Method for determining spring coefficient of underground structure foundation based on reaction displacement method

Abstract

The invention discloses a method for determining the spring coefficient of an underground structure foundation based on a reaction displacement method, which takes structure size / burial depth / soil parameters and the thickness from the bottom of a structure to bedrock as variables, adopts a finite element calculation method to solve the spring coefficient of the foundation at different parts of the structure, and combines a data fitting method to determine the spring coefficient of the underground structure foundation. The invention provides a method for accurately determining the spring coefficient of the underground structure foundation based on a reaction displacement method. When a homogeneous soil body is popularized to a layered soil body, a suggested value of the influence range of the spring coefficient of each position of the structure by the surrounding soil body is given. Compared with a traditional foundation spring coefficient formula method, the method is simple, convenient and efficient, the defects of an existing foundation spring coefficient valuing method are overcome, the difference between the foundation spring coefficients of all positions of the structure is considered, various influence factors of the foundation spring coefficients of the underground structure can be comprehensively and truly reflected, and the method is suitable for popularization and application. The influence range of the spring coefficient of each position of the layered foundation subsurface structure on the surrounding soil body is defined, so that the calculation precision is greatly improved, and the method can be popularized and used in subsurface structure anti-seismic analysis.

Description

Technical Field

[0001] The invention relates to the technical field of underground structure earthquake resistance, and is particularly applicable to a method for determining a foundation spring coefficient of an underground structure based on a reaction displacement method. Background Art

[0002] When analyzing the seismic response of underground structures, the dynamic time-history analysis method is considered to be the most effective method that can reflect the true response of the structure. However, its application in the seismic design of conventional underground projects is difficult. The main reason is that the calculation results of the dynamic time-history analysis method are affected by many factors, such as the difference in seismic waves, boundary conditions, damping selection, etc., and the amount of calculation is large. Therefore, simplified methods are often used in the actual seismic analysis of underground projects. Among them, the response displacement method is a method with clear physical concepts and rigorous theories, which can reflect the seismic response characteristics of underground structures to a certain extent. This method is simple and convenient to operate, so it has been widely used in many domestic design specifications.

[0003] The reaction displacement method is based on the load-structure model. It simulates the constraints of the surrounding soil layer by introducing a concentrated foundation spring. Therefore, the value of the foundation spring coefficient in the calculation process is very critical and directly related to the reliability of the calculation results. To this end, many experts and scholars have conducted in-depth research on the solution of the foundation spring coefficient. In actual engineering, when using the reaction displacement method to perform seismic analysis on underground structures, it is obviously more convenient to obtain the foundation spring coefficient using the empirical formula method than numerical simulation and experiment. Although some recommended formulas for foundation spring coefficients have been proposed in existing specifications and academic research, most of them do not take into account the particularities of different parts of the structure, especially the factors affecting the value of the foundation spring coefficient of underground structures. At the same time, for layered soil foundations, in the traditional solution method of the foundation spring coefficient, the spring coefficients of the top and side surfaces of the structure consider the influence of the overall soil layer of the model, and the foundation spring coefficient of the bottom surface of the structure considers the influence of the soil layer below the bottom plate. In actual engineering, if the properties of the upper and lower layers of soil are very different or the structure is shallowly buried, the traditional solution method will have a large error. The above problems lead to low calculation accuracy of the reaction displacement method, thus limiting its application in engineering practice. Summary of the invention

[0004] The present invention aims to provide a method for accurately determining the spring coefficient of the foundation of an underground structure based on the reaction displacement method.

[0005] To achieve the above object, the present invention adopts the following technical solutions: The method for accurately determining the spring coefficient of the underground structure foundation based on the reaction displacement method of the present invention comprises the following steps: S1, determine the optimal solution form of the foundation spring coefficient in the reaction displacement method; S2, according to the optimal foundation spring coefficient solution form, the static finite element solution method is used to calculate several groups of foundation spring coefficients with soil shear wave velocity, structure height, structure width, burial depth and soil thickness from the structure bottom plate to the bedrock surface as variables; S3, determine the relationship function between each variable and the foundation spring coefficient; S4, based on the traditional foundation spring coefficient calculation formula, considering the relationship between each variable in step S3 and the foundation spring coefficient, a new foundation spring coefficient calculation formula is constructed; S5, verify the new foundation spring coefficient calculation formula; S6, generalize the verified foundation spring coefficient calculation formula from homogeneous soil to layered soil, and determine the recommended value of the foundation spring coefficient at each location affected by the soil layer.

