A compression-resistant composite anti-floating anchor rod integrated mechanical model design method

Abstract

The application discloses a design method of an integrated mechanical model of a compression-resistant composite anti-floating anchor rod, and specifically comprises the following steps: obtaining a parameter set of a multi-layer structure of a target geotechnical engineering anti-floating anchor rod, analyzing the hierarchical interface mechanical behavior, generating an interface shear stress transfer function, embedding the function into an axisymmetric stress analysis framework, obtaining an axial force and a side resistance distribution function of the whole length of the anchor rod, constructing an integrated mechanical balance equation set, segmentally numerically solving the equation set, outputting mechanical response characteristic curves at different depths, and finally determining a limit anti-floating bearing capacity prediction value according to the curves as a design output.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering anchoring technology, specifically to a design method for an integrated mechanical model of a compressive composite anti-buoyancy anchor. Background Technology

[0002] Existing mechanical model design methods for anti-buoyancy anchors typically treat the anchor as a single homogeneous structure, ignoring its multi-layered composite characteristics consisting of reinforcing bars, grout, anti-corrosion sleeves, and surrounding soil and rock. In conventional design processes, most methods use empirical formulas or simplified elastic theories to estimate the distribution of axial force and lateral resistance of the anchor. Interface shear stress transfer is only generalized through average frictional resistance, failing to distinguish the differences in mechanical properties between interfaces of different structural layers.

[0003] Moreover, existing models mostly analyze the interface behavior of each segment independently, such as the steel bar and grout, the grout and casing, and the casing and soil. They lack a coupling analysis method that integrates the shear stress transfer function of multiple interfaces into the axisymmetric stress frame from the perspective of overall stress. This staged and fragmented modeling method leads to insufficient accuracy in describing the mechanical response of the anchor bolt along its entire length. Especially when the anchor bolt is buried at a large depth or the geological conditions are complex, the load transfer path is significantly affected by the nonlinear slippage of each interface. Traditional methods are unable to predict the true distribution of axial force and side resistance, which in turn leads to a large deviation between the predicted value of the ultimate pull-out bearing capacity and the actual test results.

[0004] The shortcomings of existing technical solutions are as follows: they cannot obtain the shear stress transfer function between structural layers from the analytical level of the mechanical behavior of the interface, resulting in a lack of refined interface constitutive relation input for subsequent stress analysis; they lack an overall model that integrates the four structural layers of steel reinforcement, grouting body, anti-corrosion casing and soil into a set of differential equilibrium equations, and the axial force and side resistance of each layer cannot be solved simultaneously under the condition of continuous interface displacement; and the numerical solution does not consider the different requirements of material properties of different sections for the integration step size, making it difficult to balance the accuracy and efficiency of segmented calculations. Summary of the Invention

[0005] This invention addresses the shortcomings of existing technologies by providing an integrated mechanical model design method for a compressive composite anti-buoyancy anchor bolt, thereby improving the accuracy of predicting the bearing capacity of the anti-buoyancy anchor bolt.

[0006] The objective of this invention can be achieved through the following technical solutions: A design method for an integrated mechanical model of a compressive-resistant composite anti-buoyancy anchor bolt, specifically including the following steps: Step S1: Obtain the multi-layer structural parameter set of the anti-buoyancy anchor in the target geotechnical engineering, wherein the multi-layer structural parameter set includes anchor reinforcement parameters, grouting body parameters, anti-corrosion sleeve parameters and surrounding soil and rock parameters; Step S2: Perform hierarchical interface mechanical behavior analysis on the multi-layer structure parameter set to generate the interface shear stress transfer function between each structural layer; Step S3: Embed the interface shear stress transfer function into the axisymmetric force analysis framework of the composite anti-buoyancy anchor to obtain the axial force distribution function and side resistance distribution function over the entire length of the anchor. Step S4: Construct an integrated set of mechanical equilibrium equations for the compressive composite anti-buoyancy anchor rod based on the axial force distribution function and the side resistance distribution function; Step S5: Solve the integrated mechanical equilibrium equations piecewise numerically and output the mechanical response characteristic curves of the anchor at different burial depths. Step S6: Determine the predicted value of the ultimate pull-out bearing capacity of the anchor rod based on the mechanical response characteristic curve, and use the predicted value of the ultimate pull-out bearing capacity as the design output result of the integrated mechanical model.

[0007] In this embodiment, step S2 specifically includes the following steps: The rib height and rib spacing on the surface of the anchor rod are extracted from the anchor rod parameters, and the first interface roughness coefficient between the anchor rod and the grouting body is calculated based on the rib height and rib spacing. The elastic modulus and Poisson's ratio of the grout body are extracted from the grout body parameters, and the second interface bonding stiffness between the grout body and the anti-corrosion sleeve is calculated based on the elastic modulus and Poisson's ratio of the grout body. The friction angle and wall thickness of the outer wall of the casing are extracted from the parameters of the anti-corrosion casing, and the friction coefficient of the third interface between the anti-corrosion casing and the surrounding rock and soil is calculated based on the friction angle and wall thickness of the outer wall of the casing. Substituting the roughness coefficient of the first interface, the bonding stiffness of the second interface, and the friction coefficient of the third interface into the elastoplastic interface constitutive model, respectively, generates the first shear stress transfer function of the interface between the reinforcing bar and the grout, the second shear stress transfer function of the interface between the grout and the anti-corrosion sleeve, and the third shear stress transfer function of the interface between the anti-corrosion sleeve and the surrounding soil and rock. The first shear stress transfer function, the second shear stress transfer function, and the third shear stress transfer function constitute the interface shear stress transfer function.

