Method for estimating grouting screw anchoring ultimate bearing capacity in gravelly soil based on finite element

Abstract

The invention provides a finite element-based method for estimating pulling-out ultimate bearing capacity of a grouting screw anchor in gravelly soil, and relates to the technical field of civil structure engineering.A three-dimensional finite element model containing the grouting screw anchor and surrounding gravelly soil is established, model parameters cover the structure and material characteristics of the grouting screw anchor, and the grouting screw anchor and the surrounding gravelly soil are subjected to finite element modeling; a coordinate axis is established with the center of the anchor bottom as an original point for grid division, a stress concentration area is analyzed, principal stress is calculated to serve as critical bearing stress, vertical pull-out loads are applied step by step through a grouting pull-out test, a pull-out stress influence area is determined, soil stress of the area is analyzed, and soil binding power and friction force are calculated. And a grouting coefficient and a rock crack coefficient are generated, soil parameters are corrected, and the ultimate pulling bearing capacity of the grouting screw anchor is comprehensively obtained. According to the method, the pulling ultimate bearing capacity of the grouting screw anchor is accurately evaluated by establishing the three-dimensional finite element model and the graded loading experiment.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of civil engineering, in particular to a method for estimating the ultimate bearing capacity of a grouting spiral anchor in gravel soil based on finite elements. BACKGROUND

[0002] Due to the harsh environment in some western regions, the power grid construction is greatly challenged, so a more stable foundation form is needed to anchor the upper power transmission tower. Traditional pile foundations are widely used throughout the country, but their high cost, high labor intensity, slow construction speed, poor bearing capacity and other shortcomings make them less cost-effective. In the western region, there are a large number of gravel soil areas, which have high terrain and strong wind, and the wind erosion is serious, so the bearing capacity of the foundation is required to be high. For gravel soil with large soil cracks, pressure grouting is an effective measure to improve the bearing capacity. At present, a large number of spiral anchor studies are focused on clay, soft soil and sand, which is obviously limited in China with complex terrain, and pressure grouting of gravel soil outside the spiral anchor is even rarer.

[0003] In the prior art, the estimation of the pull-out ultimate bearing capacity of the spiral anchor is mostly dependent on empirical formulas or simple theoretical analysis, without considering the interaction between the soil and the anchoring body, and ignoring the nonlinear strain of the spiral anchor itself in stress loading simulation, which is easy to cause damage and destruction of the spiral in the experiment. In addition, the existing technology cannot accurately locate the stress influence area of the spiral anchor, and the traditional method usually uses fixed soil parameters for calculation, without considering the change of mechanical properties caused by the interaction between the grouting material and the soil.

[0004] Therefore, it is necessary to provide a method for estimating the pull-out ultimate bearing capacity of a grouting spiral anchor in gravel soil based on finite elements to solve the above problems.

[0005] The above information disclosed in the background section is only used to enhance the understanding of the background of the present disclosure, and therefore it can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0006] The purpose of the present application is to provide a method for estimating the pull-out ultimate bearing capacity of a grouting spiral anchor in gravel soil based on finite elements to solve the problems raised in the background.

[0007] To achieve the above purpose, the present application provides the following technical solutions: A method for estimating the pull-out ultimate bearing capacity of a grouting spiral anchor in gravel soil based on finite elements, comprising the following specific steps: Step 1: Based on the grouting spiral anchor modeling parameters and gravel soil parameters, a three-dimensional finite element model of the grouting spiral anchor and the surrounding gravel soil is established, the grouting spiral anchor modeling parameters including the structural parameters of the grouting spiral anchor and the grouting material parameters; Step 2: Establish a three-dimensional coordinate axis with the bottom center position of the grouting spiral anchor as the origin, divide the established three-dimensional finite element model into grids, and perform stress analysis on the grouting spiral anchor to determine the stress concentration area of the grouting spiral anchor, and calculate the principal stress of the stress concentration area in the three-dimensional state as the critical bearing stress; Step 3: Perform grouting uplift experiment on the grouting spiral anchor, and apply vertical upward pullout load at the top end of the grouting spiral anchor and gradually increase in a step-by-step loading manner until the grouting spiral anchor pulls out the gravel soil, record the maximum pullout force and the corresponding displacement of the grouting spiral anchor at this time, and determine the uplift stress influence area; Step 4: Perform soil stress analysis on the uplift stress influence area based on the micro-element method, and calculate the soil cohesion and soil friction in the uplift stress influence area; Step 5: Generate grouting coefficient and rock fracture coefficient according to grouting material parameters and gravel soil parameters, modify the soil cohesion and soil friction in the uplift stress influence area based on the generated grouting coefficient and rock fracture coefficient, and generate the pullout ultimate bearing capacity of the grouting spiral anchor by comprehensively using the modified soil cohesion and soil friction.

