includes the following steps: S1. Input geometric dimensions of the slope such as slope angle and height; unit weight γ of soil, effective height h of the row piles i， internal friction angle φ of the soil r , cohesion c of the soil r and other slope strength parameters; geometric parameters of the anti-slide piles; inclination angle α of the anchor cables; spacing D1 between the anti-slide piles; position x of the pile-anchor combination reinforcementF / L E Construct a three-dimensional slope calculation model;

[0085] S2. Based on the internal force of the pile body on the sliding surface obtained by the limit analysis method and Ito plastic deformation theory, the corresponding anchor cable tension T at the critical failure state of the slope after the coordinated deformation of the pile and anchor is completed is inferred. i ; According to the sliding state of the soil around the pile, the effective height of the pile row h is obtained i According to the displacement restriction condition of the anti-sliding pile head, the deflection y of the anti-sliding pile and the anchor cable tension T are calculated by continuous integration. i ; Through the distribution of effective earth pressure on the critical pile side, the calculation of foundation reaction force based on the elastic foundation beam K method under the sliding surface, and the deflection differential equation based on structural mechanics, the deflection above and below the sliding surface of the anti-sliding pile is obtained. According to the connection conditions of the anchor cable at the anti-sliding pile head, the above formulas can be combined to obtain the anchor cable tension T i The integral constant can be used to calculate the anchor cable tension T according to the displacement restriction condition of the anti-sliding pile head. i and effective height of pile row h i ;

[0086] S3. According to the principle of virtual work, the internal energy consumption is equal to the external power, and the energy consumption relationship is obtained. The synergistic reinforcement mechanism of the pile-anchor combination is constructed, and the pile-anchor combination failure mode is constructed. The influence of different pile-anchor combination reinforcement parameters on the slope stability is explored to provide a scientific basis for the design and reinforcement of slope engineering. The external power and internal power are calculated separately. The external power is calculated in three parts: soil self-weight power, seismic force power, and anchor cable power. The soil self-weight power is divided into three parts: three-dimensional slider soil self-weight power, plane insertion block soil self-weight power, and three-dimensional composite The power of the soil body of the destruction mechanism is calculated by its own weight; the internal power is calculated in terms of the energy consumption of the velocity discontinuity surface and the energy consumption of the anti-sliding piles. The energy consumption of the velocity discontinuity surface is calculated in terms of the energy consumption of the three-dimensional sliding surface velocity, the energy consumption of the plane inserted block sliding surface velocity, and the energy consumption of the three-dimensional composite destruction mechanism sliding surface velocity; the energy consumption of the anti-sliding piles is calculated in terms of the lateral force energy consumption of the three-dimensional sliding body anti-sliding piles, the lateral force energy consumption of the plane inserted block anti-sliding piles, and the lateral force energy consumption of the three-dimensional composite destruction mechanism anti-sliding piles. The internal and external powers are fully considered to obtain the energy consumption relationship and establish an effective coordinated reinforcement mechanism.

[0087] S4. According to the functional relationship of the upper limit method of limit analysis, solve the safety factor of the slope under the combined pile-anchor reinforcement state; optimize and solve the minimum stability coefficient of the slope.

[0088] This embodiment fully considers the geometric dimensions of the three-dimensional slope, the three-dimensional dimensions of the pile-anchor combined structure, and especially the pulse effect peculiar to earthquakes, establishes a state equation based on the limit analysis method, fully considers the internal and external power, constructs a pile-anchor reinforcement structure and energy dissipation balance model, obtains the energy consumption relationship, and establishes an effective collaborative reinforcement mechanism.

