A method for designing a slope height

Abstract

A kind of slope height design method, comprising the following steps: (1) determining the geometric model of subgrade slope;(2) obtain the safety factor variation curve of slope height design value under different slope starting point positions;(3) establish the safety factor F S The response surface function between the soil strength parameters;(4) calculate the failure probability of slope;(5) draw the relationship curve of slope height design value H and failure probability;(6) draw the relationship curve of slope height design value and failure probability under different slope starting point positions of slope, finally according to the required slope starting point position and expected failure probability of engineering practice, query curve to determine the optimal slope height design value of slope.The present application can effectively select the optimal slope height design value of different slope starting point positions in a number of set slope starting point positions, so as to improve the safety factor of slope under the premise of meeting the engineering requirements, avoid or reduce the risk of instability of slope caused by its own design problem.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of safety evaluation and disaster prevention of roadbed slope, and particularly relates to a slope height design method. BACKGROUND

[0002] In the rapid development and construction of infrastructure such as railways and highways, the problem of disasters caused by slope instability is particularly prominent. Once slope instability occurs, it will disrupt normal traffic order, increase traffic pressure, and in severe cases, will pose a great threat to human life and property safety. Research shows that one of the main reasons for slope instability due to its own problems is the unreasonable design of the slope, including the selection of slope height and slope starting point position. In actual engineering, the position of the slope starting point is often determined according to the requirements of engineering planning and the surrounding environment, that is, the slope height design value should be optimized for the determined slope starting point position and meet the requirements of safety, economy and aesthetics. However, the influence of slope height design corresponding to different slope starting points on slope stability is also important, but it is often ignored in actual construction, leading to inadequate consideration of slope safety. Therefore, it is necessary to optimize the slope height design for different slope starting points. SUMMARY

[0003] To overcome the shortcomings of the prior art, the present application discloses a slope height design method, which aims to avoid slope instability caused by its own design problems and provides a new method that can effectively select the optimal slope height design value for different slope starting point positions.

[0004] To achieve the above-mentioned purpose, the technical solution of the present application is as follows:

[0005] A slope height design method, comprising the following steps:

[0006] (1) determining the geometric model of the roadbed slope, the soil parameters, the design of M slope starting point positions A1, A2,..., A M , and giving N slope height design values, denoted as H1, H2,..., H N ;

[0007] (2) at a certain slope starting point position A i , change the slope height design value, calculate the safety factor F Sj of the slope height H1, H2,..., H N , respectively, and use (H j , F Sj )j = 1, 2,..., N to draw the variation curve of the safety factor F Sj under different design slope heights, change the slope starting point position, and repeat the above calculation to obtain the safety factor variation curve of the slope height design value under different slope starting point positions.

[0008] (3) In M slope starting points and corresponding N slope height design values, F Sj of M slope starting points corresponding to k slope height design values(A i ,H j ) are filtered one by one, and the response surface method is combined to establish the response surface function of the safety factor F i and the soil strength parameters for the selected slope starting point position and slope height design value(A j ,H S ) one by one.

[0009] (4) At a selected slope starting point position A i and slope height design value H j , the soil strength parameters cohesion c and internal friction angle are taken as random variables, and n groups of random samples x1, x2,..x n are extracted according to the lognormal distribution using the Monte Carlo sampling method. The response surface function is used to calculate the safety factors F n ,F S1 ,...F S2 corresponding to x1, x2,..x Sn ; if F Si <1, the random sample x i is considered as a failure sample, and the calculation is repeated to obtain q failure samples, and then the failure probability p fi of the slope is calculated p fi =q / n.

[0010] (5) Keep the slope starting point position A i unchanged, change the slope height design value H j , and repeat step (4) to calculate the slope failure probabilities p f1 ,p f2 ,...p fk corresponding to the slope heights H1, H2,..., H k , and use(H j ,p fj ) to draw the relationship curve of the slope height design value H and the failure probability p f .