[0006] Furthermore, step S1 specifically includes: S1.1, establish the seismic finite element analysis model of underground structure and perform mesh division; Soild unit is used for soil and beam unit is used for structure; S1.2, the dynamic response of underground structures solved by the dynamic time history method using measured seismic waves as input; S1.3, use the static finite element solution method to solve the spring coefficient of the underground structure foundation, and obtain the foundation spring coefficient corresponding to different solution forms; S1.4, establish a calculation model of the reaction displacement method, apply the foundation spring coefficient obtained in step S1.3 and the measured seismic wave in step S1.2 respectively, and obtain the structural dynamic response corresponding to the reaction displacement method solution form of different foundation spring coefficient solutions; S1.5, taking the structural dynamic response obtained in step S1.2 as the reference solution, determine the solution form of the foundation spring coefficient corresponding to the structural dynamic response with the smallest error as the optimal solution form of the foundation spring coefficient in the reaction displacement method.

[0007] Furthermore, step S3 specifically includes fitting the data of several groups of foundation spring coefficients in step S2 with the corresponding soil shear wave velocity, structure height, structure width, burial depth and thickness of soil layer from structure bottom plate to bedrock surface, so as to obtain the relationship function of soil shear wave velocity, structure height, structure width, burial depth and thickness of soil layer from structure bottom plate to bedrock surface to foundation spring coefficient.

[0008] Furthermore, the calculation formula of the new foundation spring coefficient in step S4 is: , where w cs 、w H 、w B 、w h and w mThey respectively represent the influence coefficients related to soil shear wave velocity, structure height, structure width, burial depth, and the thickness of the soil layer from the structure bottom plate to the bedrock surface.

[0009] Furthermore, step S5 specifically includes: S5.1, using the static finite element solution method, with the soil shear wave velocity, structure height, structure width, burial depth, and thickness of the soil layer from the structure bottom plate to the bedrock surface as variables, recalculate several groups of foundation spring coefficients; S5.2, substitute the same variable values ​​into the new foundation spring coefficient calculation formula to calculate the corresponding foundation spring coefficient; S5.3, using the calculation result of the static finite element solution method as a reference value, calculate the error of the calculation value of the new foundation spring coefficient calculation formula, and determine whether the calculation accuracy of the new foundation spring coefficient calculation formula is greater than or equal to the accuracy threshold. If it is lower than the accuracy threshold, re-execute steps S2, S3 and S5 until the accuracy meets the requirements.

[0010] Furthermore, in step S6, the recommended values ​​of the range of influence of soil layers on the foundation spring coefficient at each position are determined. In the solution of the normal spring coefficient of the top surface of the layered soil, the influence range of the soil layer is 0~3.07h; in the solution of the tangential spring coefficient of the top surface of the layered soil, the influence range of the soil layer is 0~3.25h; in the solution of the tangential spring coefficient of the top surface of the layered soil, the influence range of the soil layer is 0~2.44(h+H); in the solution of the tangential spring coefficient of the top surface of the layered soil, the influence range of the soil layer is 0~2.91 (h+H); in the solution of the normal spring coefficient of the bottom surface of the layered soil, the influence range of the soil layer is h~h+H+m; in the solution of the tangential spring coefficient of the bottom surface of the layered soil, the influence range of the soil layer is h-0.5H~h+H+m; h is the buried depth of the structure, H is the height of the structure, and m is the thickness from the bottom plate to the bedrock.

[0011] The advantage of the present invention is that it uses the structure size / burial depth / soil parameters and the thickness from the bottom of the structure to the bedrock as variables, adopts the finite element calculation method, solves the foundation spring coefficients of different parts of the structure, and then combines the data fitting method to propose a method for accurately determining the foundation spring coefficient of the underground structure based on the reaction displacement method. When generalizing from homogeneous soil to layered soil, a recommended value of the range of influence of the spring coefficient at each position of the structure on the surrounding soil is given. Compared with the traditional foundation spring coefficient formula method, the present invention is simple, convenient, and efficient, overcomes the shortcomings of the existing foundation spring coefficient value-taking method, takes into account the differences between the foundation spring coefficients at each position of the structure, and can comprehensively and truly reflect the various influencing factors of the foundation spring coefficient of the underground structure, and clarifies the range of influence of the spring coefficient at each position of the underground structure on the layered foundation on the surrounding soil, thereby greatly improving the calculation accuracy, and can be promoted for use in the seismic analysis of underground structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 The figure is a schematic diagram of the process of the method of the present invention.

[0013] Figure 2 Schematic diagram of the dynamic time history analysis model.

[0014] Figure 3 Schematic diagram of the reaction displacement method analysis model.

[0015] Figure 4 Schematic diagram of the measured seismic wave acceleration time history curve.

[0016] Figure 5 Schematic diagram of the solution form of 6 foundation spring coefficients.

[0017] Figure 6 Error analysis diagram of structural dynamic response analysis obtained by 6 solutions of foundation spring coefficients and dynamic time history analysis method.

[0018] Figure 7 The finite element calculation model established for the present invention and the schematic diagram of each variable.

[0019] Figure 8 Schematic diagram of the relationship function between soil shear wave velocity and foundation spring coefficient determined by fitting.

