Method for determining optimal pulling strength of anchor rod in reinforced slope

Abstract

The invention discloses a method for determining the optimal pulling strength of an anchor rod in a reinforced side slope, and belongs to the technical field of side slope reinforcement. Comprising the following steps: establishing a mathematical model of the anchor rod reinforced slope, and obtaining a curve graph of the relationship between the safety coefficient of the slope and the pulling strength of the anchor rods under different anchor rod numbers and bonding lengths; obtaining a change curve of the slope failure probability and the pulling strength of the anchor rods under the condition of different anchor rod numbers and bonding lengths; and obtaining an optimal design value of the pulling strength of the anchor rods for reinforcing the slope. The failure probability is introduced into an anchor rod supporting project, and the reliability of the slope anchor rod supporting project is reflected through the failure probability; and the rule among the anti-pulling strength, the anchor rod number, the bonding strength and the slope stability coefficient is effectively obtained. In the slope reinforcing project, the anti-pulling characteristic of the anchor rods is fully exerted, the number and bonding strength of the anchor rods correspond to the optimal anti-pulling strength, waste of engineering materials is avoided, and the economical efficiency of the supporting project is improved while the slope safety is guaranteed.

Description

Technical Field

[0001] The present invention belongs to the technical field of stability evaluation and disaster prevention of reinforced slopes, and in particular relates to a method for determining the optimal pull-out strength of an anchor rod in a reinforced slope. Background Art

[0002] With the continuous development of my country's social economy, the number of artificial soil slopes has increased rapidly due to the continuous construction of various infrastructures. However, in recent years, due to the influence of various comprehensive factors, a large number of artificial soil slopes have experienced landslides, resulting in great economic losses and casualties. Therefore, in the past few decades, relevant technical personnel have been working hard to explore effective measures to improve the stability of slopes. Among them, anchor rods are an effective measure that has been proven to reinforce slopes and are widely used in practical projects. In the actual engineering of anchor rod reinforcement of slopes, the selection of anchor rod pull-out strength needs to reasonably consider the influence of anchor rod number, bonding length and slope stability. At present, anchor rod reinforcement is mainly based on the calculation method to obtain the required anchoring force, and then calculate the required number of anchor rods and bonding length through the anchoring force, and finally verify the pull-out strength and correct the bonding length of the anchor rod. The number of anchor rods and bonding length obtained in this way are single, and the pull-out strength is not directly taken into account during the calculation process. The obtained pull-out strength is not optimal. Therefore, the law between the pull-out strength, the number of anchor rods and the bonding strength cannot be effectively obtained. In the slope reinforcement project, the optimal pull-out resistance of the anchor rod is not fully utilized, resulting in a certain degree of waste of engineering materials. Summary of the invention

[0003] In view of the above shortcomings, an object of the present invention is to provide a method for determining the optimal pull-out strength of an anchor in a reinforced slope.

[0004] The technical solution adopted by the invention is: a method for determining the optimal pull-out strength of an anchor in a reinforced slope, the technical key points of which are as follows: A mathematical model of anchor-reinforced slope is established, and different numbers of anchors are selected. Different anchor bonding lengths are designed under different numbers of anchors. Different anchor pull-out strengths are obtained under corresponding numbers of anchors and bonding lengths. The slope safety factor corresponding to different anchor pull-out strengths is calculated using the limit equilibrium method. By changing the number of anchors and bonding lengths, the above calculation process is repeated until a curve showing the relationship between the slope safety factor and the anchor pull-out strength under different numbers of anchors and bonding lengths is obtained. The anchor pull-out strength design values ​​corresponding to all slope safety factors greater than 1 under different numbers of anchors and bonding lengths are selected, and the failure samples of the slope are obtained by using the Monte Carlo sampling method combined with the response surface method. The slope failure probability corresponding to all the selected design values ​​of the anchor pull-out strength is calculated, and the variation curve of the slope failure probability and the anchor pull-out strength under different numbers of anchors and bonding lengths is obtained. The optimal design value of the anchor pull-out strength of the reinforced slope is obtained according to the variation curve.