[0008] Further, a three-dimensional finite element model of the grouting spiral anchor and the surrounding gravel soil is established, and the method is as follows: Determine the structure parameters of the grouting spiral anchor and the grouting material parameters, the structure parameters include the total length of the grouting spiral anchor, the length of the spiral blade, the diameter of the grouting anchor rod, the diameter of the spiral blade, the grouting material parameters include the compressive strength, the elastic modulus, the Poisson's ratio of the grouting material, the gravel soil parameters include the soil layer size, the soil density, the friction angle, the elastic modulus and the Poisson's ratio of the gravel soil; Based on the ABAQUS finite element analysis software, a three-dimensional finite element model is established, a three-dimensional finite element model of the grouting spiral anchor is created in the software according to the obtained structure parameters of the grouting spiral anchor, the length, diameter and blade characteristics are defined, the grouting spiral anchor is formed through stretching, rotating and shearing operation, and according to the obtained gravel soil parameters, a surrounding body is established around the grouting spiral anchor, so that the size of the soil layer covers the surrounding area of the grouting spiral anchor to form a three-dimensional finite element model of the gravel soil, and the connection relationship between the grouting spiral anchor and the surrounding gravel soil is defined by using the ABAQUS finite element analysis software.

[0009] Further, the established three-dimensional finite element model is divided into grids, and the stress concentration area of the grouting spiral anchor is determined, and the method is as follows: The three-dimensional finite element model is meshed by selecting a tetrahedral mesh element with a size of 10 cm*10 cm*10 cm, a curvature threshold of the grouting spiral anchor is set, the curvature of each part of the grouting spiral anchor is calculated based on the ABAQUS finite element analysis software, the parts exceeding the preset curvature threshold are proportionally refined, the size of the refined mesh element is set to 1 / 2 of the original tetrahedral mesh, the equivalent stress of each tetrahedral mesh element after meshing is calculated according to the stress tensor method, and the formula is: ; ; wherein, represents the stress tensor of the mesh element, represents the equivalent stress of the tetrahedral mesh element, 、 、 respectively represent normal stresses in 、 、 three directions, is the stress acting on the face along the direction, is the stress acting on the face along the direction, is the stress acting on the face along the direction, due to the symmetry of the stress tensor, 、 、 , is the stress acting on the face along the direction, is the stress acting on the face along the direction, is the stress acting on the face along the direction; the stress at the center position of the bottom of the grouting spiral anchor is taken as a reference stress, a stress concentration threshold is set, the ratio of the equivalent stress of each tetrahedral mesh element to the reference stress is defined as a stress concentration coefficient , the tetrahedral mesh element of is defined as a stress concentration mesh element, and based on the connectivity rule of adjacent elements, adjacent stress concentration mesh elements are connected together to form a stress concentration area of the grouting spiral anchor.

[0010] Further, the principal stress of the stress concentration area in the three-dimensional state is calculated as a critical bearing stress, and the method is as follows: For each stress concentration grid cell in the stress concentration area, the stress tensor performs eigenvalue calculation, multiplies the stress tensor of each grid cell by the eigenvalue unit matrix, and substitutes it into the corresponding stress tensor to obtain the first stress matrix of each stress concentration grid cell , by expanding the determinant of the first stress matrix and setting its determinant value to zero to obtain a cubic polynomial equation about the eigenvalue, and by solving this cubic polynomial equation to obtain three eigenvalues of the stress tensor of the stress concentration grid cell 、 、 The three eigenvalues 、 、 respectively correspond to the maximum, intermediate and minimum of the principal stress of the grid cell in the three-dimensional state, and the calculation formula of the principal stress of each stress concentration grid cell in the stress concentration area in the three-dimensional state is: ; Wherein, represents the principal stress value of the th stress concentration grid cell in the stress concentration area, 、 、 respectively represent the maximum, intermediate and minimum of the principal stress of the th stress concentration grid cell in the three-dimensional state, is the index of the stress concentration grid cell in the stress concentration area, and , is the total number of stress concentration grid cells in the stress concentration area; The principal stress values of all stress concentration grid cells in the stress concentration area are superimposed, that is, the critical bearing stress of the stress concentration area.

[0011] Further, the uplift stress influence area is determined, and the method is: The grouting spiral anchor is installed at a predetermined position according to the design depth and angle, and is fixed, grouting material is injected around the grouting spiral anchor, the grouting material is ensured to fully fill the pores around the grouting spiral anchor, and the anchoring effect is enhanced, after the grouting is completed, the initial pulling force is applied after the grouting material reaches the specified strength, the method of step loading is adopted, the pulling force is gradually increased, the critical bearing stress is set as the total pulling force, the pulling force increment of each level is set as 20% of the critical bearing stress, if the grouting spiral anchor starts to produce obvious displacement or strain at each loading stage, whether the pulling force at this time exceeds the critical bearing force is evaluated, until the grouting spiral anchor is pulled out, and the maximum pulling force and the corresponding displacement of the grouting spiral anchor at this time are recorded; The relationship between the pulling force and the displacement of the grouting spiral anchor is established, and the distance between the pulling force application point and the farthest measuring point in the horizontal plane is calculated, and the formula is as follows: ; Among them, is the vertical stress of the measuring point at , indicating the influence degree of the applied pulling load on the soil at , is the pulling force applied to the grouting spiral anchor, is the displacement of the grouting spiral anchor, indicates the distance between the pulling force application point and the farthest measuring point in the horizontal plane; The maximum pulling stress and the corresponding displacement of the grouting spiral anchor are substituted into the relationship formula, the distance between the maximum pulling stress application point and the farthest measuring point in the horizontal plane when the grouting spiral anchor is pulled out is calculated, and a cylindrical region is drawn with the distance as the radius and the central axis of the grouting spiral anchor as the center, according to the preset anchoring depth , which is defined as the anti-pulling stress influence area.