[0020] Fig. 9 The results of foundation spring coefficient obtained by using finite element static solution method and the calculation formula method proposed by the present invention are compared.

[0021] Fig.10 This is the variation law of soil layer influence range coefficient α1 and error in solving the spring coefficient of the top surface of layered soil.

[0022] Fig.11 This figure shows the variation law of soil layer influence range coefficient α2 and error in solving the lateral spring coefficient of layered soil.

[0023] Fig.12 The variation law of soil layer influence range and error in solving the bottom spring coefficient of layered soil. DETAILED DESCRIPTION

[0024] The technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0025] Example 1 like Figure 1As shown, the present invention is a method for accurately determining the foundation spring coefficient of an underground structure based on the reaction displacement method. First, the calculation result of the dynamic time history method is used as a reference solution, and different foundation spring coefficient solution forms are compared and analyzed to determine the optimal solution method. Then, the foundation spring coefficients of different parts of the structure are solved for variables such as structure size, burial depth, soil parameters, and thickness from the bottom of the structure to the bedrock, and a formula for solving the foundation spring coefficient that takes these factors into consideration is proposed using a data fitting method. The rationality of these formulas is verified and analyzed through numerical examples. When expanding from homogeneous soil to layered soil, the range to which the spring coefficients at each position of the structure are affected by the surrounding soil is studied, and corresponding recommended values ​​are proposed. The specific steps are as follows: S1, determine the optimal solution form of the foundation spring coefficient in the reaction displacement method. The specific steps are as follows: S1.1, establish the seismic finite element analysis model of underground structure. The seismic finite element analysis model of underground structure includes the underground structure and its surrounding soil. The soil adopts Soild unit and the structure adopts beam unit.

[0026] S1.2, the dynamic response of the underground structure solved by the dynamic time history method using the measured seismic waves as input.

[0027] S1.3, the static finite element solution method is used to solve the foundation spring coefficient of the underground structure, and the foundation spring coefficient corresponding to different solution forms is obtained.

[0028] S1.4, establish the reaction displacement method calculation model, apply the foundation spring coefficients obtained in step S1.3 respectively, and use the measured seismic waves in step S1.2 as input to obtain the structural dynamic response solved by the reaction displacement method corresponding to different foundation spring coefficient solution forms.

[0029] S1.5. Taking the dynamic response of the underground structure obtained by the dynamic time history method in step S1.2 as the reference value, calculate the error between the structural dynamic response solved by the reaction displacement method and the reference value corresponding to different foundation spring coefficient solution forms. The foundation spring coefficient solution form corresponding to the structural dynamic response solved by the reaction displacement method with the smallest error is the optimal solution form of the foundation spring coefficient in the reaction displacement method.

[0030] The principle of this step is that the engineering community currently believes that the dynamic time history method is the most accurate method for solving the dynamic response of underground structures, which is closer to the actual solution. However, the calculation process of the dynamic time history method is too cumbersome, time-consuming and labor-intensive, and is rarely used in actual engineering.

[0031] The foundation spring coefficient is required when solving the dynamic response of underground structures using the reaction displacement method. However, there are many ways to solve the foundation spring coefficient, and the spring coefficient values ​​obtained by each solution form are quite different, which directly affects the solution results of the reaction displacement method.

[0032] In order to improve the accuracy of the reaction displacement method in solving the dynamic response of underground structures, the inventors of this application used the dynamic response of underground structures calculated by the dynamic time history method as a reference. Controlling other variables unchanged, the errors of the dynamic response of underground structures solved by the reaction displacement method and the values ​​calculated by the dynamic time history method were compared under different foundation spring coefficient solution forms, and the foundation spring coefficient solution form with the smallest error of the reaction displacement method was found. This foundation spring coefficient solution form was used as the optimal foundation spring coefficient solution form in the reaction displacement method solution.

[0033] S2, according to the optimal foundation spring coefficient solution form, the static finite element solution method is used to calculate several groups of foundation spring coefficients with soil shear wave velocity, structure height, structure width, burial depth and soil thickness from the structure bottom plate to the bedrock surface as variables.

[0034] S3, determine the relationship function between each variable and the foundation spring coefficient. The specific steps are as follows: The data of several groups of foundation spring coefficients in step S2 were fitted with the corresponding soil shear wave velocity, structure height, structure width, burial depth and thickness of soil layer from structure bottom plate to bedrock surface to obtain the relationship function of soil shear wave velocity, structure height, structure width, burial depth and thickness of soil layer from structure bottom plate to bedrock surface to foundation spring coefficient.

[0035] S4: Based on the traditional foundation spring coefficient calculation formula, considering the relationship between the variables in step S3 and the foundation spring coefficient, a new foundation spring coefficient calculation formula is constructed, as shown in formula (2).

