A multi-factor coupling gravity type retaining wall reliability evaluation and optimization method

Abstract

The application provides a multi-factor coupled gravity retaining wall reliability evaluation and optimization method, and belongs to the technical field of geotechnical engineering. The method comprises the following steps: a physical model containing parameters such as self-weight, friction coefficient, height, filling weight, and compaction degree is constructed; a multi-factor dynamic coupling model is established, including a water level time-varying model, a seismic coefficient probability model, and a compaction degree degradation model; a limit state function of comprehensive earth pressure, water pressure, and seismic inertia force is constructed; a time-varying failure probability is calculated through random numerical simulation; the importance of each factor is quantitatively evaluated by using a standardized index; optimization measures such as improving compaction degree, reducing water level fluctuation, and increasing self-weight are proposed, and the effects are verified. The method solves the problems of single-factor analysis, static modeling, and qualitative evaluation of importance in the traditional method, realizes dynamic coupling analysis of three factors such as earthquake, water level fluctuation, and compaction degree degradation, and provides a scientific basis for the design and maintenance of gravity retaining walls.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of geotechnical engineering, and particularly relates to a multi-factor coupling gravity retaining wall reliability evaluation and optimization method. BACKGROUND

[0002] The gravity retaining wall is a kind of retaining structure relying on its own gravity to maintain stability, which is widely used in road, railway, water conservancy and other infrastructure construction. The reliability of gravity retaining wall is directly related to the safety and economic benefits of the project, so it is of great significance to accurately evaluate its reliability.

[0003] The traditional reliability analysis method of gravity retaining wall is mainly based on deterministic analysis or simplified probabilistic analysis. In deterministic analysis, the safety factor method is usually used to consider various uncertain factors through the safety factor determined by experience. However, this method cannot quantitatively describe the failure probability of the structure, and it is also difficult to reflect the randomness and time-varying nature of various influencing factors.

[0004] With the development of reliability theory, probabilistic analysis methods have been gradually applied to the reliability evaluation of gravity retaining wall. The existing probabilistic analysis methods have significant limitations in dealing with influencing factors. First, most studies only consider the influence of a single factor, such as only considering the effect of earthquake or only considering the effect of soil pressure, ignoring the interaction and coupling effect between multiple factors. Even if there are studies considering multi-factor analysis, they mostly use static treatment method, regarding each factor as a time-invariant random variable, failing to reflect the characteristics of each factor changing over time in actual engineering.

[0005] In engineering practice, the key factors affecting the stability of gravity retaining wall have obvious time-varying characteristics. Water level will fluctuate periodically and randomly due to seasonal changes, rainfall and other factors; the compaction degree of the fill will gradually deteriorate over time, while being affected by various random factors; the earthquake action has randomness and uncertainty. The existing analysis methods simplify these time-varying factors as constant values or static random variables, resulting in a large deviation between the analysis results and the actual engineering.

[0006] In addition, the existing methods mainly rely on engineering experience and qualitative judgment in the evaluation of the importance of influencing factors, lacking quantitative evaluation indicators and scientific evaluation methods. This makes it difficult for engineers to accurately identify key influencing factors and to develop targeted optimization measures.

[0007] In terms of selection and verification of optimization measures, the traditional methods are mainly based on engineering experience and qualitative analysis, lacking quantitative effect verification means. Engineers often choose optimization measures based on experience, but cannot accurately predict the specific improvement effect of these measures on the reliability of retaining wall, nor can they compare the effect difference of different optimization measures, leading to the blindness of optimization scheme selection.

[0008] The prior art also has the problem of limited scope of application. Many research methods consider factors such as external load and soil cohesion, but these factors are not universal in actual engineering, so the related methods are only applicable to specific types of engineering. At the same time, some important universal influencing factors, such as water pressure and seismic inertia force, are not fully considered in the existing methods.

[0009] Therefore, the existing reliability evaluation method of gravity retaining wall has the technical problems of strong single-factor analysis limitation, large deviation between static model and engineering practice, low quantitative degree of important factor evaluation, and lack of verification means for optimization measures. SUMMARY

[0010] The purpose of the present application is to provide a multi-factor coupled gravity retaining wall reliability evaluation and optimization method that can comprehensively consider multi-factor dynamic coupling, accurately reflect time-varying characteristics, quantitatively evaluate the importance of influencing factors, and scientifically verify the optimization effect.