[0089] Combination Figure 2 Schematic diagram of physical quantity representation in the three-dimensional slope reinforced by the pile-anchor combination and Figure 3 As shown in the schematic diagram of the calculation model of the three-dimensional slope reinforced by the pile-anchor combination, in the specific implementation process, the geometric dimensions of the slope such as the slope angle and height of the slope are collected; the unit weight of soil γ, the effective height of the row pile h i， Internal friction angle φ of soil body r , cohesion c of soil body r and other slope strength parameters; geometric parameters of the anti-slide pile; inclination angle α of the anchor cable; spacing D1 of the anti-slide piles are obtained, and the safety factor under the reinforced state can be obtained; and through optimization, the minimum stability factor of the slope can be solved. Guide the setting of the effective height of the anti-slide pile, the inclination angle of the anchor cable, and the spacing of the anti-slide piles in the pile-anchor combined structure to improve the stability of the actual three-dimensional slope. Specific Embodiment 2

[0091] Quickly and accurately evaluate the seismic slope stability, explore the influence of pile-anchor combination reinforcement parameters, solve the technical bottlenecks in aspects such as the simulation of three-dimensional terrain dynamic response, the quantification of pile-anchor collaborative working mechanism, and the analysis of seismic energy transfer path, and provide a quantitative decision-making basis for seismic reinforcement design under complex geological conditions. It is applicable to major projects threatened by near-field earthquakes such as highway slopes in high-intensity earthquake areas, dam shoulders of hydropower projects, and open-pit mine slopes;

[0092] The present invention can also collect the geometric parameters of the highway slope in the high-intensity earthquake area, the unit weight of soil, the effective height of the row pile h i， Internal friction angle of soil body, cohesion of soil body and other slope strength parameters; geometric parameters of the anti-slide pile; inclination angle of the anchor cable; spacing of the anti-slide piles are collected, and the safety factor under the reinforced state can be obtained; and through optimization, the minimum stability factor of the slope can be solved. Guide the setting of the effective height of the anti-slide pile, the inclination angle of the anchor cable, and the spacing of the anti-slide piles in the pile-anchor combined structure to improve the stability of the actual three-dimensional slope.

[0093] Certainly, without departing from the spirit and essence of the present invention, those skilled in the art should be able to make various corresponding changes and deformations according to the present invention, but these corresponding changes and deformations should all fall within the protection scope of the appended claims of the present invention.

Claims

1. A method for analyzing the stability of pile-anchor slopes under near-fault earthquakes based on energy balance, characterized in that: Including the following steps: S1. Construct a three-dimensional slope calculation model: Input the slope geometric dimensions, slope strength parameters, anti-slide pile geometric parameters, cable anchor inclination angle α, anti-slide pile spacing D1, and the position x of the pile-anchor combined reinforcement F / L E ; S2. Establish the combined pile-anchor collaborative reinforcement mechanism: Obtain the corresponding cable anchor tension T at the critical failure state of the slope after the pile body deformation is completed according to the limit analysis method and Ito's plastic deformation theory i ; The effective height h of the row piles i ; The deflection y of the anti-slide pile and the cable anchor tension T i ; S3. Construct the pile-anchor combined failure mode: According to the principle of virtual work, the internal energy consumption is equal to the external power, and the energy consumption relationship is obtained; S4. According to the functional relationship of the upper bound method of limit analysis, solve the safety factor of the slope under the combined pile-anchor reinforcement state; optimize and solve the minimum stability factor of the slope.

2. A method for analyzing the stability of pile-anchor slopes under near-fault earthquakes based on energy balance according to claim 1, characterized in that: The effective height h of the row piles in step S2 i and the anchor cable tension T i are specifically calculated; S21. The distribution of the critical effective soil pressure on the pile side is: p(z′) = k1 - k2z′(0.1) where k1 and k2 are the calculation constants of the effective soil pressure on the pile side, and the height of the anti-slide pile from the top to point E is z; The foundation reaction force calculated by the K method of the elastic foundation beam under the sliding surface is: p = ky(0.2) Obtain the deflection differential equation based on structural mechanics: where y1 and y2 are the deflections above and below the sliding surface of the anti-slide pile respectively; E P is the deflection of the anti-slide pile; I P is the moment of inertia of the anti-slide pile; E S is the soil deformation modulus; h i is the effective height of the row pile; Obtain the deflections y1 and y2 above and below the sliding surface of the anti-slide pile: According to the connection conditions of the anchor cable at the anti-sliding pile head, the above formulas can be combined to obtain the anchor cable tension T i Integration constant A i , B i The expression is: According to the anti-slide pile head displacement limit condition, the cable anchor tension T can be calculated i Expression:

3. A method for analyzing the stability of pile-anchor slopes under near-fault earthquakes based on energy balance according to claim 1, characterized in that: The external power and internal power are respectively: S31. For the external power, it is divided into three parts: the self-weight power of the soil mass, the seismic force power, and the anchor cable power; S32. For the internal power, it is divided into two parts: the energy consumption of the velocity discontinuity surface and the energy consumption of the anti-slide pile.