[0008] In this embodiment, the constitutive model of the elastoplastic interface adopts a bilinear softening model to describe the shear stress-slip relationship of the interface.

[0009] In this embodiment, step S3 specifically includes the following steps: dividing the entire length of the anchor rod into multiple micro-segments with the anchor rod axis as the longitudinal coordinate axis; applying axial equilibrium conditions to each micro-segment to establish a differential relationship between the axial force increment and the interface shear stress of that micro-segment; substituting the interface shear stress transfer function into the differential relationship to obtain the axial force differential equation corresponding to each micro-segment; integrating the axial force differential equation along the entire length of the anchor rod to obtain the axial force variation function along the longitudinal coordinate within the entire length of the anchor rod as the axial force distribution function; differentiating the axial force distribution function with respect to the longitudinal coordinate to obtain the side resistance variation function along the longitudinal coordinate within the entire length of the anchor rod as the side resistance distribution function.

[0010] In this embodiment, step S4 specifically includes the following steps: The axial force distribution function is assigned the value of the external load at the top of the anchor rod and the value of zero at the bottom of the anchor rod to form the first boundary condition; The displacement continuity condition is applied to the side drag distribution function at the interface of each structural layer to form a second boundary condition; Based on the first boundary condition and the second boundary condition, the axial force distribution function and the side resistance distribution function are combined to obtain the first equilibrium equation of the anchor reinforcement, the second equilibrium equation of the grouting layer, the third equilibrium equation of the anti-corrosion casing layer, and the fourth equilibrium equation of the surrounding rock and soil layer. The first equilibrium equation, the second equilibrium equation, the third equilibrium equation, and the fourth equilibrium equation are combined to form an integrated set of mechanical equilibrium equations.

[0011] In this embodiment, step S5 specifically includes the following steps: Based on the thickness and material properties of each structural layer in the multi-layer structure parameter set, the entire length of the anchor rod is divided into a steel reinforcement-dominated section, a grouting-dominated section, an anti-corrosion sleeve-dominated section, and a soil-dominated section. Within each dominant segment, a numerical integration step size matching the structural layer of that segment is selected; The integrated mechanical equilibrium equations are solved piece by piece according to the numerical integration step size, and the axial force, side resistance and displacement values ​​are calculated at the end of each integration step size. The calculated axial force, side resistance, and displacement values ​​are respectively fitted to curves according to the burial depth to generate axial force variation curves, side resistance variation curves, and displacement variation curves as mechanical response characteristic curves.

[0012] In this embodiment, the step of selecting a numerical integration step size that matches the structural layer of each dominant segment specifically includes: Within the main section of the reinforcing steel, the upper limit of the first integral step is determined based on the yield strain of the reinforcing steel. Within the dominant section of the grouting body, the upper limit of the second integral step is determined based on the elastic limit strain of the grouting body; Within the dominant section of the anti-corrosion sleeve, the upper limit of the third integral step is determined based on the radial stiffness of the anti-corrosion sleeve. Within the dominant section of the rock and soil mass, the upper limit of the fourth integral step is determined based on the shear wave velocity of the rock and soil mass; Values ​​smaller than the first integration step size upper limit, the second integration step size upper limit, the third integration step size upper limit, and the fourth integration step size upper limit are selected as the numerical integration step size for each dominant segment.

[0013] In this embodiment, the step of solving the integrated mechanical equilibrium equations piecewise according to the numerical integration step size, and calculating the axial force, side resistance, and displacement at the end of each integration step, specifically includes: Starting from the top of the anchor bolt, the top boundary condition is used as the initial value. The first equilibrium equation of the first dominant section is solved by using the prediction-correction iterative format to obtain the first axial force value and the first displacement value at the end of each integral step in the section. Using the first axial force value and the first displacement value as the initial conditions of the second dominant section, the second equilibrium equation is solved by advancing the solution to obtain the second axial force value and the second displacement value at the end point of each integral step in the second dominant section. Using the second axial force value and the second displacement value as the initial conditions of the third dominant section, the third equilibrium equation is solved by advancing the solution to obtain the third axial force value and the third displacement value at the end point of each integral step in the third dominant section. Using the third axial force value and the third displacement value as the initial conditions of the fourth dominant section, the fourth equilibrium equation is solved by advancing the solution to obtain the fourth axial force value and the fourth displacement value at the end point of each integral step in the fourth dominant section. Differentiate the axial force value at the end of each integration step with respect to the longitudinal coordinate to obtain the side resistance value at the corresponding end of the integration step.

[0014] In this embodiment, step S6, which involves determining the predicted value of the ultimate pull-out bearing capacity of the anchor rod based on the mechanical response characteristic curve, specifically includes: Extract the complete curve of the axial force at the top of the anchor bolt as the external load increases from the mechanical response characteristic curve as the load-displacement response curve; Calculate the tangential stiffness values ​​between adjacent data points sequentially on the load-displacement response curve; When the tangent stiffness value at a certain measuring point first drops to a preset proportion of the initial tangent stiffness value, the corresponding top axial force value is determined as the yield load value. The predicted value of the ultimate tensile bearing capacity is obtained by multiplying the yield load value by a preset safety factor.