[0011] To achieve the above-mentioned purpose, the present application realizes the following technical solutions:

[0012] A multi-factor coupled gravity retaining wall reliability evaluation and optimization method, characterized in that it comprises the following steps:

[0013] S1: Construct a physical parameter model of the gravity retaining wall, the physical parameters including the self-weight of the gravity retaining wall W , the base friction coefficient , the height of the gravity retaining wall , the effective unit weight of the fill , the unit weight of water , the initial internal friction angle , the influence coefficient of compaction degree on internal friction angle , the initial compaction degree , the annual degradation rate of compaction degree , the minimum compaction degree , and the standard deviation of compaction degree fluctuation ;

[0014] S2: Establish a multi-factor dynamic coupling model, including a water level time-varying model, a seismic coefficient probability model, and a fill compaction degree degradation model;

[0015] S3: Establish a limit state function , wherein is the earth pressure, is the water pressure, is the seismic inertia force;

[0016] S4: Calculate the time-varying failure probability of the gravity retaining wall by a random numerical simulation method.

[0017] S5: Calculate the importance index of each influencing factor and identify the key influencing factors;

[0018] S6: Propose optimization measures based on the importance analysis results and quantitatively verify the optimization effect.

[0019] Further: the water level time-varying model in step S2 is:

[0020] ,

[0021] wherein is the average water level, is the water level fluctuation amplitude, t is the time variable, is a random fluctuation term and obeys normal distribution , is the water level fluctuation standard deviation.

[0022] Further: the seismic coefficient probability model in step S2 is that the seismic coefficient k obeys lognormal distribution, and the calculation steps include:

[0023] generating a standard normal random number ;

[0024] calculating the standard deviation of the lognormal distribution ;

[0025] calculating the mean value of the lognormal distribution ;

[0026] calculating ;

[0027] taking the exponential to obtain the seismic coefficient ,

[0028] wherein is the mean value of the seismic coefficient, is the standard deviation of the seismic coefficient.

[0029] Further: the filling compaction degree degradation model in step S2 is:

[0030] ,

[0031] wherein is a random fluctuation term and obeys normal distribution ;

[0032] The corresponding internal friction angle calculation formula is:

[0033] .

[0034] Further: the soil pressure in step S3 is The calculation formula is:

[0035] ,

[0036] Wherein the active earth pressure coefficient ;

[0037] The water pressure The calculation formula is:

[0038] ;

[0039] The seismic inertial force The calculation formula is:

[0040] .

[0041] Further: the random numerical simulation method in the step S4 includes:

[0042] Generating random samples of the seismic coefficient , water level fluctuation and compaction fluctuation ;

[0043] According to the current time , the water level , compaction and internal friction angle ;

[0044] The earth pressure , water pressure and seismic inertial force ;

[0045] The limit state function Z value is calculated;

[0046] The number of samples of Z≤0 is counted, and the failure probability .

[0047] Further: the importance index calculation formula in the step S5 is:

[0048] ,

[0049] Wherein is the mean value of the i th factor in the failure sample, is the mean value of the i th factor in the whole sample, is the standard deviation of the i th factor in the whole sample.

[0050] Further: the optimization measures in the step S6 include at least one of the following:

[0051] Increase the initial compaction degree of filling K 0;

[0052] Reducing water level fluctuation amplitude A ;

[0053] Increasing gravity retaining wall self-weight W .

[0054] Further, the quantitative verification of the optimization measures comprises:

[0055] Re-performing random numerical simulation after modifying the corresponding parameters;

[0056] Calculating the failure probability curve of the optimized gravity retaining wall;

[0057] Comparing and analyzing the failure probability curve after optimization with the original curve to evaluate the optimization effect.

[0058] Compared with the prior art, the present application has the following beneficial effects:

[0059] 1. The present application dynamically couples three key factors of seismic action, water level fluctuation and filling soil compaction degradation to model, overcomes the limitation of the prior art which only considers single factor or static multi-factor analysis, and makes the analysis result more in line with the complexity and time variation of the engineering practice.

[0060] 2. The present application establishes a time-varying-random double composite model, considers the time-varying characteristics such as seasonal water level fluctuation and compaction degradation year by year, and solves the problem of large deviation of the traditional static model from the engineering practice.

[0061] 3. The present application establishes a standardized importance index calculation formula, solves the problem of the traditional method relying on engineering experience and qualitative judgment, and can quantitatively identify the key influencing factors.