[0036] Formula (2) In formula (2), w cs , w H , w B , w h and w m They respectively represent the influence of soil shear wave velocity, structure height, structure width, burial depth, and the thickness of the soil layer from the structure bottom plate to the bedrock surface on the foundation spring coefficient. w cs , w H , w B , w h and w m The value is calculated by the relationship function between the variables determined in step S3 and the foundation spring coefficient.

[0037] The creativity of this step lies in that the foundation spring coefficient is an important parameter in the reaction displacement method. In previous studies, scholars mostly referred to the calculation method of the foundation bed coefficient (the traditional foundation spring coefficient calculation formula), as shown in formula (1), to determine the foundation spring coefficient.

[0038] Formula (1) In formula (1): C s and υ are soil shear wave velocity and Poisson’s ratio, respectively; ρ is the soil density; B is the base width; ω is a coefficient that depends on the shape and stiffness of the foundation.

[0039] It can be seen from formula (1) that this formula only considers the width of the foundation structure and the soil properties (c s , ρ, υ), other influencing factors such as structure height, burial depth, thickness from bottom plate to bedrock, etc. are all unified into the influencing factor coefficient ω. Since the influencing factors considered in this formula are relatively single, it cannot truly reflect the changes of the spring coefficients at various positions of the structure with factors such as structure size and burial depth. Therefore, the foundation spring coefficient calculated by formula (1) has a large error.

[0040] Through a large number of tests and analyses, the applicant of the present invention found that the spring coefficients at various locations of the structure show different changing patterns with the structure size, burial depth, soil shear wave velocity, and the thickness of the soil layer from the structure bottom plate to the bedrock surface. Therefore, the applicant took into account the soil shear wave velocity c s The influence of structure width B, structure height H, burial depth h and soil thickness coefficient m from structure bottom plate to bedrock surface on foundation spring coefficient is calculated by finite element analysis and data fitting to obtain soil shear wave velocity. c s , structure width B, structure height H, burial depth h, and the relationship between the soil thickness coefficient m from the structure bottom plate to the bedrock surface and the foundation spring coefficient. And the soil shear wave velocity c s , structure width B, structure height H, burial depth h, and the relationship between the soil layer thickness coefficient m from the structure bottom plate to the bedrock surface and the foundation spring coefficient are added to the traditional foundation spring coefficient calculation formula, so that the influencing factors related to the foundation spring coefficient can be fully considered and the calculation accuracy of the foundation spring coefficient can be improved.

[0041] S5, verify the new foundation spring coefficient calculation formula. The specific steps are: S5.1, using the static finite element solution method, with the soil shear wave velocity, structure height, structure width, burial depth, and thickness of the soil layer from the structure bottom plate to the bedrock surface as variables, recalculate several groups of foundation spring coefficients.

[0042] S5.2, substitute the same variable values ​​into the new foundation spring coefficient calculation formula to obtain the corresponding foundation spring coefficient.

[0043] S5.3, using the calculation result of the static finite element solution method as a reference value, calculate the error of the calculation value of the new foundation spring coefficient calculation formula, and determine whether the calculation accuracy of the new foundation spring coefficient calculation formula is greater than or equal to the accuracy threshold. If it is lower than the accuracy threshold, re-execute steps S2, S3 and S5 until the accuracy meets the requirements.

[0044] S6. Extend the verified calculation formula of the spring coefficient of the new foundation from homogeneous soil to layered soil, and determine the recommended value of the spring coefficient of the foundation at each location within the range affected by the soil layer.

[0045] Since the verified formula for calculating the spring coefficient of the new foundation is based on the assumption of a homogeneous soil layer, and the distribution of the actual soil layer is very complex, in order to extend the verified formula for calculating the spring coefficient of the new foundation from homogeneous soil to layered soil, the multi-layered soil layer can be converted into a single soil layer using formula (3), and the converted homogeneous soil layer parameters can be used to solve the foundation spring coefficient at each position of the underground structure.

[0046] Formula (3) In formula (3), c s represents the equivalent soil shear wave velocity after conversion, h i Represents the height of each layer of soil ( i =1… n , which means from 1 to n layer soil material), c si represents the shear wave velocity of the i-th soil layer.

[0047] Then, a finite element analysis model of layered soil is established, and the foundation spring coefficient of each position of the layered soil structure calculated by finite element is used as the reference solution. By setting different foundation layered soil depths and soil property parameters, the causes of errors in the traditional solution formula method are analyzed. The structure burial depth, soil quality, and the height of each layered soil are used as variables to solve the foundation spring coefficient of each position of the structure under different soil ranges, and the error fitting curve is obtained. Based on this, the recommended value of the soil influence range for the calculation of the structure spring coefficient under layered soil is given.

[0048] Example 2 The specific implementation mode of the method of the present invention is introduced by taking a certain underground station project as an example.

[0049] The first step is to determine the optimal solution form of the foundation spring coefficient in the reaction displacement method.