[0012] Further, the soil stress analysis of the anti-pulling stress influence area is carried out, and the soil cohesion and soil friction in the anti-pulling stress influence area are calculated, and the method is as follows: Based on the physical properties of the anti-pulling stress influence area being a cylinder, including the cylinder radius and the depth , the micro-element method is used to divide the cylindrical region into micro-elements with height increment and side area , the cohesion of each micro-element is , and the cohesion of the entire cylindrical region is integrated to obtain the soil cohesion of the anti-pulling stress influence area, and the formula is as follows: ; wherein, represents the soil cohesion force of the uplift stress affected area, represents the cohesion strength per unit of micro-element area, represents the height increment of the micro-element; The soil friction force is generated by the vertical stress and the friction angle of the micro-element, and its expression is The friction force of each micro-element is expressed as The friction force of the entire cylindrical area is integrated to obtain the soil friction force of the uplift stress affected area, and the formula is: ; wherein, represents the soil friction force of the uplift stress affected area, represents the vertical stress acting on the micro-element, which is caused by the self-weight and the applied load of the grouting spiral anchor.

[0013] Further, the pullout ultimate bearing capacity of the grouting spiral anchor is generated comprehensively, and the method is: The grouting coefficient is defined based on the compressive strength and the elastic modulus of the grouting material, and the rock fracture coefficient is defined based on the elastic modulus of the grouting material and the elastic modulus of the soil, and the formula is: ; ; wherein, , respectively represent the grouting coefficient and the rock fracture coefficient, is the compressive strength of the grouting material, is the elastic modulus of the grouting material, is the elastic modulus of the soil; The soil cohesion force and the soil friction force of the uplift stress affected area are corrected by using the generated grouting coefficient and rock fracture coefficient to obtain the soil cohesion force correction value and the soil friction force correction value: ; ; wherein, , respectively represent the soil cohesion force correction value and the soil friction force correction value; The pullout ultimate bearing capacity of the grouting spiral anchor is generated comprehensively based on the effective cohesion area of the grouting spiral anchor and the effective length of the anchor rod obtained by combining the corrected soil cohesion force and soil friction force, and the formula is: ; wherein, represents the pullout ultimate bearing capacity of the grouting spiral anchor, is the effective cohesion area of the grouting spiral anchor, Effective length of the anchor rod.

[0014] Compared with the prior art, the present application has the beneficial effects that: The present application uses the finite element analysis method to model the anchoring system, further determines the critical bearing capacity of the anchoring system through the stress concentration area of the grouting spiral anchor, and protects the anchoring system from being damaged when the load is loaded. In addition, the present application determines the stress influence area of the anchoring system by the method of combining stereographic geometry and stress analysis, and corrects the stress calculation result by using the related grouting material parameters, soil mechanical parameters and actual grouting effect and soil performance, so that the obtained grouting spiral anchor pullout ultimate bearing capacity is more accurate. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 It is the whole method flow diagram of the present application. DETAILED DESCRIPTION

[0016] In order to make the purpose, technical scheme and advantages of the present application more clear and explicit, the present application is further described in detail below in combination with specific embodiments.

[0017] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present application should be understood as the usual meaning understood by those skilled in the art to which the present application belongs. The "first", "second" and similar words used in the present application do not represent any order, quantity or importance, but are only used to distinguish different components. "Include" or "contain" and similar words mean that the elements or objects before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connected" or "connected" and similar words are not limited to physical or mechanical connection, but can include electrical connection, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to represent the relative positional relationship, when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0018] Embodiment: Please refer to Figure 1 A grouting spiral anchor pullout ultimate bearing capacity estimation method based on finite elements in gravel soil, the specific steps comprising: Step 1: based on the grouting spiral anchor modeling parameters and gravel soil parameters, a three-dimensional finite element model of the grouting spiral anchor and the surrounding gravel soil is established, the grouting spiral anchor modeling parameters including the structure parameters of the grouting spiral anchor and the grouting material parameters; Step 2: Establish a three-dimensional coordinate system with the center of the bottom of the grouting screw anchor as the origin, mesh the established three-dimensional finite element model, and perform stress analysis on the grouting screw anchor to determine the stress concentration area of the grouting screw anchor, and calculate the principal stress of the stress concentration area in the three-dimensional state as the critical bearing stress; Step 3: Perform grouting uplift test on the grouting screw anchor, apply vertical upward pullout load at the top of the grouting screw anchor, and gradually increase the load in a stepwise manner until the grouting screw anchor pulls out the gravel soil, record the maximum pullout force and the corresponding displacement of the grouting screw anchor at this time, and determine the uplift stress influence area; Step 4: Perform soil stress analysis on the uplift stress influence area based on the micro-element method, and calculate the soil cohesion and soil friction in the uplift stress influence area; Step 5: Generate grouting coefficients and rock fracture coefficients based on grouting material parameters and gravel soil parameters, modify the soil cohesion and soil friction in the uplift stress influence area based on the generated grouting coefficients and rock fracture coefficients, and generate the ultimate bearing capacity of the grouting screw anchor by comprehensively using the modified soil cohesion and soil friction.