[0011] (6) Change the slope starting point position A i , repeat steps (4) and (5), calculate and draw the relationship curves of the slope height design value H and the failure probability p f at different slope starting point positions A1, A2,..., A M , and finally according to the required slope starting point position and expected failure probability of the project, the optimal slope height design value of the slope is determined by querying the curve.

[0012] The slope height design method has the beneficial effects that: the slope height design method can effectively select optimal slope height design values of different slope starting point positions from a plurality of set slope starting point positions, thereby improving the safety factor of the slope under the premise of meeting the engineering requirements, and avoiding or reducing the instability risk of the slope caused by the design problem of the slope itself. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 The flowchart of the present application;

[0014] Figure 2 The roadbed slope model diagram (slope starting point A1, d1=15m);

[0015] Figure 3 The roadbed slope model diagram (slope starting point A2, d2=10m);

[0016] Figure 4 The roadbed slope model diagram (slope starting point A3, d3=5m);

[0017] Figure 5 The safety factor change curve of the slope height design value under different slope starting point positions;

[0018] Figure 6 The relationship curve between the slope height design value and the failure probability under different slope starting point positions. DETAILED DESCRIPTION

[0019] The following description is only a preferred embodiment of the present application, and is not used to limit the protection scope of the present application, and any modification, equivalent replacement and improvement made within the spirit and principle of the present application should be included in the protection scope of the present application.

[0020] The slope height design method of the present application, as shown in Figure 1 , comprises the following steps:

[0021] (1) determining the geometric model of the roadbed slope, the soil parameters, and the design of M slope starting point positions A1, A2,..., A M , giving N slope height design values, denoted as H1, H2,..., H N ;

[0022] (2) under a certain slope starting point A i position, changing the slope height design value, respectively calculating the safety factors F N of the slope heights H1, H2,..., H Sj , and using (H j , F Sj )j=1, 2,..., N to draw the safety factor F Sjthe change curve of the safety factor F, change the position of the starting point of the slope, repeat the above calculation to obtain the change curve of the safety factor F of the slope height design value under different positions of the starting point of the slope;

[0023] (3) in the M starting points of the slope and the corresponding N slope height design values, F Sj >1 is selected one by one i , and the response surface method is used to establish the response surface function between the safety factor F j and the soil strength parameters for the selected position of the starting point of the slope and the slope height design value (A i , H j ); S

[0024] (4) under the selected position A i of the starting point of the slope and the slope height design value H j , the cohesion c and the internal friction angle of the soil strength parameters are taken as random variables, n groups of random samples x1, x2,..x n are extracted according to the lognormal distribution by using the Monte Carlo sampling method, and the safety factor F n , F S1 ,...F S2 corresponding to x1, x2,..x Sn is calculated by using the established response surface function; if F Si <1, the random sample x i is regarded as a failure sample, and the calculation is repeated to obtain q failure samples, and then the failure probability p fi of the slope is calculated as p i =q / n;

[0025] (5) keeping the position A j of the starting point of the slope unchanged, changing the slope height design value H k , repeating step (4) to calculate the slope failure probability p f1 , p f2 ,...p fk corresponding to the slope height H1, H2,..., H j , and using (H fj , p f ) to draw the relationship curve of the slope height design value H and the failure probability p i ;

[0026] (6) changing the position A M of the starting point of the slope, repeating steps (4) and (5), calculating and drawing the relationship curve of the slope height design value H and the failure probability p f ​The relationship curve is finally obtained according to the required slope starting point position and expected failure probability of the engineering practice, and the optimal slope height design value of the slope is determined by inquiring the curve.

[0027] The accompanying drawings are briefly described below Figures 2-4 The examples are described.

[0028] The subgrade slope is 35m wide, the base is 5m thick, the slope starting point position is dm away from the left edge of the slope base, the slope is composed of average soil, the average value of the cohesion c of the soil strength parameter is 10kpa, the standard deviation is 3, the internal friction angle The average value is 21°, the standard deviation is 6.3, and the unit weight is 20kN / m 3 The design slope height H is 4-16m, Figure 2 The slope starting point position A1 is d1=15m away from the left edge of the slope base, Figure 3 The slope starting point position A2 is d2=10m away from the left edge of the slope base, Figure 4 The slope starting point position A3 is d3=5m away from the left edge of the slope base.