[0015] In this embodiment, the step of extracting the complete curve of the axial force at the top of the anchor bolt changing with the increase of external load from the mechanical response characteristic curve as the load-displacement response curve specifically includes: The point where the burial depth of the anchor top is zero in the mechanical response characteristic curve is used as the top monitoring point; The axial force and displacement values ​​under different external load levels are read from the top monitoring point; By using the axial force value under each external load level as the ordinate and the displacement value as the abscissa, a discrete data point pair sequence is generated. The discrete data point pairs are sorted in a monotonically increasing order, and the sorted discrete data point pairs are connected sequentially with line segments to generate the load-displacement response curve.

[0016] By adopting the above solution, the present invention has the following beneficial effects: 1. The steps of this invention include parameter acquisition, interface analysis, function derivation, equation construction, piecewise solution, and bearing capacity determination. The steps are progressive and closed-loop, and the calculation system is standardized, which is convenient for programmed calculation and engineering design applications. Moreover, it abandons the traditional homogeneous simplification assumption and models a four-layer composite structure of steel reinforcement, grouting body, anti-corrosion sleeve, and soil and rock mass. It distinguishes the mechanical differences of multiple interfaces, reduces theoretical modeling errors from the source, and effectively solves the problem of calculation distortion in traditional methods under deep-buried anchor bolts and complex strata conditions. It improves the prediction accuracy of the bearing capacity of the anti-buoyancy anchor bolt mechanical model and can accurately output the distribution law of axial force, side resistance, and displacement along the burial depth.

[0017] 2. This invention quantifies key parameters such as interface roughness, bonding stiffness, and friction coefficient. Combined with a bilinear softening constitutive model, it can realistically reflect nonlinear stress characteristics such as interlayer interlocking, bonding friction, and slip damage, and accurately characterize the shear stress transmission law. It breaks the traditional segmented calculation mode, relies on an axisymmetric force frame, and combines multiple equilibrium equations with continuous displacement boundary conditions to completely restore the real load transmission path, making the stress analysis more in line with engineering practice.

[0018] 3. This invention divides the calculation sections into independent calculation segments based on the material properties of each layer and matches differentiated integration step sizes to avoid the defects of uniform step sizes. This not only ensures the calculation accuracy in deep burial and complex strata, but also improves the calculation efficiency. Based on the full load-displacement response curve, the yield critical point is determined by the change of tangent stiffness, and the ultimate bearing capacity is converted by combining the safety factor. The judgment logic conforms to the actual failure mechanism of anchor bolts, and the prediction results have small deviations. Attached Figure Description

[0019] Figure 1This is a flowchart of the process of the present invention.

[0020] Figure 2 This is a flowchart of the process for solving the axial force distribution function and the side resistance distribution function of the present invention.

[0021] Figure 3 This is a flowchart of the construction of the integrated mechanical equilibrium equation system of the present invention. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] like Figure 1 As shown, a design method for an integrated mechanical model of a compressive composite anti-buoyancy anchor bolt includes the following steps: Step S1: Obtain the multi-layer structural parameter set of the anti-buoyancy anchor in the target geotechnical engineering, wherein the multi-layer structural parameter set includes anchor reinforcement parameters, grouting body parameters, anti-corrosion sleeve parameters and surrounding soil and rock parameters; Step S2: Perform hierarchical interface mechanical behavior analysis on the multi-layer structure parameter set to generate the interface shear stress transfer function between each structural layer; Specifically: Extract the rib height and rib spacing of the steel bar surface from the anchor bar parameters obtained in step S1, and use the ratio of the rib height of the steel bar surface to the rib spacing of the steel bar surface as the first interface roughness coefficient. Extract the elastic modulus and Poisson's ratio of the grout body from the grout body parameters obtained in step S1. Use the elastic interface stiffness calculation formula to substitute the elastic modulus and Poisson's ratio of the grout body into the elastic interface stiffness calculation formula to obtain the second interface bonding stiffness. Extract the outer wall friction angle and wall thickness of the casing from the anti-corrosion casing parameters obtained in step S1, and use the product of the tangent of the outer wall friction angle and the wall thickness of the casing as the friction coefficient of the third interface. Substituting the roughness coefficient of the first interface, the bonding stiffness of the second interface, and the friction coefficient of the third interface into the elastoplastic interface constitutive model, respectively, generates the first shear stress transfer function of the interface between the steel bar and the grout, the second shear stress transfer function of the interface between the grout and the anti-corrosion sleeve, and the third shear stress transfer function of the interface between the anti-corrosion sleeve and the surrounding rock and soil. The first shear stress transfer function, the second shear stress transfer function, and the third shear stress transfer function constitute the interface shear stress transfer function. The constitutive model of the above-mentioned elastoplastic interface uses a bilinear softening model to describe the shear stress-slip relationship of the interface; the bilinear softening model includes four parameters: peak shear stress, peak slip, residual shear stress, and residual slip; the bilinear softening model expresses the shear stress as a piecewise linear function of the slip: When the slip is less than the peak slip, the shear stress increases linearly with the slip to the peak shear stress; When the slip is greater than the peak slip and less than the residual slip, the shear stress decreases linearly with the slip to the residual shear stress. When the slip is greater than the residual slip, the shear stress remains at the residual shear stress. For the interface between the steel bar and the grout, the first interface roughness coefficient is used as the calculation input parameter for the peak shear stress and substituted into the bilinear softening model to obtain the first shear stress transfer function. For the interface between the grouting body and the anti-corrosion sleeve, the second interface bonding stiffness is used as the calculation input parameter for the ratio of the peak shear stress to the peak slip, and substituted into the bilinear softening model to obtain the second shear stress transfer function. For the interface between the anti-corrosion sleeve and the surrounding rock and soil, the friction coefficient of the third interface is used as the input parameter for calculating the residual shear stress. Substituted into the bilinear softening model, the third shear stress transfer function is obtained. Step S3: Embed the interface shear stress transfer function into the axisymmetric force analysis framework of the composite anti-buoyancy anchor to obtain the axial force distribution function and side resistance distribution function over the entire length of the anchor. like Figure 2 As shown, the entire length of the anchor bolt is divided into multiple micro-segments with the anchor bolt axis as the longitudinal coordinate axis. An axial equilibrium condition is applied to each micro-segment, and a differential relationship is established between the incremental axial force and the interface shear stress in the micro-segment. The expression for this differential relationship is: ; in, For anchor bolts at the burial depth position The axial force at the point, measured in kilonewtons; The coordinates are longitudinal along the anchor bolt axis, with the top of the anchor bolt as the zero point and downward as the positive direction, and the unit is meters; The contact perimeter of the anchor bolt micro-element segment is given in meters. Burial depth The interfacial shear stress at the point is expressed in kilopascals. Substituting the interface shear stress transfer function obtained in step S2 into the above differential equation, we obtain the axial force differential equation corresponding to each micro-element. Specifically, we select the corresponding shear stress transfer function according to the interface type of the micro-element and substitute it. The axial force differential equation is based on the differential equation, replacing the interface shear stress in the differential equation with the interface shear stress transfer function. , forming about axial force A first-order ordinary differential equation; The axial force differential equation is solved by integration along the entire length of the anchor bolt, yielding the axial force distribution function as a function of the variation of the axial force along the longitudinal coordinate within the entire length of the anchor bolt. During the integration, the lower limit of integration is set at the top of the anchor bolt. Given that the axial force at the top of the anchor bolt is equal to the external load, and using this external load as the initial condition, the differential equation of the axial force is applied from the top of the anchor bolt to the burial depth. By performing definite integrals, the axial force distribution function is obtained. The expression; The variation function of the side resistance along the longitudinal coordinate is obtained by differentiating the axial force distribution function with respect to the longitudinal coordinate, and this function is used as the side resistance distribution function. The value of the side resistance distribution function at each burial depth along the entire length of the anchor bolt is the interface shear stress value at that location. Therefore, the side resistance distribution function at each burial depth is... From the axial force distribution function For the vertical axis Take the negative value of the first derivative and divide by the perimeter of the interface contact. To obtain, that is Side drag distribution function The unit is kilopascal.