[0019] It should be noted that establishing a three-dimensional finite element model of the grouting screw anchor and its surrounding gravel soil is crucial, as it provides a scientific basis for evaluating the bearing capacity of the anchoring system. By specifying the structural parameters of the grouting screw anchor and the grouting material parameters, the performance of the anchoring system under different working conditions can be accurately reflected. By using the soil layer size in the gravel soil parameters, including the soil layer thickness, soil layer width, and soil layer length, the ABAQUS finite element analysis software is used to create a geometric model and define its material properties, which can effectively simulate the stress distribution during the anchoring process and the interaction between the soil and the anchoring body. This modeling method not only improves the accuracy of the analysis, but also helps to identify potential stress concentration areas and failure modes, thereby providing important guidance for engineering design optimization, safety evaluation, and construction schemes, reducing engineering risks, and improving economic benefits.

[0020] Therefore, it is necessary to establish a three-dimensional finite element model of the grouting screw anchor and its surrounding gravel soil, and the method is as follows: Determine the structural parameters of the grouting screw anchor and the grouting material parameters, the structural parameters include the total length of the grouting screw anchor, the length of the spiral blade, the diameter of the grouting anchor rod, the diameter of the spiral blade, the grouting material parameters include the compressive strength, elastic modulus, and Poisson's ratio of the grouting material, the gravel soil parameters include the soil layer size, soil density, friction angle, elastic modulus, and Poisson's ratio of the gravel soil; The three-dimensional finite element model is established based on the ABAQUS finite element analysis software, a three-dimensional finite element model of the grouting spiral anchor is created in the software according to the obtained structural parameters of the grouting spiral anchor, the length, diameter and blade characteristics of the grouting spiral anchor are defined, the grouting spiral anchor is formed through stretching, rotating and shearing operations, and according to the obtained gravel soil parameters, a surrounding body is established around the grouting spiral anchor, so that the size of the soil layer covers the surrounding area of the grouting spiral anchor to form a three-dimensional finite element model of the gravel soil, and the connection relationship between the grouting spiral anchor and the surrounding gravel soil is defined by using the bonding in the ABAQUS finite element analysis software.

[0021] It should be noted that meshing the three-dimensional finite element model and identifying the stress concentration area are key steps for evaluating the performance of the grouting spiral anchor. By reasonably selecting the size of the tetrahedral mesh element and refining the area with larger curvature, the accuracy of the model calculation can be improved, ensuring that the stress distribution of the anchoring system is truly reflected. The equivalent stress of each mesh element is calculated using the stress tensor method, which helps to identify weak parts of the bearing capacity and timely detect potential safety hazards. Setting the stress concentration threshold can effectively evaluate the stress area beyond the safe range, guide the subsequent design optimization and construction scheme, and thus improve the overall stability and reliability of the grouting spiral anchor, ensuring project safety and economic benefits.

[0022] Therefore, the established three-dimensional finite element model needs to be meshed, and the stress concentration area of the grouting spiral anchor needs to be determined, and the method is as follows: The three-dimensional finite element model is meshed by selecting a tetrahedral mesh element with a size of 10cm*10cm*10cm, the curvature threshold of the grouting spiral anchor is set, the curvature of each part of the grouting spiral anchor is calculated based on the ABAQUS finite element analysis software, the parts exceeding the preset curvature threshold are proportionally refined, the size of the refined mesh element is set to 1 / 2 of the original tetrahedral mesh, and the equivalent stress of each tetrahedral mesh element after division is calculated according to the stress tensor method. The formula is: ; ; Among them, represents the stress tensor of the divided mesh element, represents the equivalent stress of the tetrahedral mesh element, , , respectively represent the normal stress in , , three directions, is the stress acting on the face along the direction, is the stress acting on the face along the stress in the direction, is the stress acting on the surface in the direction, due to the symmetry of the stress tensor, , , , is the stress acting on the surface in the direction, is the stress acting on the surface in the direction, is the stress acting on the surface in the direction, is the stress acting on the surface in the direction, is the stress acting on It should be noted that the curvature value of each point on the surface of the established grouting spiral anchor three-dimensional finite element model is calculated by the derivative of the surface normal, the curvature distribution data obtained by analysis is used to identify the area with large curvature change, and the 95% quantile of the overall curvature distribution is selected to ensure that the mesh refinement is carried out in these high curvature areas to more accurately capture the stress concentration phenomenon. Through this method, the appropriate curvature threshold can be effectively determined, and the results of finite element analysis are more reliable.

[0023] The stress at the center of the bottom of the grouting spiral anchor is taken as the reference stress, and the stress concentration threshold is set The ratio of the equivalent stress of each tetrahedral mesh element to the reference stress is defined as the stress concentration coefficient The tetrahedral mesh element of is defined as the stress concentration mesh element, and based on the connectivity rules of adjacent elements, the adjacent stress concentration mesh elements are connected together to form the stress concentration area of the grouting spiral anchor. It should be noted that the stress at the reference point is taken as the reference stress, and combined with the yield strength and safety factor of the material, a suitable proportion coefficient is set through the recommended value in the grouting spiral anchor design specification, for example, 1.5 to 2.0 times the reference stress, to define the stress concentration threshold, to ensure that there is enough safety margin for potential high stress areas in actual engineering to adapt to the bearing capacity of the material and construction risk.

[0024] It should be noted that calculating the principal stress of the stress concentration area in the three-dimensional state as the critical bearing stress is of great significance, as it provides a key basis for evaluating the bearing capacity and safety of the grouting spiral anchor. By performing eigenvalue calculation on the stress tensor of the stress concentration grid element, the maximum, average and minimum values of the principal stress can be obtained, thereby comprehensively reflecting the stress state in the region. This analysis not only helps to identify possible failure modes, but also provides a scientific basis for design optimization, ensuring the stability and reliability of the anchoring system in practical applications, thereby effectively reducing engineering risks and improving safety standards.