[0029] The new technology provided by the application has the advantages that:

[0030] The subgrade slope geometry model is established by using the Slope / W module in the Geo-studio software, the slope starting point positions of the three slopes are designed as d1=15m, d2=10m and d3=5m, and the design values of the slope heights are H1=4m, H2=5m,..., and H 13 The safety factors of the slope heights H1=4m, H2=5m,..., and H 13 =16m are F S1 =1.364, F S2 =1.235,..., and F S13 =0.720 when the slope starting point position is d1=15m. 13 The safety factors of the slope heights H1=4m, H2=5m,..., and H S1 =16m are F S2 =2.117, F S13 =1.789,..., and F 13 =0.861 when the slope starting point position is d2=10m. S1 The safety factors of the slope heights H1=4m, H2=5m,..., and H S2 =16m are F S13 =2.762, F j =2.282,..., and F SjPlot the safety factor variation curves of the slope height design value for different slope initiation point positions, where j = 1, 2, ... 13. Figure 5 As shown.

[0031] Among the three slope initiation points A1, A2, and A3, the slope safety factor F is selected. Sj >1 corresponds to the design value H of the slope height. j These are (A1,H1), (A1,H2), (A1,H3), (A1,H4) corresponding to the starting point A1, (A2,H1), (A2,H2), (A2,H3), (A2,H4), (A2,H5), (A2,H6), (A2,H7), (A2,H8) corresponding to the starting point A2, and (A3,H1), (A3,H2), (A3,H3), (A3,H4), (A3,H5), (A2,H6), (A2,H7), (A2,H8) corresponding to the starting point A3, and (A3,H9), (A3,H4), (A3,H5), (A3,H6), (A3,H7), (A3,H8), ... 10 (A3,H) 11 (A3,H) 12 ); Use response surface methodology to select (A) i H j Establish the response surface function between the safety factor and the slope soil strength parameters.

[0032] Considering the uncertainty of slope soil strength parameters, at the starting point A of a certain slope... i Design value of slope height H j Below, using soil strength parameters cohesion c and internal friction angle... Treating them as random variables, their distribution is assumed to be log-normal. 10 samples are randomly selected using the Monte Carlo sampling method. 4 Group soil parameter samples x1, x2, ... x 10000 10 Calculations based on the established response surface function 4 The safety factor corresponding to the soil parameter sample group is denoted as F. S1 F S2 F S10000 If F Si If the value is less than 1, then the random sample x i Each failure sample is considered a separate failure sample, and this process is repeated to obtain q failure samples. The failure probability p of the slope is then calculated. fi =q / n. Maintain the slope initiation point position A. i Keeping the slope height unchanged, change the design value of the slope height and repeat the above calculations to obtain the relationship curves between different slope height design values ​​and failure probability; change the starting point location and repeat the above steps to obtain the relationship curves between different slope starting point locations, slope height design values, and failure probability. Figure 6As shown, at the slope starting point position A1 (d1=15m), the slope height of 4m, 5m, 6m, 7m, the corresponding failure probability is p f1 =0.24%, p f2 =3.23%, p f3 =20.06%, p f4 =41.92%; slope starting point position A2 (d2=10m), the slope height of 4m, 5m, 6m, 7m, 8m, 9m, 10m, 11m, the corresponding failure probability is p f1 =0.07%, p f2 =0.11%, p f3 =0.18%, p f4 =0.25%, p f5 =1.17%, p f6 =5.12%, p f7 =17.29%, p f8 =32.42%; slope starting point position A3 (d2=5m), the slope height of 4m, 5m, 6m, 7m, 8m, 9m, 10m, 11m, 12m, 13m, 14m, 15m, the corresponding failure probability is p f1 =0.01%, p f2 =0.02%, p f3 =0.09%, p f4 =0.15%, p f5 =0.20%, p f6 =0.28%, p f7 =0.33%, p f8 =1.33%, p f9 =4.28%, p f10 =11.53%, p f11 =23.29%, p f12 =37.38%. According to the actual needs of the slope starting point position and the desired failure probability, the relationship curve is queried to determine the optimal slope height design value of the slope, for example, when the required starting point position is A2 (d2=10m) and the desired failure probability is 1%, the optimal slope height design value of the slope is 7.82m. Figure 6