[0050] S1-1, the buried depth of an underground station structure is 4.8 m. The middle columns are distributed at equal intervals of 3.5 m along the longitudinal direction of the station. The equivalent elastic modulus of the middle columns is 8.57×10 3 MPa, and the density is 7.14×10 2 kg / m 3 The elastic modulus of the top and bottom plates and side walls of the structure is taken as 3×10 4 MPa, the density is taken as 2.5×10 3 kg / m 3 Taking unit length as the research object, based on the finite element analysis software, the dynamic time history method analysis models are established respectively. Figure 2 As shown in Figure 2, and the reaction displacement method analysis model is as follows Figure 3 shown.

[0051] The dynamic time history analysis model is meshed, with Soild units used for the soil and beam units used for the structure.

[0052] S1-2, using the measured seismic wave after amplitude modulation as input, such as Figure 4 As shown in the figure, the dynamic time history analysis method is used to analyze the dynamic response of soil-structure and obtain the structural internal force and deformation response.

[0053] S1-3. Use the static finite element solution method to solve the foundation spring coefficients at each location of the structure, and obtain the foundation spring coefficients corresponding to different solution forms. Figure 5 As shown. The process of solving the foundation spring coefficient is to add a unit force to the soil surface after removing the structure, and then get the displacement and then substitute it into the relevant formula to get the foundation spring coefficient. When adding a unit force to the soil surface after removing the structure, different ways of adding unit force correspond to different solutions for the foundation spring coefficient. Figure 5 (1) shows the standard method of adding unit force to the soil surface. It needs to be loaded six times, that is, each time a single-direction force is loaded on one side, and then the foundation spring coefficient at different positions is solved six times. Figure 5 (2) shows the method of applying unit force to a single surface horizontally and vertically at the same time. It needs to be loaded three times, that is, two directional forces are loaded on a single surface each time, and then the foundation spring coefficients at different positions are solved three times. Figure 5 (3) The loading is divided into two steps, i.e., horizontal force is applied once on all surfaces and vertical force is applied once on all surfaces. Figure 5 (4) is loaded once, i.e. horizontal and vertical forces are applied simultaneously on all surfaces. Figure 5 (5) The loading is divided into two steps: one step to apply radial force on all surfaces and one step to apply tangential force on all surfaces. Figure 5 (6) is loaded once, i.e. radial force and tangential force are applied simultaneously on all surfaces.

[0054] S1-4. Apply the foundation spring coefficient calculated in S1-3, and also use the measured seismic waves in S1-2 as input to perform dynamic response analysis of the soil-structure using the reaction displacement method.

[0055] Taking the structural internal force response obtained by S1-2 as the reference solution, the optimal spring coefficient solution form among the six foundation spring coefficient solution forms in S1-3 is determined by comparing and analyzing the structural dynamic response errors under the six foundation spring coefficient solution forms.

[0056] like Figure 6 The following are the error analysis diagrams of the structural dynamic response analysis obtained by the six solutions of the foundation spring coefficient and the dynamic time history analysis method. The 1, 2, 3, 4, 5, and 6 on the horizontal axis represent Figure 5 The six solutions for the foundation spring coefficient are shown in the figure. The vertical axis is the error value between the structural dynamic response results obtained by the reaction displacement method and the structural dynamic response results obtained by the dynamic time history analysis method. In the figure, ■●▼◆ represents the structural dynamic response results at different positions in the structure. It can be seen from the figure that the errors of method 1 and method 2 are small. Among them, method 1 requires 6 finite element calculations for single-sided loading, while method 2 only requires three loading calculations, and the calculation result accuracy is slightly better. Therefore, it is recommended to use method 2 to solve the foundation spring coefficient value. In the second step, method 2 was used to calculate the structure size (width B, height H), soil properties (shear wave velocity c s ), burial depth (burial depth h) and thickness from bottom plate to bedrock (m) are used as variables, and the foundation spring coefficient is determined using the static finite element solution method. Figure 7 Shown is the established finite element calculation model and a schematic diagram of each variable.

[0057] The third step is to compare the obtained several groups of foundation spring coefficients with the corresponding structural dimensions (width B, height H), soil properties (shear wave velocity c s ), burial depth (burial depth h) and thickness from bottom plate to bedrock (m) were fitted to obtain the relationship function between soil shear wave velocity, structure height, structure width, burial depth and thickness of soil layer from structure bottom plate to bedrock surface and foundation spring coefficient.

[0058] like Figure 8 The figure shows a soil width of 200m, a Poisson's ratio of 0.3, and a density of 1900kg / m 3 , 9 sets of values ​​randomly selected from the range of 80~400m / s for the soil shear wave velocity, and a schematic diagram of the relationship between the soil shear wave velocity and the foundation spring coefficient determined by data fitting. In the figure, ■□▲△▼▽ represents different positions in the structure.

[0059] The fourth step is to construct a new foundation spring coefficient calculation formula based on the traditional foundation spring coefficient calculation formula and the relationship between the variables and the foundation spring coefficient in the third step.