[0025] Therefore, the principal stress of the stress concentration area in the three-dimensional state as the critical bearing stress needs to be calculated, and the method is as follows: For each stress concentration grid element in the stress concentration area, the stress tensor is subjected to eigenvalue calculation, the stress tensor of each grid element is multiplied by the eigenvalue unit matrix, and then substituted into the corresponding stress tensor to obtain the first stress matrix of each stress concentration grid element By expanding the determinant of the first stress matrix and setting its determinant value to zero, a cubic polynomial equation about the eigenvalue is obtained, and by solving this cubic polynomial equation, three eigenvalues of the stress tensor of the stress concentration grid element are obtained 、 、 The three eigenvalues 、 、 respectively correspond to the maximum, intermediate and minimum principal stresses of the grid element in the three-dimensional state, and the calculation formula of the principal stress of each stress concentration grid element in the stress concentration area in the three-dimensional state is as follows: ; Wherein, represents the principal stress value of the th stress concentration grid element in the stress concentration area, 、 、 respectively represent the maximum, intermediate and minimum principal stresses of the th stress concentration grid element in the three-dimensional state, is the index of the stress concentration grid element in the stress concentration area, and , is the total number of stress concentration grid elements in the stress concentration area; The principal stress values of all stress concentration grid elements in the stress concentration area are superimposed to obtain the critical bearing stress of the stress concentration area.

[0026] It is noted that the cubic polynomial equation for eigenvalue is derived from the stress tensor of the grid element The formula for calculating the eigenvalue of the stress tensor of a grid element is as follows: ; wherein is the eigenvalue of the stress tensor of the grid element, is the unit matrix, is the determinant, which is used to represent the solution of the eigenvalue equation, and then the eigenvalue equation is expanded to obtain the first matrix of the stress tensor of the grid element , and the determinant is set to zero to obtain a cubic polynomial for the eigenvalue of the stress tensor of the grid element, wherein , is the trace of the stress tensor, is the second-order deviation of the stress tensor, is the determinant of the stress tensor, and by solving the cubic polynomial equation, three eigenvalues , are obtained; It is noted that we use the maximum value of the principal stress , the intermediate value of the principal stress and the minimum value of the principal stress in the three-dimensional state to replace the principal stress value of the stress concentration grid element, and by using the average value of the principal stress to estimate the principal stress value of the stress concentration grid element, the calculation process can be simplified, and the use of the average value can help identify potential weaknesses and failure modes.

[0027] The principal stress values of all stress concentration grid elements in the stress concentration area are superimposed to obtain the critical bearing stress of the stress concentration area.

[0028] It is noted that determining the uplift stress influence area is crucial for evaluating the performance of the grouting screw anchor, as it helps to understand the degree of influence of the applied pullout force on the surrounding soil. By systematically conducting uplift tests, gradually loading and recording the displacement and maximum pullout force of the grouting screw anchor, the critical bearing capacity and its influence range can be accurately identified. This analysis provides data support for design and construction, ensuring that the anchoring system has sufficient safety margin in practical application, and laying a foundation for subsequent optimization design, thereby improving the overall safety and reliability of the project.

[0029] Therefore, the method for determining the uplift stress influence area is as follows: Grouting pull-out tests were conducted on the grouting spiral anchors. The grouting spiral anchors were installed at the predetermined positions according to the designed depth and angle, and their fixation was ensured. Grouting material was injected around the grouting spiral anchors to ensure that the grouting material fully filled the pores around the grouting spiral anchors and enhanced the anchoring effect. After grouting was completed, the initial pull-out force was applied after the grouting material reached the specified strength. A graded loading method was adopted to gradually increase the applied pull-out force. The critical bearing stress was set as the total pull-out force, and the pull-out force increment for each grade was set to 20% of the critical bearing stress. If the grouting spiral anchors began to produce significant displacement or strain at each loading stage, it was assessed whether the pull-out force at this time exceeded the critical bearing capacity. The maximum pull-out force and the corresponding displacement of the grouting spiral anchors were recorded until the grouting spiral anchors were pulled out. The relationship between pull-out force and grouting helical anchor displacement is established, and the distance from the point where the pull-out force is applied to the farthest measurement point on the horizontal plane is calculated using the following formula: ; in, The measurement point is at The vertical stress at the point represents the effect of the applied pull-out load on the load. The degree of influence on the soil. It is the pull-out force applied to the grouting spiral anchor. It is the displacement of the grouting spiral anchor. It represents the distance on the horizontal plane from the point where the pull-out force is applied to the farthest measurement point; Maximum pull-out stress Substituting the corresponding displacement of the grouting helical anchor into the formula, calculate the distance on the horizontal plane from the point of maximum pull-out stress application to the farthest measurement point when the grouting helical anchor is pulled out. Using this distance as the radius and the central axis of the grouting helical anchor as the center, calculate the anchoring depth according to the preset formula. Define a cylindrical region and define this cylindrical region as the region affected by pull-out stress.