[0024] Step S4: Construct an integrated set of mechanical equilibrium equations for the compressive composite anti-buoyancy anchor rod based on the axial force distribution function and the side resistance distribution function; like Figure 3 As shown, the axial force distribution function is assigned the value of the external load at the top of the anchor bolt and zero at the bottom of the anchor bolt, forming the first boundary condition; the longitudinal coordinate corresponding to the top of the anchor bolt... The bottom of the anchor bolt corresponds to the longitudinal coordinate. ,in For the total length of the anchor bolt, in meters, the axial force distribution function is... The function value at the specified location is set as the external load value, where the external load value is the axial tensile force applied to the top of the anchor bolt, in kilonewtons; the axial force distribution function is then set at... The function value at the point is set to zero, and the displacement continuity condition is applied to the side resistance distribution function at the interface of each structural layer to form the second boundary condition; The structural layer interfaces include the interface between the reinforcing steel and the grout, the interface between the grout and the anti-corrosion sleeve, and the interface between the anti-corrosion sleeve and the surrounding rock and soil. The displacement continuity condition means that the axial displacement values ​​of two adjacent structural layers at the same interface are equal. Based on the first and second boundary conditions, the axial force distribution function and the side resistance distribution function are combined to obtain the first equilibrium equation of the anchor reinforcement, the second equilibrium equation of the grouting layer, the third equilibrium equation of the anti-corrosion casing layer, and the fourth equilibrium equation of the surrounding soil and rock layer.

[0025] The expression for the first equilibrium equation of the anchor reinforcement is: ; in, For anchor reinforcement at the embedment depth The axial force at the point, measured in kilonewtons; The coordinates are longitudinal along the anchor bolt axis, with the top of the anchor bolt as the zero point and downward as the positive direction, and the unit is meters; The contact perimeter of the interface between the reinforcing bar and the grout is expressed in meters. For the interface between the reinforcing steel and the grouting body at the burial depth The shear stress at the point, expressed in kilopascals, and the contact perimeter of the interface between the reinforcing steel and the grout. Calculated based on the nominal diameter of the reinforcing bar; The expression for the second equilibrium equation of the grouting layer is: ; in, For the grouting layer at the burial depth The axial force at the point, measured in kilonewtons; The contact perimeter of the interface between the grout and the anti-corrosion casing is expressed in meters. For the interface between the grouting body and the anti-corrosion casing at the burial depth The shear stress at the point, expressed in kPa, and the contact perimeter of the interface between the grout and the anti-corrosion casing. Calculated based on the outer diameter of the grout layer; The expression for the third equilibrium equation of the anti-corrosion casing layer is: ; in, For the anti-corrosion casing layer at the burial depth The axial force at the point, measured in kilonewtons; The contact perimeter between the anti-corrosion sleeve and the surrounding rock and soil is expressed in meters. To ensure the interface between the anti-corrosion casing and the surrounding soil and rock at the burial depth The shear stress at the point is expressed in kilopascals (kPa), and the contact perimeter between the anti-corrosion casing and the surrounding soil and rock mass is also mentioned. Calculated based on the outer diameter of the anti-corrosion sleeve; The expression for the fourth equilibrium equation of the surrounding rock and soil layers is: ; in, The surrounding rock and soil layers at the burial depth The axial force at the point, measured in kilonewtons; The first equilibrium equation, the second equilibrium equation, the third equilibrium equation, and the fourth equilibrium equation are combined to form an integrated set of mechanical equilibrium equations. This integrated set of mechanical equilibrium equations contains four differential equations, corresponding to four unknown axial force functions. , , , The first and second boundary conditions serve as the boundary conditions for the integrated mechanical equilibrium equations.