[0005] In the above scheme, the process of determining the relationship curve between the slope safety factor and the anchor pull-out strength includes the following steps: (1) Establish a mathematical model for anchor-bolt reinforced slopes and design X and Y The required number of anchor rods and the anchor rod bonding length are expressed as A1, A2, A3, ... A X ,B1,B2,B3,......B Y , given Z The design value of the pull-out strength of the anchor is denoted as C1, C2, C3, .... C Z ; (2) At a certain required number of anchor rods A i Bonding length B with anchor rod j Under this condition, change the pull-out strength of the anchor rod to obtain C1, C2, C3, ... Z The corresponding slope safety factors FS 1, FS 2, FS 3...... FS Z , using (C i , FS i ) i =1,2,…Z, plot the curve of slope safety factor changing with different anchor pull-out strengths, keep the number of anchors unchanged, change the required anchor bonding length, repeat the above calculation until the curve of slope safety factor changing with different anchor pull-out strengths under different anchor bonding lengths is obtained, then change the number of anchors, continue to repeat the above calculation process and finally obtain the curve of slope safety factor changing with different anchor numbers and anchor bonding lengths.

[0006] In the above scheme, the steps for obtaining the variation curve of slope failure probability and anchor pull-out strength are as follows: (1) At a certain required number of anchor rods A i Bonding length B with anchor rod j Next, in Z The slope safety factor is selected one by one from the design values ​​of anchor pull-out strength FS A value greater than 1, and get the corresponding S The pull-out strength values ​​of the anchor rods are C1, C2, C3, .... C S By changing the required number of anchor rods and the anchor rod bonding length, the above operation is repeated until the required number of anchor rods and the anchor rod bonding length are obtained. Z The corresponding slope safety factor in the design value of the anchor pull-out strength FS For values ​​greater than 1, the obtained quantities are recorded as S 1, S 2, S 3,...... S r , r = X × Y , under different anchor numbers and anchor bonding lengths, the slope safety factor corresponding to the selected anchor pull-out strength design value is established one by one FS Response surface function between and soil strength parameters; (2) At a certain number of anchors A i , Anchor bonding length B j Next, select S The pull-out strength values ​​of the anchor rods are C1, C2, C3, .... C S At each selected anchor pull-out strength value, the cohesion c, internal friction angle of the soil parameters in the slope are calculated. φ Treated as a random variable ， Generated using Matlab software N soil layer parameter samples T1, T2, ..., T N , use the established response surface function to calculate T1, T2, ..., T N The corresponding safety factor FS 1, FS 2,……, FS N ;like F S i <1, then T i For failed samples, repeat the process to obtain W unstable samples, calculate the failure probability of the slope P fi = W / N , a total of corresponding SSlope failure probability P f1 , P f2 , P f3 ,...... P fS ,use( C i , P fi ) i =1,2,… S , draw the relationship curve between slope failure probability and selected anchor pull-out strength; (3) Maintain the number of anchor rods A i Keep the anchor bolt constant, change the anchor bolt bonding length, repeat step (2) to calculate different anchor bolt bonding lengths B1, B2, B3, ... B Y Below, the relationship curve between slope failure probability and selected anchor pull-out strength; (4) By changing the number of anchor rods, steps (2) and (3) are repeated until the number of anchor rods A1, A2, A3, ... A is obtained. X and different anchor bonding lengths B1, B2, B3, ... B Y Below, the relationship curve between slope failure probability and the selected anchor pull-out strength.

[0007] In the above scheme, the process of obtaining the optimal design value of the pull-out strength of the reinforced slope anchor according to the change curve is: Query the anchor pull-out strength relationship curve to determine the optimal value of the anchor pull-out strength in the reinforced slope.