[0030] It should be noted that, In reality, it is the change in depth at the measurement point after the pull-out force is applied. This change in depth at a fixed point is used to characterize the displacement of the grouting helical anchor. The height of the constructed cylinder At any measurement point, in the above formula, based on the stress transfer theory in soil mechanics, considering the stress propagation of the pull-out force in the soil, this formula expresses the depth. Due to the pull-out force The resulting stress attenuation characteristics are obtained by acquiring stress at a known depth. The vertical stress will result in the maximum pull-out stress. Substitute into The radius of the stress influence zone under the maximum pullout force can be calculated by determining the maximum stress influence zone radius and combining the predetermined anchoring depth , which forms a physical model of the stress influence zone as a cylinder.

[0031] It is important to note that soil stress analysis of the pullout stress influence zone is crucial for calculating soil cohesion and soil friction. This process helps to comprehensively evaluate the actual bearing capacity and stability of grouting spiral anchors in soil layers. By analyzing the cohesion and friction of each micro-element using the micro-element method, we can gain detailed understanding of the stress distribution in the soil at different depths and locations, providing scientific basis for optimizing design and construction plans. Soil cohesion and friction together determine the pullout resistance of the anchoring system, ensuring the safety and reliability of the anchoring structure under applied loads. Therefore, soil stress analysis not only improves the rationality of engineering design, but also reduces potential safety risks and ensures long-term stability of the project.

[0032] Therefore, soil stress analysis of the pullout stress influence zone is necessary to calculate the soil cohesion and soil friction in the pullout stress influence zone. The method used is: Based on the physical properties of the pullout stress influence zone as a cylinder, including the cylinder radius and depth , the cylinder region is divided into micro-elements with height increments of and side areas of . The cohesion of each micro-element is . The soil cohesion of the pullout stress influence zone is obtained by integrating the cohesion of the entire cylinder region, using the formula: ; where represents the soil cohesion of the pullout stress influence zone, represents the cohesion strength per unit micro-element area, represents the height increment of the micro-element. Soil friction is generated by the vertical stress of the micro-element and the friction angle, and its expression is The friction of each micro-element is represented as . The soil friction of the pullout stress influence zone is obtained by integrating the friction of the entire cylinder region, using the formula: ; where represents the soil friction of the pullout stress influence zone, is the vertical stress acting on the infinitesimal element, which is caused by the self-weight and the applied load of the grouting screw anchor, is the friction angle of the gravel soil.

[0033] It is important to note that the importance of generating the pullout ultimate bearing capacity of grouting screw anchors lies in providing a systematic theoretical basis for engineering practice to ensure the safety and reliability of anchoring structures. In this process, by defining the grouting coefficient and rock fracture coefficient, the interaction between the grouting material and the soil can be accurately reflected, and the soil cohesion and friction can be effectively modified, thus more realistically reflecting the actual bearing capacity, effective bonding area and effective length of the anchor rod under actual conditions. The consideration of the calculation results makes more practical sense, which can reflect the actual bearing capacity of grouting screw anchors under different working conditions. This not only helps engineers to design anchoring structures reasonably and improve their bearing capacity, but also effectively reduces potential engineering risks and avoids engineering accidents caused by unreasonable design. Therefore, the analysis method of generating the pullout ultimate bearing capacity not only strengthens the understanding of the performance of the anchoring system, but also provides scientific guidance for subsequent construction, monitoring and maintenance, laying a foundation for the long-term stability and safety of the project.

[0034] Therefore, it is necessary to generate the pullout ultimate bearing capacity of grouting screw anchors based on the following method: The grouting coefficient is defined based on the compressive strength and elastic modulus of the grouting material, and the rock fracture coefficient is defined based on the elastic modulus of the grouting material and the elastic modulus of the soil. The formula is: ; ; wherein, , are the grouting coefficient and the rock fracture coefficient, respectively, is the compressive strength of the grouting material, is the elastic modulus of the grouting material, is the elastic modulus of the soil; The soil cohesion and soil friction in the stress influence area are modified using the generated grouting coefficient and rock fracture coefficient to obtain the soil cohesion correction value and soil friction correction value: ; ; wherein, , are the soil cohesion correction value and the soil friction correction value, respectively; The pullout ultimate bearing capacity of grouting screw anchors is generated based on the effective bonding area and the effective length of the anchor rod obtained by combining the modified soil cohesion and soil friction. The formula is: ; wherein, represents the pull-out limit bearing capacity of the grouting screw anchor, is the effective bonding area of the grouting screw anchor, is the effective length of the anchor rod.

[0035] The above formulas are all dimensionless numerical calculations, the formulas are obtained by software simulation of a large number of data to obtain the most real situation, and the preset parameters in the formulas are set by the person skilled in the art according to the actual situation.

[0036] The above embodiments can be realized wholly or partially by software, hardware, firmware or any other combination. When realized by software, the above embodiments can be realized wholly or partially in the form of a computer program product. Those skilled in the art can realize that the units and algorithm steps of the examples described in combination with the embodiments disclosed herein can be realized by electronic hardware or a combination of computer software and electronic hardware. Whether the functions are realized by hardware or software methods depends on the specific application and design constraints of the technical solutions.

[0037] The units described as separate components can or can not be physically separated, and the components shown as units can or can not be physical units, which can be located in one place or distributed on multiple network units. Part or all of the units can be selected to achieve the purpose of the embodiments according to actual needs.

[0038] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of changes or replacements within the technical range disclosed in the present application, which should be covered within the protection scope of the present application.