[0062] 4. The present application establishes a quantitative verification method, which can evaluate the optimization effect by comparing the failure probability curves before and after optimization, and solves the problem of the traditional method lacking quantitative verification means and relying on engineering experience. BRIEF DESCRIPTION OF DRAWINGS

[0063] Figure 1 is a simulation flowchart;

[0064] Figure 2 is a gravity retaining wall failure probability graph;

[0065] Figure 3 is an influence factor importance graph;

[0066] Figure 4 is an optimization measure effect graph;

[0067] Figure 5 is a Weifang pumped storage power station gravity retaining wall failure probability graph. DETAILED DESCRIPTION

[0068] The technical solutions of the present application will be described clearly and completely in combination with the drawings. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0069] In the description of the present application, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer" and the like indicate the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application. In addition, the terms "first", "second", "third" are only for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0070] The multi-factor coupled gravity retaining wall reliability evaluation and optimization method provided by the present application realizes by constructing a gravity retaining wall physical parameter model, establishing a multi-factor dynamic coupling model, calculating time-varying failure probability, analyzing the importance of influencing factors and proposing optimization measures.

[0071] First, a gravity retaining wall physical parameter model is constructed. The model includes the physical parameters of the gravity of the gravity retaining wall W , the base friction coefficient , the height of the gravity retaining wall , the effective unit weight of the fill , the unit weight of water , the initial internal friction angle , the influence coefficient of compaction degree on internal friction angle , the initial compaction degree , the annual degradation rate of compaction degree , the minimum compaction degree , and the standard deviation of compaction degree fluctuation . In order to balance between calculation efficiency, engineering practicability and model accuracy, reasonable assumptions are made for the physical model: the gravity retaining wall is a rigid structure, and its deformation is not considered to affect the stability; the fill is a homogeneous material, and its physical properties are uniformly distributed in space; the degradation of compaction degree is linear and affected by random fluctuations.

[0072] Next, a multi-factor dynamic coupling model is established, including a water level time-varying model, an earthquake coefficient probability model and a fill compaction degree degradation model. The water level time-varying model considers the periodic variation and random fluctuation characteristics of the water level, and the expression is , where is the average water level, is the water level fluctuation amplitude, t is the time variable, is the random fluctuation term and obeys normal distribution , is the water level fluctuation standard deviation. The model assumes that the water level fluctuation has periodicity, the period is 1 year, the random fluctuation term obeys normal distribution, which represents the random change of water level. The traditional research method takes the water level as a constant value, ignoring the influence of water level change. The present invention introduces the time variable t and the normal distribution disturbance term , and builds a time-varying-random double composite model, which is more in line with the actual hydrological environment than the traditional static model.

[0073] In the seismic coefficient probability model, the seismic coefficient k obeys lognormal distribution to reflect its non-negative property. The specific calculation steps are: generating standard normal random number ; calculating the standard deviation of lognormal distribution ; calculating the mean of lognormal distribution ; calculating ; taking the exponential to get the seismic coefficient . The model assumes that the earthquake is independent in time, and does not consider the influence of aftershocks or earthquake sequence.

[0074] The fill compaction degradation model is , where is the random fluctuation term and obeys normal distribution . The traditional research method sets the fill compaction as a constant value, ignoring the influence of compaction degradation on the retaining wall. The present invention establishes a linear degradation model of compaction, which realizes the dynamic correlation between compaction and internal friction angle through the coefficient α , and reveals the time-varying law of material performance. The corresponding internal friction angle calculation formula is . The model assumes that the compaction degrades linearly with time, the degradation rate is a , the random fluctuation term obeys normal distribution, and the compaction will not be lower than the minimum value K .

[0075] Then the limit state function is established. The traditional research method considers the static combination of soil pressure, external load and soil cohesion, or only considers the action of soil pressure, which can only be applied to the retaining wall of a specific project. Because different retaining walls of different projects may have no external load and non-cohesive soil, at the same time, the external load and cohesion have little effect on the failure probability of the retaining wall, in order to improve the calculation efficiency and expand the application range, the external load and cohesion are not considered, and the action of water pressure and earthquake force which exist in all retaining walls is considered instead. The limit state function is , where the soil pressure , the active earth pressure coefficient ; the water pressure ; seismic inertial force . When Z ≤0, the gravity retaining wall fails.