4. A method for analyzing the stability of pile-anchor slopes under near-fault earthquakes based on energy balance according to claim 3, characterized in that: The external power and internal power are respectively: Specifically, step S31 is: S311. The self-weight power of the three-dimensional slider soil mass can be expressed as: The self-weight power of the plane inserted block soil mass can be expressed as: The self-weight power of the three-dimensional composite failure mechanism soil mass is: Among them, θ0 is the initial rotation angle, θ is the rotation angle, ω is the angular velocity of the rotation center, H is the slope height, β is the slope angle, R is the radius of the circular section of the curved cone, and r m is the average radius of the upper and lower logarithmic spirals, and its locus is the position of the center of the circular section of the curved cone. The distances a and d from the slope surface to the center line of the curved cone can be obtained from geometric relationships as follows: R＝(r-r') / 2(0.12)； r m ＝(r+r') / 2(0.13)； b = B - B max (0.18); S312. The seismic power of the three-dimensional slider can be expressed as: The seismic power of the plane inserted block soil mass can be expressed as: The seismic power of the three-dimensional composite failure mechanism is: S313. Tensile force T of k prestressed anchor cables i The work done is as follows: W Ti = T i ·v E ·sin(θ E - α)(0.22); W T = ΣW Ti (0.23).

5. A method for analyzing the stability of pile-anchor slopes under near-fault earthquakes based on energy balance according to claim 3, characterized in that: Specifically, step S32 is: S321. The velocity energy consumption of the three-dimensional sliding surface can be expressed as: The velocity energy consumption of the plane inserted block sliding surface can be expressed as: The velocity energy consumption of the three-dimensional composite failure mechanism sliding surface is: S322. The lateral force energy consumption of the anti-slide pile in the three-dimensional sliding body is: The lateral force energy consumption of the anti-slide pile in the plane inserted block is: The lateral force energy consumption of the anti-slide pile in the three-dimensional composite failure mechanism is:

6. A method for analyzing the stability of pile-anchor slopes under near-fault earthquakes based on energy balance according to claim 4 or 5, characterized in that: Based on step S3, according to the functional relationship of the upper bound method of limit analysis, solve the safety factor of the slope under the combined pile-anchor reinforcement state. Specifically: S41. In the constructed pile-anchor combined failure mode, according to the principle of virtual work, the internal energy consumption is equal to the external power: Based on the upper bound theorem of limit analysis, combined with the strength reduction method, the implicit function expression of the safety factor Fs of the reinforced slope is as follows: The optimization variables related to Fs satisfy the following constraints:

7. A method for analyzing the stability of pile-anchor slopes under near-fault earthquakes based on energy balance according to claim 6, characterized in that: The effective height h of the row of piles in step S2 i Specifically: S22, the effective height h of the row of piles i It is achieved by establishing equations and solving them in combination with boundary conditions. The earth pressure and foundation reaction are determined according to (1.1) and (1.2). The deflection differential equation is established according to (1.3), and the general solution of the deflection is solved according to (1.4). The integral constants a0, a1, a2, and a3 can be determined according to the continuity conditions (1.3.1), (1.3.2), (1.3.3), and (1.3.4) of the deflection curve of the anti-slide pile at the sliding surface. After determining all the integral constants A and B (1.5), according to the differential equation of the elastic curve of the anti-slide pile, the deflection y of the anti-slide pile and the cable anchor tension h are obtained by successive integration i ; Since in the established equation system, the effective height h of the row piles i is interrelated with other parameters. After knowing other parameters and the relevant data determined through the above steps, the effective height h of the row piles can be deduced inversely i ;

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