[0026] Step S5: Solve the integrated mechanical equilibrium equations piecewise numerically and output the mechanical response characteristic curves of the anchor at different burial depths. Based on the thickness and material properties of each structural layer in the multi-layer structural parameter set obtained in step S1, the entire length of the anchor rod is divided into the steel reinforcement-dominated section, the grouting-dominated section, the anti-corrosion sleeve-dominated section, and the soil-rock-dominated section. The main section of the reinforcing steel corresponds to the structural layer where the anchor steel is located; the main section of the grouting body corresponds to the structural layer where the grouting body layer is located; the main section of the anti-corrosion sleeve corresponds to the structural layer where the anti-corrosion sleeve layer is located; and the main section of the soil and rock mass corresponds to the structural layer where the surrounding soil and rock mass layer is located. Within each dominant section, a numerical integration step size matching the structural layer of the dominant section is selected. Within the steel reinforcement dominant section, the upper limit of the first integration step size is determined based on the yield strain of the steel reinforcement. Within the grouting body dominant section, the upper limit of the second integration step size is determined based on the elastic limit strain of the grouting body. Within the anti-corrosion sleeve dominant section, the upper limit of the third integration step size is determined based on the radial stiffness of the anti-corrosion sleeve. Within the soil and rock dominant section, the upper limit of the fourth integration step size is determined based on the shear wave velocity of the soil and rock. Values ​​smaller than the upper limit of the first integration step are selected as the numerical integration step of the steel reinforcement dominant section, values ​​smaller than the upper limit of the second integration step are selected as the numerical integration step of the grouting body dominant section, values ​​smaller than the upper limit of the third integration step are selected as the numerical integration step of the anti-corrosion sleeve dominant section, and values ​​smaller than the upper limit of the fourth integration step are selected as the numerical integration step of the soil and rock dominant section.

[0027] The integrated mechanical equilibrium equations are solved step by step according to the numerical integration step size. Starting from the top of the anchor rod, the top boundary condition is used as the initial value. The first equilibrium equation of the anchor rod reinforcement in the first dominant section is solved step by step using the prediction-correction iterative format to obtain the first axial force value and the first displacement value at the end of each integration step size in the first dominant section. The first dominant section is the reinforcement dominant section. Using the first axial force value and the first displacement value as the initial conditions of the second dominant section, the second equilibrium equation of the grouting layer is solved by advancing the solution to obtain the second axial force value and the second displacement value at the end point of each integral step in the second dominant section. The second dominant section is the dominant section of the grouting body. Using the second axial force value and the second displacement value as the initial conditions of the third dominant section, the third equilibrium equation of the anti-corrosion sleeve layer is solved by advancing the solution to obtain the third axial force value and the third displacement value at the end point of each integral step in the third dominant section. The third dominant section is the dominant section of the anti-corrosion sleeve. Using the third axial force value and the third displacement value as initial conditions for the fourth dominant section, the fourth equilibrium equation of the surrounding soil and rock layers is solved to obtain the fourth axial force value and the fourth displacement value at the end of each integration step within the fourth dominant section. The fourth dominant section is the dominant section of the soil and rock mass. The axial force value at the end of each integration step is differentiated with respect to the longitudinal coordinate to obtain the side resistance value at the corresponding end of the integration step. The axial force value is determined by the first axial force value, the second axial force value, the third axial force value, or the fourth axial force value, depending on the dominant section where the integration step is located. The differentiation with respect to the longitudinal coordinate is performed using the finite difference method, and the side resistance value is obtained by dividing the difference in axial force at the end of adjacent integration steps by the difference in longitudinal coordinates. The calculated axial force, side resistance, and displacement values ​​are respectively curve-fitted according to the burial depth. The axial force values ​​include the first, second, third, and fourth axial force values. The axial force data at the full burial depth is obtained by combining the corresponding longitudinal coordinate positions. The side resistance value is the side resistance value at the end of the integral step. The displacement value is the first, second, third, and fourth displacement values. The axial force data is linearly interpolated and fitted according to the burial depth to generate an axial force variation curve along the burial depth. The side resistance value is linearly interpolated and fitted according to the burial depth to generate a side resistance variation curve along the burial depth. The displacement value is linearly interpolated and fitted according to the burial depth to generate a displacement variation curve along the burial depth. The axial force variation curve, the side resistance variation curve, and the displacement variation curve along the burial depth are used as the mechanical response characteristic curves. Step S6: Determine the predicted value of the ultimate pull-out bearing capacity of the anchor bolt based on the mechanical response characteristic curve, and use the predicted value of the ultimate pull-out bearing capacity as the design output result of the integrated mechanical model. The specific steps are as follows: Based on the mechanical response characteristic curve output in step S5, determine the predicted value of the ultimate pull-out bearing capacity of the anchor rod. Extract the complete curve of the axial force at the top of the anchor rod changing with the increase of external load from the mechanical response characteristic curve as the load-displacement response curve. Locate the point in the mechanical response characteristic curve where the burial depth of the top of the anchor rod is zero as the top monitoring point. Read the axial force and displacement values ​​under different external load levels from the top monitoring point. Each external load level corresponds to a specific external load value. Starting from zero external load, the load is gradually increased according to the set load increment to the preset maximum load value. Under each level of external load, the axial force and displacement values ​​at the top monitoring point are extracted from the mechanical response characteristic curve. The axial force value under each external load level is used as the ordinate and the displacement value as the abscissa to generate a discrete data point pair sequence. Each data point pair consists of the displacement value (i.e., the abscissa) and the axial force value (i.e., the ordinate) under that load level. The discrete data point pair sequence is monotonically sorted in ascending order, and the discrete data point pairs are rearranged in ascending order of displacement value. The sorted discrete data point pair sequence is then connected sequentially with line segments to generate the load-displacement response curve.