[0033] ​Therefore, it is found that the influence of slope height design corresponding to different slope starting points on the stability of the slope is often ignored, leading to insufficient consideration of the safety of the slope, and the present application changes the slope height design value by designing different slope starting point positions of the slope, calculates the safety factor change curve of different slope height designs, screens the slope height design value corresponding to the slope starting point position of the safety factor greater than 1, considers the uncertainty of the soil parameters, calculates the failure probability corresponding to the slope height design value under different slope starting point positions by using the Monte Carlo method, and obtains the optimal slope height design value of the slope according to the required slope starting point position and expected failure probability of the engineering practice. Figure 5 As shown in the figure, when the slope starting point position is certain, the safety factor of the slope decreases with the increase of the slope height design value, under the slope starting point position A1(d1=15m), the maximum slope height design value meeting the safety requirement is 7.36m, under the slope starting point position A2(d1=10m), the maximum slope height design value meeting the safety requirement is 11.95m, under the slope starting point position A3(d1=5m), the maximum slope height design value meeting the safety requirement is 15.93m, and the failure probability of the slope under the three slope starting point positions increases with the increase of the slope height design value. The above fully verifies the influence of the slope height on the stability of the slope when the slope is cut, and verifies the effectiveness of the present application, and the optimal slope height design value of the slope is determined according to the required slope starting point position and expected failure probability of the engineering practice.

Claims

1. A method of designing a slope height reduction, characterized by comprising The following steps: (1) determine the geometric model of the roadbed slope, the soil parameters, the design M slope starting point positions, A1, A2,..., A M , give N slope height design values, denoted as H1, H2,..., H N ; (2) in a certain side slope starting point A i position, change the slope height design value, respectively, calculate the slope height H1, H2,..., H N The safety factor F Sj , using (H j , F Sj ) j = 1, 2,..., N, draw the safety factor F Sj The change curve under different design slope height, change the starting point position, repeat the above calculation to obtain the safety factor change curve of the slope height design value under different starting point position; (3) In M slope starting points and corresponding N slope height design values, F Sj of the M slope starting points corresponding to k slope height design values (A i ,H j ) are selected one by one, and the response surface method is combined to establish the response surface function between the safety factor F i and the soil strength parameters for the selected slope starting point position and slope height design value (A j ,H S ). (4) at a selected position A of a certain slope starting point i and slope height design value H j , the soil strength parameters cohesion c and internal friction angle are taken as random variables, and n groups of random samples x1, x2,..x n are extracted according to a lognormal distribution by using a Monte Carlo sampling method, the corresponding safety factors F n are calculated by using the built response surface function for x1, x2,..x S1 , F S2 ,..F Sn ; if F Si <1, the random sample x i is regarded as a failure sample, and the calculation is repeated to obtain q failure samples, and then the failure probability p fi of the slope is calculated as p fi =q / n; (5) Keep the slope starting point position A i unchanged, change the slope height design value H j , repeat step (4) to calculate the slope height H1, H2, …, Hn in turn k The corresponding slope failure probability p f1 , f2 … p fk , use (H j , p fj ) to draw the relationship curve of slope height design value H and failure probability p f ; (6) Change the position of the slope starting point A i , repeat steps (4), (5), calculate and draw the different slope starting point position A1, A2,..., A M , the relationship curve of the slope height design value H and the failure probability p f , finally according to the actual engineering required slope starting point position and the expected failure probability, query curve to determine the optimal slope height design value.

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