[0076] The time-varying failure probability of the gravity retaining wall is calculated by using the random numerical simulation method. By generating random numbers, the MATLAB program is used to simulate the failure probability of the gravity retaining wall and the importance of the influencing factors, as shown in the simulation flowchart of Figure 1 . The specific steps include: initializing parameters, setting the physical parameters of the gravity retaining wall, water level parameters, seismic parameters and random number simulation parameters; generating random samples of seismic coefficients , water level fluctuations and compaction degree fluctuations ; calculating the water level , compaction degree and internal friction angle according to the current time ; calculating the earth pressure , water pressure and seismic inertial force ; calculating the limit state function Z value; counting the number of samples with Z ≤0, and calculating the failure probability . By simulating a large number of samples (such as 10 million samples), the failure probability curve of the gravity retaining wall with time can be obtained, as shown in Figure 2 , the results show that the failure probability of the gravity retaining wall increases linearly with time.

[0077] The importance index of each influencing factor is calculated to identify the key influencing factors. The traditional method mainly relies on experience to determine the importance of the influencing factors. The invention quantitatively calculates the standardized importance index of the earthquake, water level and compaction degree for the failure samples, and the calculation formula is: , wherein is the mean value of the i th factor in the failure sample, is the mean value of the i th factor in all samples, is the standard deviation of the i th factor in all samples. Through the importance analysis, it can be found that the importance of the influencing factors, as shown in Figure 3 , shows that the importance ranking is: earthquake factor > water level fluctuation > filling compaction degree, and the earthquake factor is the main factor causing the failure of the gravity retaining wall, and the importance of water level fluctuation and filling compaction is similar and much lower than that of the earthquake factor.

[0078] Based on the importance analysis results, optimization measures are proposed and the optimization effects are quantitatively verified. According to the analysis results, three optimization measures are proposed: improving the initial compaction degree K0 of the filling, which is realized by improving the construction process or using higher performance filling materials, the principle is to increase the internal friction angle of the filling φ , so as to reduce K a and P soil ; reducing the water level fluctuation amplitude A , which is realized by building drainage facilities or setting water retaining structures, the principle is to reduce the fluctuation range of P water , improve the stability of the gravity retaining wall; increasing the gravity of the gravity retaining wall W , which is realized by increasing the volume of the gravity retaining wall or using higher density materials, the principle is to improve the anti-sliding stability of the gravity retaining wall, directly increase the value of the limit state function Z .

[0079] The quantitative verification of the optimization measures includes: re-running the MATLAB program simulation after modifying the corresponding parameters, calculating the failure probability curve of the optimized gravity retaining wall, comparing and analyzing the optimized failure probability curve with the original curve, and evaluating the optimization effect. As shown in the optimization measure effect diagram Figure 4 : improving the compaction degree effectively reduces the failure probability, the economy and feasibility are relatively high, and it is suitable for high filling slope, earthquake active area and long-term use gravity retaining wall; reducing the water level fluctuation reduces the failure probability effect is not obvious, it is suitable for gravity retaining wall near water, area with heavy rainfall, soft soil foundation; increasing the gravity of the gravity retaining wall reduces the failure probability effect is the most obvious, but the cost is higher, it is suitable for high intensity earthquake area, steep slope gravity retaining wall and high reliability engineering.

[0080] The specific application of the present application is illustrated by taking a pumped storage power station as an example. The gravity retaining wall is arranged at the edge of the site of the power station, the wall height is 6m, the top width is 2m, the bottom width is 4m, the bottom and back of the gravity retaining wall are sand. According to the actual situation of the gravity retaining wall and the soil, the physical parameters are set as follows: the gravity of the gravity retaining wall W =420kN / m, the friction coefficient of the base μ=0.4, the height of the gravity retaining wall =5m, the effective gravity of the filling =18kN / m³, the gravity of water =10kN / m³, the initial internal friction angle =30°, the compaction degree influence coefficient on the internal friction angle =0.1° / %, the initial compaction degree =96%, the compaction degree annual degradation rate =0.3% / year, the minimum compaction =70%, compaction degree fluctuation standard deviation =2%.

[0081] The main steps of the method of the application are: preparing a physical parameter table according to the actual situation of the gravity retaining wall and the soil quality; modifying the parameter settings in the MATLAB code; running the program and analyzing the results. According to the engineering economy, the method of improving the compaction degree of the filling soil is used to improve the safety of the gravity retaining wall. The program running results can clearly show the change curve of the failure probability of the gravity retaining wall within 50 years, such as the gravity retaining wall failure probability graph of Weifang pumped storage power station as shown in the figure. Figure 5 The safety management personnel of the power station can quantitatively analyze the safety of the gravity retaining wall, and formulate the safety maintenance cycle and scheme of the gravity retaining wall according to the failure probability curve, so as to improve the reliability of the gravity retaining wall.

