Reliability analysis method suitable for sliding failure of deep foundation pit

Abstract

The invention relates to a reliability analysis method suitable for sliding failure of a deep foundation pit, and belongs to the technical field of reliability analysis of geotechnical engineering. The invention discloses a reliability analysis method suitable for sliding failure of a deep foundation pit. The method comprises the following steps: collecting landform and soil physical and mechanical parameters of an excavation site of the deep foundation pit; establishing a finite element model according to the construction design drawing and the physical and mechanical parameters of the soil body; monitoring equipment is installed to monitor the working state of the foundation pit in real time, the result is compared with a finite element model result, and parameters of the finite element model are updated in real time; units in the finite element model are extracted, and a random field model is established according to the distribution condition of soil material parameters; calculating a safety coefficient under each random field model according to a strength reduction method; and converting the safety coefficient into a functional function, calculating the first four moments of the functional function by adopting a high-order moment method, and solving the failure probability and reliability of the foundation pit slippage. The risk of foundation pit slippage failure is evaluated, and the risk of foundation pit slippage is predicted and monitored in real time.

Description

Technical Field

[0001] The present invention relates to a reliability analysis method applicable to the slip failure of deep foundation pits, belonging to the technical field of reliability analysis of geotechnical engineering. Background Art

[0002] As an important step in urban underground space development, deep foundation pits are located in urban areas where the geological environment of the foundation pit is complex and there are many large buildings around. The construction process has great safety risks.

[0003] In geotechnical engineering, soil slip is a failure mode with great harm. Especially for urban deep foundation pits, during the excavation process of urban deep foundation pits, the original balance of the soil mass is destroyed, and slip instability failure is extremely likely to occur. At the same time, the on-site geology is complex and changeable, such as soil type, groundwater level change, geological structure. These factors will bring uncertainties to the support design and can all lead to the occurrence of foundation pit slip. Therefore, it is necessary to establish a reliability analysis method for foundation pit slip to evaluate the risk of foundation pit slip failure and predict and monitor the risk of foundation pit slip in real time. Summary of the Invention

[0004] The purpose of the present invention is to provide a reliability analysis method applicable to the slip failure of deep foundation pits in view of the problems existing in the prior art.

[0005] The technical solution provided by the present invention to solve the above technical problems is: a reliability analysis method applicable to the slip failure of deep foundation pits, including the following steps:

[0006] Step S10: Collect the topographic and geomorphic features and soil physical and mechanical parameters at the deep foundation pit excavation site;

[0007] Step S20: Establish a finite element model according to the construction design drawings and soil physical and mechanical parameters;

[0008] Step S30: Install monitoring equipment to monitor the working state of the foundation pit in real time to obtain on-site monitoring data, and compare it with the results of the finite element model to update the parameters of the finite element model in real time;

[0009] Step S40: Extract the elements in the finite element model, and establish a random field model according to the distribution of soil material parameters;

[0010] Step S50: Calculate the safety factor under each random field model according to the strength reduction method;

[0011] Step S60: Transform the safety factor into a performance function, calculate the first four moments of the performance function by using the high-order moment method, and calculate the probability distribution function and probability density function of the performance function;

[0012] Step S70. Finally, calculate the failure probability P of the foundation pit sliding according to the probability distribution function and probability density function of the function. f and the reliability β.

[0013] A further technical solution is that the physical and mechanical parameters of the soil include unit weight, elastic modulus, Poisson's ratio, internal friction angle, cohesion, and dilation angle.

[0014] A further technical solution is that the specific process of step 20 is as follows:

[0015] Step S21. Establish a geometric model: Draw a two-dimensional model of the cross-section in the finite element software according to the construction design drawings.

[0016] Step S22. Define material properties: Input the physical and mechanical parameters of different soil layers; according to the information of the supporting structure, input the elastic modulus, density, and Poisson's ratio of concrete or steel.

[0017] Step S23. Set boundary conditions and contact relationships: Apply constraints to the bottom and sides of the model. Fix all degrees of freedom at the bottom and only restrict the horizontal displacement at the sides; set surface-to-surface contact between the pile and the soil. The normal model is a hard contact, and the tangential property is selected as the penalty function; apply surface load pressure according to the instantaneous load conditions of the ground buildings; apply the corresponding water pressure according to the hydrogeological data, apply the supporting structure load according to the supporting structure conditions, and gradually apply the support reaction force according to the construction process.

[0018] Step S24. Mesh generation: Use the built-in mesh generation function of the finite element software to divide the mesh.

[0019] A further technical solution is that in step S30, according to the actual construction sequence, set multiple analysis steps to simulate the entire construction process, simulate the gradual excavation and installation of the supporting structure; at the same time, set positions corresponding to the on-site monitoring points in the model to compare the calculation results of the finite element model with the on-site monitoring data.