[0028] The tangent stiffness values ​​between adjacent data points are calculated sequentially on the load-displacement response curve. The tangent stiffness value is defined as the slope of the line connecting two adjacent data points, i.e., the difference in the vertical coordinate divided by the difference in the horizontal coordinate. Specifically, for the first... Data points and the Data points The tangential stiffness value The calculation formula is ,in This is the displacement value. The axial force value is defined as the top axial force value corresponding to the decrease of the first tangent stiffness value to a preset proportion of the initial tangent stiffness value. The initial tangent stiffness value is the slope of the first segment of the load-displacement response curve (i.e., the line connecting the first and second data points). The preset proportion is set to 0.50. Starting from the first tangent stiffness value, each tangent stiffness value is sequentially checked to see if it is less than 0.50 times the initial tangent stiffness value. When a tangent stiffness value first decreases to 0.50 times the initial tangent stiffness value, the next data point in the adjacent data points corresponding to that tangent stiffness value (i.e., the first...) is... The axial force value of each data point is determined as the yield load value. The yield load value is multiplied by a preset safety factor to obtain the predicted value of the ultimate pull-out bearing capacity. In this embodiment, the safety factor is set to 2.0.

[0029] This invention employs the above-mentioned scheme, which analyzes the hierarchical interface mechanical behavior of a multi-layered structural parameter set. It extracts the rib height and rib spacing from the anchor bar parameters to calculate the roughness coefficient of the first interface; extracts the elastic modulus and Poisson's ratio from the grout parameters to calculate the bond stiffness of the second interface; and extracts the outer wall friction angle and wall thickness from the anti-corrosion sleeve parameters to calculate the friction coefficient of the third interface. These three interface characteristic parameters are then substituted into an elastoplastic interface constitutive model to generate the first shear stress transfer function of the rebar-grout interface, the second shear stress transfer function of the grout-anti-corrosion sleeve interface, and the interface between the anti-corrosion sleeve and the surrounding soil and rock. The third shear stress transfer function quantifies the geometry, material mechanical properties, and contact state of different structural layer interfaces into a shear stress-slip relationship with clear physical meaning. This overcomes the shortcomings of traditional methods that simply replace the nonlinear behavior of multi-layer interfaces with a single average friction coefficient, allowing for a precise description of the load transfer path of each interface when embedded in the axisymmetric force analysis framework. Consequently, in the process of calculating the axial force distribution function and the side resistance distribution function, the interface shear stress of each micro-element segment is no longer a constant value, but a function that dynamically changes with the slippage at the burial depth, thus significantly improving the calculation accuracy of the mechanical response curve over the entire length of the anchor bolt.

[0030] By embedding the shear stress transfer function into an axisymmetric force analysis framework, the axial force distribution function and side resistance distribution function over the entire length of the anchor bolt are obtained. Based on the first boundary condition of assigning an external load value to the top of the anchor bolt and zero at the bottom, and the second boundary condition of applying a displacement continuity condition to the side resistance distribution function at the interfaces of each structural layer, the axial force distribution function and the side resistance distribution function are combined to establish the first equilibrium equation for the anchor bolt reinforcement, the second equilibrium equation for the grouting layer, the third equilibrium equation for the anti-corrosion casing layer, and the fourth equilibrium equation for the surrounding soil and rock layers. This set of four differential equations comprehensively describes the transfer, distribution, and equilibrium of loads between the structural layers. The load borne by the reinforcing steel is transferred to the grouting body through the shear stress at the first interface, then to the anti-corrosion sleeve through the shear stress at the second interface, and finally to the surrounding soil and rock through the shear stress at the third interface. The axial force variation in each layer strictly satisfies the differential relationship with the interface shear stress, thus providing a unified mathematical description of the mechanical behavior of the four-layer system. Furthermore, when performing piecewise numerical solutions to this equation set, this method divides the entire length of the anchor bolt into four sections based on the thickness and material properties of each structural layer: a reinforcing steel-dominated section, a grouting body-dominated section, an anti-corrosion sleeve-dominated section, and a soil and rock-dominated section. Within each dominant section, a numerical integration step size matching the material properties of the structural layer in that section is selected. For example, in the case of reinforcing steel... The upper limit of the first integration step is determined based on the yield strain in the dominant section; the upper limit of the second integration step is determined based on the elastic limit strain in the grouting body dominant section; the upper limit of the third integration step is determined based on the radial stiffness in the anti-corrosion casing dominant section; and the upper limit of the fourth integration step is determined based on the shear wave velocity in the soil and rock dominant section. Values ​​smaller than their respective upper limits are selected as the actual integration step size. Starting from the top of the anchor bolt, a predictive-correction iterative scheme is used to sequentially solve each dominant section, using the axial force and displacement results of the previous section as the initial conditions for the next section. Finally, the axial force, side resistance, and displacement values ​​at the end of each integration step are obtained, and then the axial force is fitted to generate the value. The piecewise numerical solution strategy, which considers the differences in material stiffness and deformation characteristics in different sections, along the curves of burial depth variation, lateral resistance variation, and displacement variation, adapts the integration step size to the mechanical response characteristics of the structural layer. This ensures computational accuracy while avoiding local oscillations or inefficiencies caused by fixed step sizes. Finally, the load-displacement response curve at the top of the anchor rod is extracted from the mechanical response characteristic curve. The yield load value is determined by calculating the decrease of the tangential stiffness to the preset proportion of the initial tangential stiffness. Then, the value is multiplied by the safety factor to obtain the predicted value of the ultimate pull-out bearing capacity, giving the prediction results a clear mechanical basis and reliable accuracy.