Claims

1. A method for predicting the ultimate bearing capacity of a grouting spiral anchor in gravelly soil based on the finite element method, characterized in that, The specific steps include: Step 1: Based on the grouting spiral anchor modeling parameters and the crushed stone soil parameters, establish a three-dimensional finite element model of the grouting spiral anchor and the surrounding crushed stone soil. The grouting spiral anchor modeling parameters include the structural parameters of the grouting spiral anchor and the grouting material parameters. Step 2: Establish a three-dimensional coordinate axis with the bottom center of the grouting spiral anchor as the origin, mesh the established three-dimensional finite element model, perform stress analysis on the grouting spiral anchor to determine the stress concentration area of ​​the grouting spiral anchor, and calculate the principal stress of the stress concentration area in the three-dimensional state as the critical bearing stress. Step 3: Conduct a grouting pull-out test on the grouting spiral anchor, apply a vertical upward pull-out load to the top of the grouting spiral anchor and gradually increase it in stages until the grouting spiral anchor pulls out of the gravel soil, record the maximum pull-out force and the corresponding displacement of the grouting spiral anchor at this time, and determine the area affected by the pull-out stress. Step 4: Perform soil stress analysis in the region affected by pull-out stress based on the micro-element method, and calculate the soil cohesion and soil friction in the region affected by pull-out stress; Step 5: Generate grouting coefficient and rock crack coefficient based on grouting material parameters and crushed stone soil parameters. Based on the generated grouting coefficient and rock crack coefficient, correct the soil cohesion and soil friction in the area affected by pull-out stress respectively. Use the corrected soil cohesion and soil friction to generate the ultimate pull-out bearing capacity of the grouting spiral anchor.

2. The method for predicting the ultimate bearing capacity of grouting spiral anchors in gravelly soil based on finite element method, as described in claim 1, is characterized in that... The method used to establish a three-dimensional finite element model of the grouting spiral anchor and the surrounding gravelly soil is as follows: The structural parameters and grouting material parameters of the grouting spiral anchor are determined. The structural parameters include the total length of the grouting spiral anchor, the length of the spiral blades, the diameter of the grouting anchor rod, and the diameter of the spiral blades. The grouting material parameters include the compressive strength, elastic modulus, and Poisson's ratio of the grouting material. The parameters of the gravelly soil include the soil layer size, soil density, friction angle, elastic modulus, and Poisson's ratio of the gravelly soil. A three-dimensional finite element model was established using ABAQUS finite element analysis software. Based on the obtained structural parameters of the grouting spiral anchor, a three-dimensional finite element model of the grouting spiral anchor was created in the software, defining its length, diameter, and blade characteristics. The grouting spiral anchor was formed through stretching, rotation, and shearing operations. Based on the obtained parameters of the gravelly soil, a surrounding body was established around the grouting spiral anchor, so that the size of the soil layer covers the surrounding area of ​​the grouting spiral anchor to form a three-dimensional finite element model of the gravelly soil. The bonding function in ABAQUS finite element analysis software was used to define the connection relationship between the grouting spiral anchor and the surrounding gravelly soil.

3. The method for predicting the ultimate bearing capacity of grouting spiral anchors in gravelly soil based on finite element method, as described in claim 2, is characterized in that... The established three-dimensional finite element model was meshed, and the stress concentration region of the grouting helical anchor was determined using the following method: The 3D finite element model was meshed using 10cm*10cm*10cm tetrahedral mesh elements. A curvature threshold was set for the grouting helical anchor. The curvature of each part of the grouting helical anchor was calculated using ABAQUS finite element analysis software. Parts exceeding the preset curvature threshold were proportionally refined, with the refined mesh element size set to half the size of the original tetrahedral mesh. Equivalent stress was calculated for each of the resulting tetrahedral mesh elements using the stress tensor method, based on the following formula: ； ； in, This represents the stress tensor of the divided mesh elements. This represents the equivalent stress of a tetrahedral mesh element. , , They represent in , , Normal stress in three directions, It is acting on surface edge Stress in the direction, It is acting on surface edge Stress in the direction, It is acting on surface edge Stress in the direction, due to the symmetry of the stress tensor, , , , It is acting on surface edge Stress in the direction, It is acting on surface edge Stress in the direction, It is acting on surface edge Stress in the direction; The stress at the bottom center of the grouting helical anchor is used as the reference stress to set a stress concentration threshold. The stress concentration factor is defined as the ratio of the equivalent stress to the reference stress in each tetrahedral mesh element. ,Will The tetrahedral mesh element is defined as the stress concentration mesh element, and based on the connectivity rules of adjacent elements, neighboring stress concentration mesh elements are connected together to form the stress concentration region of the grouting spiral anchor.