[0020] A further technical solution is that the specific process of step S40 is as follows:

[0021] Step S41. Determine the distribution of each soil layer parameter: According to the geological report and on-site monitoring data, determine the distribution of the elastic modulus, density, internal friction angle, and cohesion of each soil layer in the foundation pit.

[0022] Step S42. Extract elements and randomly assign values: Extract the central point coordinates of each element in the finite element model, import them into the mathematical analysis software, and at the same time write a program in the mathematical software to input the randomly generated material parameter data into the finite element model.

[0023] A further technical solution is that in step S50, the parameters cohesion and internal friction angle characterizing soil plasticity are reduced through a formula, and each reduction is calculated once. After continuous repeated reduction calculations, when a continuous plastic slip surface appears in the finite element model, a sudden change in the displacement of the characteristic point, or the finite element model calculation is interrupted, the field variable K is output at this time. r It is the safety factor.

[0024] A further technical solution is that the formula in step S50 is:

[0025] c′ = c / K r

[0026]

[0027] In the formula: c is the initial cohesion of the rock and soil mass; is the initial friction angle of the soil; K r It is the safety factor.

[0028] A further technical solution is that the calculation formula in step S60 includes:

[0029]

[0030] In the formula: μ G , δ G are respectively the mean and standard deviation of the performance function; β 2M is the second-order reliability index; α 3G is its third-order central moment; β 4M is the fourth-order reliability index.

[0031] A further technical solution is that in step S70, the minimum value of β 2M , β 3M-S , β 3M-L , β 4M is taken as the reliability β of the foundation pit stability.

[0032] Advantages of the present invention: The present invention evaluates the risk of foundation pit slip failure and predicts and monitors the risk of foundation pit slip in real time. Brief Description of the Drawings

[0033] Figure 1 It is the flow chart of the present invention;

[0034] Figure 2 It is the schematic diagram of the finite element model of the deep foundation pit;

[0035] Figure 3 It is the diagram of the internal friction angle random field model;

[0036] Figure 4 It is the diagram of the cohesion random field model;

[0037] Figure 5 It is a scatter plot of the functional function;

[0038] Figure 6 It is a probability distribution diagram of the functional function. Specific implementation manners

[0039] Next, the technical solutions of the present invention will be clearly and completely described in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0040] As Figure 1 shown, a reliability analysis method applicable to the sliding failure of deep foundation pits provided by the present invention includes the following steps:

[0041] Step S10: Collect the topographic and geomorphic features, physical and mechanical parameters of the soil mass (including unit weight, elastic modulus, Poisson's ratio, internal friction angle, cohesion, dilation angle), topographic and geological structures, groundwater hydrological data, etc. of the deep foundation pit excavation site, and consider the impact of the foundation pit excavation on the surrounding buildings, traffic, pipelines and other infrastructure.

[0042] Step S20: Establish a finite element model according to the construction design drawings and the physical and mechanical parameters of the soil mass.

[0043] Use finite element software such as abaqus and Flac3D to establish a two-dimensional finite element model of the foundation pit and its surrounding environment, define the material parameters of each soil layer, the material parameters of the support structure, the construction process, simulate the performance changes of the foundation pit support in different construction stages, and at the same time adjust the model parameters based on the on-site monitoring data, and set reasonable constraint conditions and boundary conditions based on the design drawings and the topographic and geomorphic conditions of the foundation pit.

[0044] The specific establishment process is as follows:

[0045] Step S21: Establish a geometric model: Draw a two-dimensional model of the cross-section in the finite element software according to the construction design drawings.

[0046] Step S22: Define material properties: Input the physical and mechanical parameters of different soil layers; according to the support structure information, input the elastic modulus, density, and Poisson's ratio of concrete or steel.

[0047] Step S23: Set boundary conditions and contact relationships: Apply constraints to the bottom and sides of the model, fix all degrees of freedom at the bottom, and only restrict the horizontal displacement at the sides; set surface-to-surface contact between the pile and the soil mass, the normal model is hard contact, and the tangential attribute is selected as the penalty function, and the friction coefficient is ( (where $\varphi$ is the angle of internal friction); Apply surface load pressure according to the instantaneous load conditions of the ground buildings; Apply corresponding water pressure according to the hydrogeological data, apply the supporting structure load according to the supporting structure conditions, and gradually apply the support reaction force according to the construction process;

[0048] Step S24, Mesh generation: Use the mesh generation function built in the finite element software to generate the mesh. Use finer meshes near the soil layer and the supporting structure and in the stress concentration areas, and use coarser meshes in areas far from these regions.