[0031] The foregoing has provided a detailed description of one embodiment of the present invention, but this description is merely a preferred embodiment and should not be construed as limiting the scope of the invention. All equivalent variations and modifications made within the scope of the claims of this invention should still fall within the patent coverage of this invention.

Claims

1. A design method for an integrated mechanical model of a compressive composite anti-buoyancy anchor bolt, characterized in that, Specifically, the steps include the following: Step S1: Obtain the multi-layer structural parameter set of the anti-buoyancy anchor in the target geotechnical engineering, wherein the multi-layer structural parameter set includes anchor reinforcement parameters, grouting body parameters, anti-corrosion sleeve parameters and surrounding soil and rock parameters; Step S2: Perform hierarchical interface mechanical behavior analysis on the multi-layer structure parameter set to generate the interface shear stress transfer function between each structural layer; Step S3: Embed the interface shear stress transfer function into the axisymmetric force analysis framework of the composite anti-buoyancy anchor to obtain the axial force distribution function and side resistance distribution function over the entire length of the anchor. Step S4: Construct an integrated set of mechanical equilibrium equations for the compressive composite anti-buoyancy anchor rod based on the axial force distribution function and the side resistance distribution function; Step S5: Solve the integrated mechanical equilibrium equations piecewise numerically and output the mechanical response characteristic curves of the anchor at different burial depths. Step S6: Determine the predicted value of the ultimate pull-out bearing capacity of the anchor rod based on the mechanical response characteristic curve, and use the predicted value of the ultimate pull-out bearing capacity as the design output result of the integrated mechanical model.

2. The design method for an integrated mechanical model of a compressive composite anti-buoyancy anchor bolt according to claim 1, characterized in that, Step S2 specifically includes the following steps: The rib height and rib spacing on the surface of the anchor rod are extracted from the anchor rod parameters, and the first interface roughness coefficient between the anchor rod and the grouting body is calculated based on the rib height and rib spacing. The elastic modulus and Poisson's ratio of the grout body are extracted from the grout body parameters, and the second interface bonding stiffness between the grout body and the anti-corrosion sleeve is calculated based on the elastic modulus and Poisson's ratio of the grout body. The friction angle and wall thickness of the outer wall of the casing are extracted from the parameters of the anti-corrosion casing, and the friction coefficient of the third interface between the anti-corrosion casing and the surrounding rock and soil is calculated based on the friction angle and wall thickness of the outer wall of the casing. Substituting the roughness coefficient of the first interface, the bonding stiffness of the second interface, and the friction coefficient of the third interface into the elastoplastic interface constitutive model, respectively, generates the first shear stress transfer function of the interface between the reinforcing bar and the grout, the second shear stress transfer function of the interface between the grout and the anti-corrosion sleeve, and the third shear stress transfer function of the interface between the anti-corrosion sleeve and the surrounding soil and rock. The first shear stress transfer function, the second shear stress transfer function, and the third shear stress transfer function constitute the interface shear stress transfer function.

3. The design method for an integrated mechanical model of a compressive composite anti-buoyancy anchor bolt according to claim 2, characterized in that, The constitutive model of the elastoplastic interface uses a bilinear softening model to describe the shear stress-slip relationship of the interface.

4. The design method of an integrated mechanical model for a compressive composite anti-buoyancy anchor bolt according to claim 1, characterized in that, Step S3 specifically includes the following steps: dividing the entire length of the anchor rod into multiple micro-segments with the anchor rod axis as the longitudinal coordinate axis; applying axial equilibrium conditions to each micro-segment to establish a differential relationship between the axial force increment and the interface shear stress of that micro-segment; substituting the interface shear stress transfer function into the differential relationship to obtain the axial force differential equation corresponding to each micro-segment; integrating the axial force differential equation along the entire length of the anchor rod to obtain the axial force distribution function as the axial force distribution function along the longitudinal coordinate within the entire length of the anchor rod; and differentiating the axial force distribution function with respect to the longitudinal coordinate to obtain the side resistance distribution function as the side resistance distribution function within the entire length of the anchor rod.