[0060] The spring coefficient calculation formula for different positions of the structure is as follows: Top compression spring (4a, 4b) Top shear spring: (5a, 5b) Side compression spring: (6a, 6b) Side shear spring: (7a, 7b) Bottom compression spring: (8a, 8b) Bottom shear spring: (9a, 9b) In the above fitting formula, the coefficient values ​​are shown in Table 1.

[0061] Table 1 Calculation formula for foundation spring coefficients Step 5: Verify the above foundation spring coefficient calculation formula.

[0062] The specific approach is still to use the static finite element solution method, with the soil shear wave velocity, structure height, structure width, burial depth, and soil thickness from the structure bottom plate to the bedrock surface as variables, to recalculate several sets of foundation spring coefficients. Substitute the above variable values ​​into the new foundation spring coefficient calculation formula to calculate the corresponding foundation spring coefficient. Using the calculation result of the static finite element solution method as a reference value, calculate the error of the calculation value of the new foundation spring coefficient calculation formula to determine whether the calculation accuracy of the new foundation spring coefficient calculation formula is greater than or equal to the accuracy threshold. If it is lower than the accuracy threshold, re-execute the second, third, and fifth steps mentioned above until the accuracy meets the requirements.

[0063] Fig. 9 A comparison of the foundation spring coefficient results obtained by the finite element static solution method and the calculation formula method proposed in this invention is given. Fig. 9Where ae represents the normal spring coefficient, that is, the foundation spring coefficient results obtained by the finite element static solution method and the calculation formula method proposed in the present invention are compared with the structure width, burial depth, soil thickness from the structure bottom plate to the bedrock surface, and soil shear wave velocity as variables. Fig. 9 Where fj represents the tangential spring coefficient, that is, the foundation spring coefficient results obtained by the finite element static solution method and the calculation formula method proposed in the present invention are compared with the structure width, burial depth, soil layer thickness from the structure bottom plate to the bedrock surface, and soil shear wave velocity as variables.

[0064] from Fig. 9 It can be seen that the spring coefficients at each position of the structure obtained by the calculation formula of the present invention are within 25% of the finite element calculation results, while the maximum deviation of the recommended formula given by the Japanese seismic code can reach 2800%. The method of determining the spring coefficient through geological survey and engineering experience in domestic codes also has the problem of large errors. Through the sensitivity analysis of the foundation spring coefficient, we know that compared with the change of the top spring coefficient, the change of the side spring and bottom spring coefficients has a greater impact on the internal force and deformation of the structure. The value of the spring coefficient at each position of the structure increases by 100% to 250%, and the change of the internal force at the key position of the structure is only 25% to 40%. Based on this, it can be concluded that the error of the dynamic response result of the underground structure caused by the deviation of the fitting formula result proposed by the present invention is within 4%, and the calculation accuracy meets the engineering needs.

[0065] Step 6: Extend the spring coefficient solution formula of the underground structure foundation verified in step 5 from homogeneous soil to layered soil. Determine the recommended value of the range of influence of soil layers at each location of the underground structure.

[0066] In the traditional solution of foundation spring coefficient, technicians in this field use formula (3) to convert layered soil layers into homogeneous soil layers. Substitute the converted homogeneous soil layer parameters into formula (1) to calculate and determine the foundation spring coefficient. In this process, firstly, the factors affecting the foundation spring coefficient considered in formula (1) are relatively single, resulting in insufficient calculation accuracy. Secondly, the method of directly converting layered soil layers into homogeneous soil layers through formula (3) only considers the influence of the entire soil layer on the top and side spring coefficients when determining the top and side spring coefficients of the structure, and only considers the influence of the soil layer below the bottom plate when determining the foundation spring coefficient of the bottom surface of the structure. However, in fact, if the properties of the upper and lower soil layers are greatly different or the structure is shallowly buried, the error of the foundation spring coefficient will be further enlarged. In order to improve the simulation calculation accuracy, it is necessary to study the range of influence of the soil layer at each position of the structure and determine the recommended value of the range of influence of the soil layer at each position of the underground structure.

[0067] The inventors of the present invention established a layered soil-structure model, set the structure width B=14m, the structure height H=8m, the thickness m from the structure bottom plate to the bedrock satisfied m>max(3B, 3H), selected 6 different burial depths in the range of 4~18m, studied the range of influence of soil layers on each position of the structure, and put forward corresponding recommended values.

[0068] First, according to the relationship between the soil layer influence range and the variables such as the underground structure height H, burial depth (burial depth h), and thickness from the bottom plate to the bedrock (m) in the solution of the foundation spring coefficient, different soil layer influence range coefficients are set. Then, the layered soil layer is converted into a homogeneous soil layer by formula (3), and the converted homogeneous soil layer parameters are used. The structure size (width B, height H), soil properties (shear wave velocity Cs), burial depth (burial depth h), and thickness from the bottom plate to the bedrock (m) are used as variables, and the foundation spring coefficient is calculated using the foundation spring coefficient calculation formula for each position of the structure verified in the fifth step.