[0082] The method of the application comprehensively considers the dynamic coupling effect of various influencing factors, solves the problem of the traditional research method which only considers a single factor or statically considers multiple factors; through MATLAB program generation random number simulation, considering water level fluctuation, compaction degree degradation, seismic fluctuation solves the problem of the traditional research method which does not consider time variation by using static model; through statistical method, the importance of each influencing factor is quantitatively evaluated, and the effect is quantitatively analyzed, which solves the problem of the traditional method which relies on engineering experience and lacks data support.

[0083] The above embodiments only serve to illustrate the technical concept and characteristics of the application, and the purpose is to enable those skilled in the art to understand the content of the application and implement it, and cannot limit the protection scope of the application. Any equivalent transformation or modification made according to the spirit and essence of the application should be covered within the protection scope of the application.

Claims

1. A multi-factor coupled gravity retaining wall reliability evaluation and optimization method, characterized in that, The method comprises the following steps: S1: constructing a gravity retaining wall physical parameter model, the physical parameters including gravity of the gravity retaining wall W , base friction coefficient , height of the gravity retaining wall , effective gravity of the fill , gravity of water , initial internal friction angle , influence coefficient of compaction degree on internal friction angle , initial compaction degree , annual degradation rate of compaction degree , minimum compaction degree , and compaction degree fluctuation standard deviation ; S2: a multi-factor dynamic coupling model is established, including a water level time-varying model, a seismic coefficient probability model and a fill compaction degradation model; The water level time-varying model is: ， wherein is the average water level, is the water level fluctuation amplitude, t is the time variable, is a random fluctuation term and is subject to a normal distribution , is the water level fluctuation standard deviation; The seismic coefficient probability model is that a seismic coefficient k obeys a lognormal distribution, and the calculation steps thereof comprise: Generating standard normal random numbers ; Computing a standard deviation of a lognormal distribution ; Computing the mean of a lognormal distribution ; Computing ; Taking the exponent gives the seismic coefficient , wherein is the mean of the seismic coefficients, is the standard deviation of the seismic coefficients; The fill compaction degradation model is: ， wherein is a random fluctuation term and obeys a normal distribution ; A corresponding internal friction angle calculation formula is: ； S3: Establishing limit state function wherein is the earth pressure, is the water pressure, is the seismic inertia force; The earth pressure The calculation formula is: ， where the active earth pressure coefficient ; The water pressure The calculation formula is: ； The seismic inertial force The calculation formula is: ； S4: a time-varying failure probability of the gravity retaining wall is calculated by using a random numerical simulation method; S5: an importance degree index of each influencing factor is calculated to identify a key influencing factor; S6: optimization measures are proposed based on the importance degree analysis result, and the optimization effect is quantitatively verified.

2. The reliability evaluation and optimization method of multi-factor coupled gravity retaining wall according to claim 1, characterized in that, The random numerical simulation method in the step S4 comprises: Generating seismic coefficients , water level fluctuations and compaction fluctuations of random samples; According to the current time Computing water level , compaction and internal friction angle ; calculated earth pressure , water pressure and seismic inertia forces ; Computing a limit state function Z a value; Statistics Z Number of samples with ≤ 0, calculate failure probability .

3. The reliability evaluation and optimization method of multi-factor coupled gravity retaining wall according to claim 1, characterized in that, The importance degree index calculation formula in the step S5 is: ， wherein is the mean of the factor number i in the failed samples, is the mean of the factor number i in the entire sample, is the mean of the factor number i in the entire sample.

4. The reliability evaluation and optimization method of multi-factor coupled gravity retaining wall according to claim 1, characterized in that, The optimization measures in the step S6 comprise at least one of the following: Increasing initial compaction of fill K 0; Reducing water level fluctuation A ; Increasing the self-weight of gravity retaining walls W .

5. The reliability evaluation and optimization method of multi-factor coupled gravity retaining wall according to claim 1, characterized in that, The quantitative verification of the optimization measures comprises: After the corresponding parameters are modified, the random numerical simulation is performed again; A failure probability curve of the optimized gravity retaining wall is calculated; The optimized failure probability curve is compared with the original curve to analyze and evaluate the optimization effect.

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