[0049] Step S30, Install monitoring equipment to monitor the working state of the foundation pit in real time to obtain on-site monitoring data, and compare it with the results of the finite element model to update the parameters of the finite element model in real time;

[0050] Among them, according to the actual construction sequence, set multiple analysis steps to simulate the entire construction process, simulate the progressive excavation and installation of the supporting structure; At the same time, at the positions corresponding to the on-site monitoring points in the model, use the deformation nephogram to display the stress-strain and strain displacement under each analysis step, and extract the time history change diagram of the key nodes to display the calculation results, compare the calculation results of the finite element model and the on-site monitoring data, and adjust the parameters of the finite element model to make it better simulate the actual situation;

[0051] Step S40, Extract the elements in the finite element model and establish a random field model according to the distribution of the soil material parameters;

[0052] Combine the properties of each soil layer to determine the probability distributions of the elastic modulus, density, cohesion, and angle of internal friction of the property parameters of each soil layer. According to the probability distributions of these soil layer property parameters, use mathematical software such as Matlab and Mathematica to generate the values of each parameter equal to the number of elements, and use programming software to randomly assign these values to the elements in the finite element model to simulate the spatial variability of each soil layer and establish a random field model of the soil layer. The specific steps are as follows:

[0053] Step S41, Determine the distribution of each soil layer parameter: According to the geological report and on-site monitoring data, determine the distributions (including the first four moments of the mean, variance, skewness, and kurtosis) of the elastic modulus, density, angle of internal friction, and cohesion of each soil layer in the foundation pit;

[0054] Step S42, Extract elements and random assignment: Extract the central point coordinates of each element in the finite element model and import them into the mathematical analysis software (such as Matlab, Mathematica, etc.). At the same time, write a program in the mathematical software and input the randomly generated material parameter data into the finite element model. Examples of random fields are shown in Figure 3 and Figure 4 as shown.

[0055] Step S50: Calculate the safety factor under each random field model according to the strength reduction method;

[0056] By setting the soil plastic material, the strength reduction method is used to calculate the safety factor of the foundation pit at each construction stage. The strength reduction method is to reduce the strength of the rock and soil mass until the foundation pit slope loses stability, so as to obtain the strength reserve safety factor of the foundation pit slope; the parameters cohesion and internal friction angle representing soil plasticity are reduced through formulas, and each reduction is calculated once. After continuous repeated reduction calculations, when there is a penetrating plastic slip surface in the finite element model, a sudden change in the displacement of the characteristic point, and the finite element model calculation is interrupted, the field variable K is output at this time r as the safety factor;

[0057] The calculation formula of the safety factor is as follows:

[0058]

[0059]

[0060] In the formula: c is the initial cohesion of the rock and soil mass; is the initial friction angle of the soil; K r is the safety factor;

[0061] Step S60: Transform the safety factor into a performance function, calculate the first four moments of the performance function using the high-order moment method, and calculate the probability distribution function and probability density function of the performance function;

[0062] Among them, according to the finite element analysis results, construct the performance function of the foundation pit slip failure G(x) = K r – 1, K r is the safety factor of the foundation pit, G(x)>0, the foundation pit is safe, G(x)≤0 the foundation pit fails. There are many random variables in the performance function, so the Monte Carlo method is used to calculate the first four moments of the performance function:

[0063]

[0064] Among them, μ G , δ G are the mean and standard deviation of the performance function Z = G(X) respectively; α kG is its k-th central moment; in the formula: X i =(x 1i , x 2i ,…, x ni ) is the i-th value of each random variable, i ∈ [1,…, N]; N is the number of sampling calculations, and n is the number of random variables.

[0065] If the distribution of the performance function is described by the mean and variance, the reliability index under the two-parameter distribution is:

[0066]

[0067] When the skewness of a random variable has a significant impact on the statistical characteristics of the random variable, using the two-parameter distribution theory for simulation will introduce large errors. To consider the influence of skewness on the parameters, a three-parameter distribution is used to analyze the random variable:

[0068]

[0069]

[0070] To ensure the existence of β 3M-S the following equation must hold:

[0071]

[0072] The fourth-order moment reliability index is calculated as follows:

[0073]

[0074] P F = Φ(-β 4M )

[0075]

[0076] q0 = l(2l 2 - k1 / k2 - 3) + β 2M / k2, l = l1 / l2 / 3

[0077]

[0078] To ensure the existence of l2, the following equation must be satisfied:

[0079]

[0080] Step S70: Finally, based on the probability distribution function and probability density function of the performance function, the failure probability P f of the foundation pit sliding and the reliability β are obtained;

[0081] The β 2M β 3M-S β 3M-L β 4M obtained using the above formulas, and the minimum value is taken as the reliability β of the foundation pit stability.