[0069] Afterwards, the same variable values ​​are used to solve the foundation spring coefficient using the static finite element solution method. The calculation result of the static finite element solution method is used as a reference solution to calculate the error between the calculation result of the calculation formula in the present invention and the calculation result of the static finite element solution method.

[0070] The soil layer influence range coefficient corresponding to the variable value is calculated, and the relationship function between the soil layer influence range coefficient and the error is determined by data fitting. In the relationship function between the soil layer influence range coefficient and the error, when the error is 0, it means that the calculation result of the calculation formula in the present invention is the same as the calculation result of the static finite element solution method. According to the aforementioned assumed conditions, it also means that the corresponding soil layer influence range coefficient at this time is the critical influence value.

[0071] like Fig.10 The variation law of soil layer influence range coefficient α1 and error in solving the top surface spring coefficient of layered soil is given, where α1=z / h, z is the calculation range of layered soil, and h is the buried depth of the structure. Fig.10 a is the variation law of soil layer influence range coefficient α1 and error in solving the normal spring coefficient of the top surface of layered soil. The fitting function expression is y=0.2556x-0.7843. y =0, then x is 3.07. That is, α1 is 3.07. According to α1=z / h, the maximum calculation range of soil z is 3.07h. In other words, in solving the normal spring coefficient of the top surface of layered soil, the influence range of the soil layer is 0~3.07h.

[0072] Fig.10 b is the variation law of soil layer influence range coefficient α1 and error in solving the tangential spring coefficient of the top surface of the layered soil. The fitting function expression is y=0.0032x 2+0.2612x - 0.814. Let y = 0, then x is 3.25. That is, α1 is 3.25. According to α1 = z / h, the maximum value of the soil body calculation range z is 3.25h. That is to say, in the solution of the tangential spring coefficient of the top surface of the layered soil, the soil layer influence range is 0 - 3.25h.

[0073] Such as Fig.11 shows the variation law of the soil layer influence range coefficient α2 and the error in the solution of the lateral spring coefficient of the layered soil, where α2 = z / (h + H), z is the calculation range of the layered soil body, h is the buried depth of the structure, and H is the height of the structure. Among them Fig.11 a is the variation law of the soil layer influence range coefficient α2 and the error in the solution of the normal spring coefficient of the side surface of the layered soil body. The fitting function expression is y = 0.3361x - 0.82. Let y = 0, then x is 2.44. That is, α2 is 2.44. According to α2 = z / (h + H), the maximum value of the soil body calculation range z is 2.44(h + H). That is to say, in the solution of the tangential spring coefficient of the top surface of the layered soil, the soil layer influence range is 0 - 2.44(h + H).

[0074] Fig.11 b is the variation law of the soil layer influence range coefficient α2 and the error in the solution of the tangential spring coefficient of the side surface of the layered soil body. The fitting function expression is y = 0.2829x - 0.8231. Let y = 0, then x is 2.91. That is, α2 is 2.91. According to α2 = z / (h + H), the maximum value of the soil body calculation range z is 2.91(h + H). That is to say, in the solution of the tangential spring coefficient of the top surface of the layered soil, the soil layer influence range is 0 - 2.91(h + H).

[0075] Such as Fig.12 shows that in the solution of the bottom spring coefficient of the layered soil body, five calculation ranges of the soil layer influence range (0 ≤ z3 < h + H + m), (h - 0.5H ≤ z3 < h + H + m), (h ≤ z3 < h + H + m), (h + 0.5H ≤ z3 < h + H + m), (h + H ≤ z3 < h + H + m) are respectively selected, corresponding to Fig.12 the abscissas 1 - 5 in it, and then the variation law of the soil layer influence range and the error is fitted. Fig.12a is the variation law of soil layer influence range and error in solving the normal spring coefficient of the bottom surface of layered soil. It can be seen from the figure that when solving the normal spring of the bottom surface of the structure, as the calculation range of the layered soil is reduced, the discreteness of the error percentage of the fitting formula gradually decreases under different burial depth conditions. Compared with the finite element solution, the error of the fitting formula solution in condition 3 is relatively small (<10%). That is, in solving the normal spring coefficient of the bottom surface of layered soil, the soil layer influence range of h~h+H+m is more appropriate.

[0076] Fig.12 b is the variation law of soil layer influence range and error in solving the tangential spring coefficient of the bottom surface of the layered soil. It can be seen from the figure that when solving the tangential spring of the bottom surface of the structure, compared with the finite element solution, the error of the fitting formula solution in working condition 2 is relatively small (<20%). That is, when solving the tangential spring coefficient of the bottom surface of the layered soil, the soil layer influence range of h-0.5H~h+H+m is more appropriate.