5. The design method for an integrated mechanical model of a compressive composite anti-buoyancy anchor bolt according to claim 1, characterized in that, Step S4 specifically includes the following steps: The axial force distribution function is assigned the value of the external load at the top of the anchor rod and the value of zero at the bottom of the anchor rod to form the first boundary condition; The displacement continuity condition is applied to the side drag distribution function at the interface of each structural layer to form a second boundary condition; Based on the first boundary condition and the second boundary condition, the axial force distribution function and the side resistance distribution function are combined to obtain the first equilibrium equation of the anchor reinforcement, the second equilibrium equation of the grouting layer, the third equilibrium equation of the anti-corrosion casing layer, and the fourth equilibrium equation of the surrounding rock and soil layer. The first equilibrium equation, the second equilibrium equation, the third equilibrium equation, and the fourth equilibrium equation are combined to form an integrated set of mechanical equilibrium equations.

6. The design method for an integrated mechanical model of a compressive composite anti-buoyancy anchor bolt according to claim 1, characterized in that, Step S5 specifically includes the following steps: Based on the thickness and material properties of each structural layer in the multi-layer structure parameter set, the entire length of the anchor rod is divided into a steel reinforcement-dominated section, a grouting-dominated section, an anti-corrosion sleeve-dominated section, and a soil-dominated section. Within each dominant segment, a numerical integration step size matching the structural layer of that segment is selected; The integrated mechanical equilibrium equations are solved piece by piece according to the numerical integration step size, and the axial force, side resistance and displacement values ​​are calculated at the end of each integration step size. The calculated axial force, side resistance, and displacement values ​​are respectively fitted to curves according to the burial depth to generate axial force variation curves, side resistance variation curves, and displacement variation curves as mechanical response characteristic curves.

7. The design method for an integrated mechanical model of a compressive composite anti-buoyancy anchor bolt according to claim 6, characterized in that, Within each dominant segment, the step of selecting a numerical integration step size that matches the structural layer of that segment specifically includes: Within the main section of the reinforcing steel, the upper limit of the first integral step is determined based on the yield strain of the reinforcing steel. Within the dominant section of the grouting body, the upper limit of the second integral step is determined based on the elastic limit strain of the grouting body; Within the dominant section of the anti-corrosion sleeve, the upper limit of the third integral step is determined based on the radial stiffness of the anti-corrosion sleeve. Within the dominant section of the rock and soil mass, the upper limit of the fourth integral step is determined based on the shear wave velocity of the rock and soil mass; Values ​​smaller than the first integration step size upper limit, the second integration step size upper limit, the third integration step size upper limit, and the fourth integration step size upper limit are selected as the numerical integration step size for each dominant segment.

8. The design method for an integrated mechanical model of a compressive composite anti-buoyancy anchor bolt according to claim 6, characterized in that, The steps of solving the integrated mechanical equilibrium equations piecewise according to the numerical integration step size, and calculating the axial force, side resistance, and displacement at the end of each integration step size, specifically include: Starting from the top of the anchor bolt, the top boundary condition is used as the initial value. The first equilibrium equation of the first dominant section is solved by using the prediction-correction iterative format to obtain the first axial force value and the first displacement value at the end of each integral step in the section. Using the first axial force value and the first displacement value as the initial conditions of the second dominant section, the second equilibrium equation is solved by advancing the solution to obtain the second axial force value and the second displacement value at the end point of each integral step in the second dominant section. Using the second axial force value and the second displacement value as the initial conditions of the third dominant section, the third equilibrium equation is solved by advancing the solution to obtain the third axial force value and the third displacement value at the end point of each integral step in the third dominant section. Using the third axial force value and the third displacement value as the initial conditions of the fourth dominant section, the fourth equilibrium equation is solved by advancing the solution to obtain the fourth axial force value and the fourth displacement value at the end point of each integral step in the fourth dominant section. Differentiate the axial force value at the end of each integration step with respect to the longitudinal coordinate to obtain the side resistance value at the corresponding end of the integration step.

9. The design method for an integrated mechanical model of a compressive composite anti-buoyancy anchor bolt according to claim 1, characterized in that, Step S6, the step of determining the predicted value of the ultimate pull-out bearing capacity of the anchor rod based on the mechanical response characteristic curve, specifically includes: Extract the complete curve of the axial force at the top of the anchor bolt as the external load increases from the mechanical response characteristic curve as the load-displacement response curve; Calculate the tangential stiffness values ​​between adjacent data points sequentially on the load-displacement response curve; When the tangent stiffness value at a certain measuring point first drops to a preset proportion of the initial tangent stiffness value, the corresponding top axial force value is determined as the yield load value. The predicted value of the ultimate tensile bearing capacity is obtained by multiplying the yield load value by a preset safety factor.

10. The design method of an integrated mechanical model for a compressive composite anti-buoyancy anchor bolt according to claim 9, characterized in that, The step of extracting the complete curve of the axial force at the top of the anchor bolt changing with the increase of external load from the mechanical response characteristic curve as the load-displacement response curve specifically includes: The point where the burial depth of the anchor top is zero in the mechanical response characteristic curve is used as the top monitoring point; The axial force and displacement values ​​under different external load levels are read from the top monitoring point; By using the axial force value under each external load level as the ordinate and the displacement value as the abscissa, a discrete data point pair sequence is generated. The discrete data point pairs are sorted in a monotonically increasing order, and the sorted discrete data point pairs are connected sequentially with line segments to generate the load-displacement response curve.

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