[0082] The above description is not intended to impose any form of limitation on the present invention. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any person skilled in the relevant art can make some changes or modifications within the scope of the technical solution of the present invention to obtain equivalent embodiments with equivalent changes. However, as long as it does not depart from the content of the technical solution of the present invention, any simple modification, equivalent change, and modification made to the above embodiments based on the technical essence of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A reliability analysis method applicable to the sliding failure of deep foundation pits, characterized in that, It includes the following steps: Step S10: Collect the topographic and geomorphic features and the physical and mechanical parameters of the soil at the deep foundation pit excavation site; Step S20: Establish a finite element model according to the construction design drawings and the physical and mechanical parameters of the soil; Step S30: Install monitoring equipment to monitor the working state of the foundation pit in real time to obtain on-site monitoring data, compare it with the results of the finite element model, and update the parameters of the finite element model in real time; Step S40: Extract the elements in the finite element model and establish a random field model according to the distribution of the soil material parameters; Step S50: Calculate the safety factor under each random field model according to the strength reduction method; Step S60: Transform the safety factor into a performance function, calculate the first four moments of the performance function using the high-order moment method, and calculate the probability distribution function and probability density function of the performance function; Step S70. Finally, calculate the failure probability P of the foundation pit sliding according to the probability distribution function and probability density function of the function f and the reliability β.

2. The reliability analysis method applicable to the sliding failure of deep foundation pits according to claim 1, wherein, The physical and mechanical parameters of the soil include unit weight, elastic modulus, Poisson's ratio, internal friction angle, cohesion, and dilation angle.

3. A reliability analysis method applicable to the sliding failure of deep foundation pits according to claim 1, characterized in that, The specific process of Step 20 is as follows: Step S21: Establish a geometric model: Draw a two-dimensional model of the cross-section in the finite element software according to the construction design drawings; Step S22: Define the material properties: Input the physical and mechanical parameters of different soil layers; According to the information of the supporting structure, input the elastic modulus, density, and Poisson's ratio of concrete or steel; Step S23: Set the boundary conditions and contact relationships: Apply constraints to the bottom and sides of the model, fix all degrees of freedom at the bottom, and only restrict the horizontal displacement at the sides; Set the surface-to-surface contact between the pile and the soil, the normal model is a hard contact, and the tangential property is selected as the penalty function; Apply the surface load pressure according to the instantaneous load conditions of the ground buildings; Apply the corresponding water pressure according to the hydrogeological data, apply the supporting structure load according to the supporting structure conditions, and apply the support reaction force step by step according to the construction process; Step S24: Mesh generation: Use the built-in mesh generation function of the finite element software to divide the mesh.

4. A reliability analysis method applicable to deep foundation pit sliding failure according to claim 1, characterized in that, In Step S30, according to the actual construction sequence, set multiple analysis steps to simulate the entire construction process, simulate the progressive excavation and installation of the supporting structure; At the same time, set the positions corresponding to the on-site monitoring points in the model to compare the calculation results of the finite element model with the on-site monitoring data.

5. The reliability analysis method applicable to the slip failure of deep foundation pits according to claim 1, characterized in that, The specific process of Step S40 is as follows: Step S41: Determine the distribution of the parameters of each soil layer: Determine the distribution of the elastic modulus, density, internal friction angle, and cohesion of each soil layer in the foundation pit according to the geological report and on-site monitoring data; Step S42: Extract the elements and randomly assign values: Extract the central point coordinates of each element in the finite element model, import them into the mathematical analysis software, and at the same time write a program in the mathematical software to input the randomly generated material parameter data into the finite element model.

6. The reliability analysis method applicable to the sliding failure of deep foundation pits according to claim 1, characterized in that, In step S50, the cohesion and internal friction angle, which are parameters representing soil plasticity, are reduced through a formula, and the calculation is performed each time a reduction is made. After continuous repeated reduction calculations, when a continuous plastic slip surface appears in the finite element model, the displacement of the characteristic point suddenly changes, and the finite element model calculation is interrupted, the field variable K is output at this time. r is the safety factor.

7. A reliability analysis method applicable to the sliding failure of deep foundation pits according to claim 6, characterized in that The formula in Step S50 is: c′ = c / K r Where: c is the initial cohesion of the rock and soil mass; is the initial friction angle of the soil; K r is the safety factor.

8. The reliability analysis method applicable to the sliding failure of deep foundation pits according to claim 1, wherein The calculation formulas in Step S60 include: where: μ G , δ G are the mean and standard deviation of the performance function respectively; β 2M is the second-order reliability index; α 3G is its third central moment; β 4M is the fourth-order reliability index.

9. The reliability analysis method applicable to the sliding failure of deep foundation pits according to claim 1, characterized in that, In step S70, take the minimum value of β 2M , β 3M-S , β 3M-L , β 4M as the reliability β of the foundation pit stability.

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