Claims

1. A method for determining the spring coefficient of an underground structure foundation based on a reaction displacement method, characterized in that: The steps include: S1, determine the optimal solution form of the foundation spring coefficient in the reaction displacement method; S2, according to the optimal foundation spring coefficient solution form, the static finite element solution method is used to calculate several groups of foundation spring coefficients with soil shear wave velocity, structure height, structure width, burial depth and soil thickness from the structure bottom plate to the bedrock surface as variables; S3, determine the relationship function between each variable and the foundation spring coefficient; S4, based on the traditional foundation spring coefficient calculation formula, considering the relationship between each variable in step S3 and the foundation spring coefficient, a new foundation spring coefficient calculation formula is constructed; S5, verify the new foundation spring coefficient calculation formula; S6, generalize the verified foundation spring coefficient calculation formula from homogeneous soil to layered soil, and determine the recommended value of the foundation spring coefficient at each location affected by the soil layer.

2. The method for determining the spring coefficient of the underground structure foundation based on the reaction displacement method according to claim 1 is characterized in that: Step S1 specifically includes: S1.1, establish the seismic finite element analysis model of underground structure and perform mesh division; Soild unit is used for soil and beam unit is used for structure; S1.2, the dynamic response of underground structures solved by the dynamic time history method using measured seismic waves as input; S1.3, use the static finite element solution method to solve the spring coefficient of the underground structure foundation, and obtain the foundation spring coefficient corresponding to different solution forms; S1.4, establish a calculation model of the reaction displacement method, apply the foundation spring coefficient obtained in step S1.3 and the measured seismic wave in step S1.2 respectively, and obtain the structural dynamic response corresponding to the reaction displacement method solution form of different foundation spring coefficient solutions; S1.5, taking the structural dynamic response obtained in step S1.2 as the reference solution, determine the solution form of the foundation spring coefficient corresponding to the structural dynamic response with the smallest error as the optimal solution form of the foundation spring coefficient in the reaction displacement method.

3. The method for determining the spring coefficient of the underground structure foundation based on the reaction displacement method according to claim 1, characterized in that: Step S3 specifically includes fitting the data of several groups of foundation spring coefficients in step S2 with the corresponding soil shear wave velocity, structure height, structure width, burial depth, and thickness of soil layer from structure bottom plate to bedrock surface, so as to obtain the relationship function of soil shear wave velocity, structure height, structure width, burial depth, and thickness of soil layer from structure bottom plate to bedrock surface to foundation spring coefficient.

4. The method for determining the spring coefficient of the underground structure foundation based on the reaction displacement method according to claim 1, characterized in that: The calculation formula of the new foundation spring coefficient in step S4 is: , where w cs 、w H 、w B 、w h and w m They respectively represent the influence coefficients related to soil shear wave velocity, structure height, structure width, burial depth, and the thickness of the soil layer from the structure bottom plate to the bedrock surface.

5. The method for determining the spring coefficient of the underground structure foundation based on the reaction displacement method according to claim 1, characterized in that: Step S5 specifically includes: S5.1, using the static finite element solution method, with the soil shear wave velocity, structure height, structure width, burial depth, and thickness of the soil layer from the structure bottom plate to the bedrock surface as variables, recalculate several groups of foundation spring coefficients; S5.2, substitute the same variable values ​​into the new foundation spring coefficient calculation formula to calculate the corresponding foundation spring coefficient; S5.3, using the calculation result of the static finite element solution method as a reference value, calculate the error of the calculation value of the new foundation spring coefficient calculation formula, and determine whether the calculation accuracy of the new foundation spring coefficient calculation formula is greater than or equal to the accuracy threshold; If it is lower than the accuracy threshold, re-execute steps S2, S3 and S5 until the accuracy meets the requirement.

6. The method for determining the spring coefficient of the underground structure foundation based on the reaction displacement method according to claim 1, characterized in that: In step S6, the recommended values ​​of the range of influence of soil layers on the foundation spring coefficient at each position are determined. In the solution of the normal spring coefficient of the top surface of the layered soil, the influence range of the soil layer is 0~3.07h; in the solution of the tangential spring coefficient of the top surface of the layered soil, the influence range of the soil layer is 0~3.25h; in the solution of the tangential spring coefficient of the top surface of the layered soil, the influence range of the soil layer is 0~2.44(h+H); in the solution of the tangential spring coefficient of the top surface of the layered soil, the influence range of the soil layer is 0~2.91 (h+H); in the solution of the normal spring coefficient of the bottom surface of the layered soil, the influence range of the soil layer is h~h+H+m; in the solution of the tangential spring coefficient of the bottom surface of the layered soil, the influence range of the soil layer is h-0.5H~h+H+m; h is the buried depth of the structure, H is the height of the structure, and m is the thickness from the bottom plate to the bedrock.

Images