4. The method for predicting the ultimate bearing capacity of grouting spiral anchors in gravelly soil based on finite element method, as described in claim 3, is characterized in that... The method used to calculate the principal stresses in the stress concentration region under three-dimensional conditions as the critical bearing stress is as follows: For each stress-concentrated grid cell in the stress concentration region, the eigenvalues ​​of the stress tensor are calculated. The stress tensor of each grid cell is multiplied by the eigenvalue identity matrix, and then substituted into the corresponding stress tensor to obtain the first stress matrix for each stress-concentrated grid cell. By expanding the determinant of the first stress matrix and setting its determinant to zero, a cubic polynomial equation in terms of the eigenvalues ​​is obtained. Solving this cubic polynomial equation yields the three eigenvalues ​​of the stress tensor of the stress-concentrated mesh element. , , Three eigenvalues , , These correspond to the maximum, median, and minimum values ​​of the principal stress components in the three-dimensional state, respectively. The formula for calculating the principal stress of each stress concentration grid element in the stress concentration region in the three-dimensional state is as follows: ； in, Indicates the first stress concentration region Principal stress values ​​of stress concentration grid elements , , They represent the first The principal stresses of a stress concentration mesh element are the maximum, median, and minimum values ​​of the component stresses in three dimensions. This is the index of the stress concentration mesh element in the stress concentration region, and , This represents the total number of stress concentration grid elements in the stress concentration region. The critical bearing stress of the stress concentration region is obtained by superimposing the principal stress values ​​of all stress concentration grid elements in the stress concentration region.

5. The method for predicting the ultimate bearing capacity of grouting spiral anchors in gravelly soil based on finite element method, as described in claim 4, is characterized in that... The method used to determine the region of influence of pull-out stress is as follows: Grouting pull-out tests were conducted on the grouting spiral anchors. The grouting spiral anchors were installed at the predetermined positions according to the designed depth and angle, and their fixation was ensured. Grouting material was injected around the grouting spiral anchors to ensure that the grouting material fully filled the pores around the grouting spiral anchors and enhanced the anchoring effect. After grouting was completed, the initial pull-out force was applied after the grouting material reached the specified strength. A graded loading method was adopted to gradually increase the applied pull-out force. The critical bearing stress was set as the total pull-out force, and the pull-out force increment for each grade was set to 20% of the critical bearing stress. If the grouting spiral anchors began to produce significant displacement or strain at each loading stage, it was assessed whether the pull-out force at this time exceeded the critical bearing capacity. The maximum pull-out force and the corresponding displacement of the grouting spiral anchors were recorded until the grouting spiral anchors were pulled out. The relationship between pull-out force and grouting helical anchor displacement is established, and the distance from the point where the pull-out force is applied to the farthest measurement point on the horizontal plane is calculated using the following formula: ； in, The measurement point is at The vertical stress at the point represents the effect of the applied pull-out load on the load. The degree of influence on the soil. It is the pull-out force applied to the grouting spiral anchor. It is the displacement of the grouting spiral anchor. It represents the distance on the horizontal plane from the point where the pull-out force is applied to the farthest measurement point; Maximum pull-out stress Substituting the corresponding displacement of the grouting helical anchor into the formula, calculate the distance on the horizontal plane from the point of maximum pull-out stress application to the farthest measurement point when the grouting helical anchor is pulled out. Using this distance as the radius and the central axis of the grouting helical anchor as the center, calculate the anchoring depth according to the preset formula. Define a cylindrical region and define this cylindrical region as the region affected by pull-out stress.

6. The method for predicting the ultimate bearing capacity of grouting spiral anchors in gravelly soil based on finite element method, as described in claim 5, is characterized in that... Soil stress analysis was performed in the area affected by pull-out stress to calculate soil cohesion and soil friction in the area affected by pull-out stress. The method used was as follows: Based on the physical property that the region affected by pull-out stress is a cylinder, including the cylinder with a radius of... Depth is The cylindrical region is divided using the infinitesimal element method. The height increment is lateral area is The infinitesimal elements, each with a cohesive force of [value missing]. The soil cohesion in the region affected by pull-out stress is obtained by integrating the cohesion force over the entire cylindrical region, using the following formula: ； in, This indicates the soil cohesion in the area affected by pull-out stress. Represents the bond strength per unit area of ​​a micro-element. This represents the height increment of a micro-element; Soil friction is generated by the vertical stress and friction angle of a infinitesimal element, and its expression is: The frictional force for each infinitesimal element is expressed as: The soil friction force in the region affected by pull-out stress is obtained by integrating the friction force over the entire cylindrical region, using the following formula: ； in, This indicates the soil friction force in the area affected by pull-out stress. This represents the vertical stress acting on the infinitesimal element, caused by the self-weight of the grouting helical anchor and the applied load. The friction angle of the gravelly soil.

7. The method for predicting the ultimate bearing capacity of a grouting spiral anchor in gravelly soil based on the finite element method, as described in claim 6, is characterized in that... The method used to comprehensively generate the ultimate bearing capacity of the grouting spiral anchor is as follows: The grouting coefficient is defined based on the compressive strength and elastic modulus of the grouting material, and the rock crack coefficient is defined based on the elastic modulus of the grouting material and the elastic modulus of the soil. The formulas used are as follows: ； ； in, , These represent the grouting coefficient and the rock fracture coefficient, respectively. The compressive strength of the grouting material, The elastic modulus of the grouting material. The elastic modulus of the soil; The generated grouting coefficient and rock crack coefficient are used to correct the soil cohesion and soil friction in the area affected by pull-out stress, resulting in corrected values ​​for soil cohesion and soil friction. ； ； in, , These represent the soil cohesion correction value and the soil friction correction value, respectively. The pull-out ultimate bearing capacity of the grouting spiral anchor is calculated by combining the effective bonding area and effective length of the anchor rod, obtained from the modified soil cohesion and soil friction. The formula used is as follows: ； in, This indicates the pull-out ultimate bearing capacity of the grouting spiral anchor. This represents the effective bonding area of ​​the grouting spiral anchor. This is the effective length of the anchor bolt.

Images