[0008] The beneficial effect of the present invention is that the method for determining the optimal pull-out strength of the anchor in the reinforced slope includes: the steps of establishing a mathematical model of the anchor reinforced slope, obtaining a curve diagram of the relationship between the slope safety factor and the anchor pull-out strength under different anchor numbers and bonding lengths; obtaining a change curve of the slope failure probability and the anchor pull-out strength under different anchor numbers and bonding lengths, and obtaining the optimal design value of the anchor pull-out strength of the reinforced slope according to the change curve. The method introduces the concept of failure probability into the anchor support project, and reflects the reliability of the slope anchor support project through the failure probability. Taking the pull-out strength into consideration, the law between the pull-out strength and the number of anchors, the bonding strength and the slope stability coefficient is effectively obtained. In the slope reinforcement project, the pull-out characteristics of the anchor are fully utilized. At the optimal pull-out strength, the number of anchors and the bonding strength correspond to each other, thereby avoiding the waste of engineering materials, and improving the economy of the support project while ensuring the safety of the slope. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0010] Figure 1 Flow chart of a method for determining the optimal pull-out strength of an anchor in a reinforced slope according to the present invention Figure 2 This is a model diagram of a slope reinforcement (two anchor rods) in an embodiment of the present invention; Figure 3 This is a diagram of a slope reinforcement model (three anchor rods) in an embodiment of the present invention; Figure 4 This is a diagram of a slope reinforcement model (four anchor rods) in an embodiment of the present invention; Figure 5 The safety factor of the slope and the pull-out strength curve of the anchor rod under the conditions of the number of two anchor rods and the bonding length in the embodiment of the present invention; Figure 6 The safety factor of the slope and the pull-out strength curve of the anchor rods under the conditions of the number of anchor rods and the bonding length of three anchor rods in the embodiment of the present invention; Figure 7 The safety factor of the slope and the pull-out strength curve of the anchor rods under the conditions of the number of 4 anchor rods and the bonding length in the embodiment of the present invention; Figure 8 The failure probability of the slope and the pull-out strength of the anchor rods under the conditions of the number of two anchor rods and the bonding length in the embodiment of the present invention are shown in FIG. Fig. 9 The failure probability of the slope and the pull-out strength of the anchor rods under the conditions of the number of anchor rods and the bonding length in the embodiment of the present invention are shown in FIG. Fig.10 This is a curve diagram of slope failure probability and anchor pull-out strength under the condition of 4 anchors and bonding length in the embodiment of the present invention. DETAILED DESCRIPTION

[0011] To make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the following is a brief description of the present invention in conjunction with the attached Figure 1-Figure 10 The present invention is further described in detail with reference to the accompanying drawings and specific embodiments.

[0012] The soil slope to be reinforced in this embodiment has a height of 10m and a foundation thickness of 5m. The slope is composed of silty clay, and the average value of its soil cohesion c is 7kpa, the coefficient of variation is 0.3, the standard deviation is 2.1, the average value of the internal friction angle φ is 22°, the coefficient of variation is 0.3, the standard deviation is 6.6, and the bulk density γ is 20kN / m3. Figure 2 , 3, 4 are the slope model diagrams corresponding to the reinforcement of two, three and four anchor rods respectively.

[0013] A method for determining the optimal pull-out strength of an anchor in a reinforced slope according to this embodiment is as follows: Figure 1 As shown, the specific steps are as follows: Geo-studio software was used to establish a numerical model of anchor-reinforced slopes. Three anchor reinforcement numbers were designed: A1=2, A2=3, and A3=4. Three anchor bonding lengths were selected under each anchor reinforcement number: B1=1m, B2=2m, and B3=3m. Seven anchor pull-out strengths were selected under each anchor bonding length: C1=40kpa, C2=50kpa, C3=60kpa, C4=70kpa, C5=80kpa, C6=90kpa, and C7=100kpa. Under different anchor reinforcement numbers and anchor bonding lengths, the limit equilibrium method was used to calculate the safety factors corresponding to the pull-out strengths of the seven selected anchors. i , B j , C k ) i =1,2,3, j =1,2,3, k =1,2,3...7, draw the relationship curve between slope safety factor and anchor pull-out strength under different anchor reinforcement numbers and anchor bonding lengths, such as Figure 5 , 6 , as shown in 7.

[0014] Among the three anchor reinforcement numbers Ai and three anchor bonding lengths Bj, the anchor pull-out strength design values ​​corresponding to the slope safety factor FS greater than 1 are selected one by one. The four anchor pull-out strength design values ​​corresponding to the anchor number A1=2 and the anchor bonding length B3=3m are (2, 3m, 70kpa), (2, 3m, 80kpa), (2, B3, 90kpa), (2, 3m, 100kpa); the five anchor pull-out strength design values ​​corresponding to the anchor number A2=3 and the anchor bonding length B2=2m are (3, 2m, 60kpa), (3, 2m, 70kpa), (3, 2m, 80kpa), (3, 2m, 90kpa) ), (3, 2m, 100kpa); The number of anchors is A2=3, and the anchor bonding length is B3=3m. The corresponding 7 anchor pull-out strength design values ​​are (3, 3m, 40kpa), (3, 3m, 50kpa), (3, 3m, 60kpa), (3, 3m, 70kpa), (3, 3m, 80kpa), (3, 3m, 90kpa), (3, 3m, 100kpa); The number of anchors is A3=4, and the anchor bonding length is B1=1m. The corresponding 4 anchor pull-out strength design values ​​are The calculated values ​​are (4, 1m, 70kpa), (4, 1m, 80kpa), (4, 1m, 90kpa), (4, 1m, 100kpa); the number of anchors is A3 = 4, the anchor bonding length is B2 = 2m, and the corresponding 7 anchor pull-out strength design values ​​are (4, 2m, 40kpa), (4, 2m, 50kpa), (4, B2, 60kpa), (4, 2m, 70kpa), (4, 2m, 50kpa), (4, 2m, 90kpa), (4, 2m, 100kpa) kpa); The number of anchors is A3=4, and the anchor bonding length is B3=3m, corresponding to the 7 anchor pull-out strength design values ​​(4, 3m, 40kpa), (4, 3m, 50kpa), (4, 3m, 60kpa), (4, 3m, 70kpa), (4, 3m, 80kpa), (4, 3m, 90kpa), (4, 3m, 100kpa); the response surface function between the safety factor FS corresponding to the selected anchor pull-out strength design value and the shear strength parameter of the slope soil is established one by one.

[0015] In each of the above selected anchor pull-out strength design values, the uncertainty of the slope soil shear strength parameter is considered and its cohesion is c and internal friction angle φ Treated as a log-normal random variable, randomly generated using Matlab software N =10 5 random samples T1,T2,......,T 100000 , and then use the established response surface function to calculate 10 5 The slope safety factor corresponding to the random samples is expressed as FS 1, FS 2,……, FS 10000 .exist N =10 5 Among the safety factors, if the safety factor of the slope is FS i <1, then T i For the failed samples, a total of W Failure samples, according to the failure probability calculation formula P fi = W / 10 5 The failure probability corresponding to the design value of the pull-out strength of all selected anchors is obtained, and the calculation results are as follows: Figure 8 , 9 , as shown in Figure 10. When the number of anchors is A1=2 and the anchor bonding length is B3=3m, the failure probabilities corresponding to the design values ​​of the pull-out strength of the four anchors are 42.41%, 23.70%, 21.71%, and 20.43% respectively; when the number of anchors is A2=3 and the anchor bonding length is B2=2m, the failure probabilities corresponding to the design values ​​of the pull-out strength of the five anchors are 28.83%, 7.38%, 1.30%, 0.93%, and 0.67% respectively; when the number of anchors is A2=3 and the anchor bonding length is B3=3m, the failure probabilities corresponding to the design values ​​of the pull-out strength of the seven anchors are 30.47%, 4.19%, 2.91%, 1.41%, 0.82%, 0.75%, and 0.58% respectively; When the number of anchors is A3=4 and the anchor bonding length is B1=1m, the failure probabilities corresponding to the design values ​​of the pull-out strength of the four anchors are 45.09%, 19.98%, 7.43% and 1.31% respectively; when the number of anchors is A3=4 and the anchor bonding length is B2=2m, the failure probabilities corresponding to the design values ​​of the pull-out strength of the seven anchors are 20.07%, 1.34%, 0.45%, 0.14%, 0.09%, 0.07% and 0.06% respectively; when the number of anchors is A3=4 and the anchor bonding length is B3=3m, the failure probabilities corresponding to the design values ​​of the pull-out strength of the seven anchors are 0.39%, 0.25%, 0.20%, 0.13%, 0.11%, 0.08% and 0.05% respectively. Under the design values ​​of the pull-out strength of the anchors selected in different numbers of anchors and anchor bonding lengths, using (C i , P fi ) respectively draw the relationship curve between slope failure probability and anchor pull-out strength, and query the required number of anchors, anchor bonding length and expected failure probability. Figure 8-10The relationship curve is used to determine the optimal pull-out strength of the anchor in the reinforced slope; for example, when the required number of anchors and the bonding length of the anchors are 4 and 2 m respectively, the expected failure probability is 0.45%, and the optimal pull-out strength design value of the anchor in the reinforced slope is 60 kPa.

[0016] Therefore, the comparison found that the influence of the pull-out strength of the anchor rod on the stability of the reinforced slope is often often ignored, resulting in insufficient consideration of the safety of the slope. The present invention designs different numbers of anchor rods and anchor rod bonding lengths, selects different anchor rod pull-out strength design values, and obtains the curve of the slope safety factor with the pull-out strength of the anchor rod under different numbers of anchor rods and anchor rod bonding lengths. Then, according to the specification, the anchor rod pull-out strength design value corresponding to all slope safety factors greater than 1 under different numbers of anchor rods and anchor rod bonding lengths is selected. Considering the uncertainty of soil parameters, the response surface method is used to calculate the slope failure probability with the above selected anchor rod pull-out strength design value under different numbers of anchor rods and anchor rod bonding lengths. Finally, the optimal value of the pull-out strength of the anchor rod in the reinforced slope is obtained according to the required number of anchor rods, anchor rod bonding length and expected failure probability. Engineering examples have verified that when the number of anchors and the bonding length are constant, the probability of slope failure decreases with the increase of the pull-out strength of the anchors. This fully verifies the influence of the pull-out strength of the anchors on the stability of the slope. Finally, the curve can be queried to determine the optimal pull-out strength of the anchors in the reinforced slope according to the required number of anchors, the bonding length of the anchors and the expected failure probability.

[0017] In actual engineering, after calculation, the number of anchor rods and bonding strength corresponding to the optimal pull-out strength can be further obtained, which can achieve better slope reinforcement effect in a more economical way.

[0018] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for determining the optimal pull-out strength of an anchor in a reinforced slope, characterized in that: The following steps are involved: A mathematical model of anchor-reinforced slope is established, different numbers of anchors are selected, and different anchor bonding lengths are designed under different numbers of anchors. Different anchor pull-out strengths are obtained under corresponding numbers of anchors and bonding lengths, and the slope safety factor corresponding to different anchor pull-out strengths is calculated using the limit equilibrium method. By changing the number of anchors and bonding lengths, the above calculation process is repeated until a curve diagram showing the relationship between the slope safety factor and the anchor pull-out strength under different numbers of anchors and bonding lengths is obtained. The design values ​​of anchor pull-out strength corresponding to all slopes with safety factors greater than 1 under different numbers of anchors and bonding lengths were selected, and the failure samples of the slope were obtained by using the Monte Carlo sampling method combined with the response surface method. The failure probability of the slope corresponding to the design values ​​of the anchor pull-out strength selected above was calculated, and the variation curves of slope failure probability and anchor pull-out strength under different numbers of anchors and bonding lengths were obtained. The optimal design value of anchor pull-out strength for reinforced slopes was obtained according to the variation curves.

2. The method for determining the optimal pull-out strength of an anchor in a reinforced slope according to claim 1, characterized in that: The process of determining the slope safety factor and anchor pullout strength curve includes the following steps: (1) Establish a mathematical model for anchor-bolt reinforced slopes and design X and Y The required number of anchor rods and the anchor rod bonding length are expressed as A1, A2, A3, ... A X ,B1,B2,B3,......B Y , given Z The design value of the pull-out strength of the anchor is denoted as C1, C2, C3, .... C Z ; (2) At a certain required number of anchor rods A i Bonding length B with anchor rod j Under this condition, change the pull-out strength of the anchor rod to obtain C1, C2, C3, ... Z The corresponding slope safety factors FS 1, FS 2, FS 3...... FS Z , using (C i , FS i ) i =1,2,…Z, plot the curve of slope safety factor changing with different anchor pull-out strengths, keep the number of anchors unchanged, change the required anchor bonding length, repeat the above calculation until the curve of slope safety factor changing with different anchor pull-out strengths under different anchor bonding lengths is obtained, then change the number of anchors, continue to repeat the above calculation process and finally obtain the curve of slope safety factor changing with different anchor numbers and anchor bonding lengths.

3. The method for determining the optimal pull-out strength of an anchor in a reinforced slope according to claim 1, characterized in that: The steps to obtain the variation curve of slope failure probability and anchor pull-out strength are as follows: (1) At a certain required number of anchor rods A i Bonding length B with anchor rod j Next, in Z The slope safety factor is selected one by one from the design values ​​of anchor pull-out strength FS A value greater than 1, and get the corresponding S The pull-out strength values ​​of the anchor rods are C1, C2, C3, .... C S By changing the required number of anchor rods and the anchor rod bonding length, the above operation is repeated until the required number of anchor rods and the anchor rod bonding length are obtained. Z The corresponding slope safety factor in the design value of the anchor pull-out strength FS For values ​​greater than 1, the obtained quantities are recorded as S 1, S 2, S 3,...... S r , r = X × Y , under different anchor numbers and anchor bonding lengths, the slope safety factor corresponding to the selected anchor pull-out strength design value is established one by one FS Response surface function between and soil strength parameters; (2) At a certain number of anchors A i , Anchor bonding length B j Next, select S The pull-out strength values ​​of the anchor rods are C1, C2, C3, .... C S At each selected anchor pull-out strength value, the cohesion c, internal friction angle of the soil parameters in the slope are calculated. φ Treated as a random variable ， Generated using Matlab software N soil layer parameter samples T1, T2, ..., T N , use the established response surface function to calculate T1, T2, ..., T N The corresponding safety factor FS 1, FS 2,……, FS N ;like F S i <1, then T i For failed samples, repeat the process to obtain W unstable samples, calculate the failure probability of the slope P fi = W / N , a total of corresponding S Slope failure probability P f1 , P f2 , P f3 ,...... P fS ,use( C i , P fi ) i =1,2,… S , draw the relationship curve between slope failure probability and selected anchor pull-out strength; (3) Maintain the number of anchor rods A i Keep the anchor bolt constant, change the anchor bolt bonding length, repeat step (2) to calculate different anchor bolt bonding lengths B1, B2, B3, ... B Y Below, the relationship curve between slope failure probability and selected anchor pull-out strength; (4) Repeat steps (2) and (3) by changing the number of anchor rods until the solution with different numbers of anchor rods A1, A2, A3, ... A is obtained. X and different anchor bonding lengths B1, B2, B3, ... B Y Below, the relationship curve between slope failure probability and the selected anchor pull-out strength.

4. The method for determining the optimal pull-out strength of an anchor in a reinforced slope according to claim 1, characterized in that: The process of obtaining the optimal design value of the pull-out strength of the reinforced slope anchor according to the variation curve is as follows: Query the anchor pull-out strength relationship curve to determine the optimal value of the anchor pull-out strength in the reinforced slope.

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