Method, device and medium for prestressed anchor arrangement based on virtual stiffness iteration

Abstract

The present application relates to the technical field of underground structure anti-floating engineering, and aims to provide a prestressed anchor rod arrangement method, device and medium based on virtual stiffness iteration. The present application can simplify the coupling calculation between prestress application and real stiffness of the anchor rod, and through iterative optimization on the virtual stiffness of the prestressed anchor rod and arrangement nodes, the reasonable arrangement of the prestressed anchor rod is realized on the basis of meeting the deformation coordination and vertical stress requirements of the upper structure, and the safety and economy of the anti-floating design of the underground structure are improved.

Description

Technical Field

[0001] This invention relates to the field of anti-buoyancy engineering technology for underground structures, specifically to a method, equipment, and medium for arranging prestressed anchor bolts based on virtual stiffness iteration. Background Technology

[0002] In underground engineering construction in areas with high groundwater levels, groundwater buoyancy is the core cause of overall uplift of underground structures, heave and cracking of the foundation slab, and damage and failure of components. Prestressed anti-buoyancy anchors, with their advantages of actively applying prestress, pre-constraining structural deformation, and stable anti-buoyancy performance, have become the mainstream technical means for anti-buoyancy design of underground structures.

[0003] The existing design and placement technology for prestressed anti-buoyancy anchors has three major technical defects: First, traditional design methods determine the number of anchor bolts solely by "total net buoyancy ÷ single anchor design pull-out force," employing an empirical, uniform, full-span arrangement. This approach fails to consider the coordinated deformation relationships between the base slab, prestressed anchor bolts, soil, and superstructure, and cannot achieve structural force balance based on deformation coordination. This easily leads to overload of anchor bolts in the mid-span area and redundant stress in the column sub-area. The deformation coordination control accuracy is low, the anchor bolt arrangement is coarse, and it is difficult to balance safety and economy.

[0004] Second, a few design schemes that consider deformation coordination must fully account for the coupling and superposition effects of the prestressing application process with the actual axial stiffness of the anchor rod, the stiffness of the base plate, the soil constraint stiffness, and the stiffness of the superstructure. This results in complex calculations of the coupling between prestressing and anchor rod stiffness, highly complex models, and difficulties in convergence, making them difficult to implement in engineering design.

[0005] Third, existing technologies have not achieved the cyclic iterative design of anchor virtual stiffness and anchor position, and cannot construct a stiffness iteration to lock the anchor internal force and position adjustment iteration to control the vertical internal force of the superstructure. They cannot accurately achieve the overall force balance of the structure while ensuring deformation coordination, and it is difficult to achieve the optimal anchor arrangement.

[0006] In summary, developing a prestressed anti-buoyancy anchor arrangement method that simplifies calculations, is based on deformation coordination, and simultaneously achieves force balance has become an urgent technical problem to be solved in this field. Summary of the Invention

[0007] The purpose of this invention is to provide a method, equipment, and medium for arranging prestressed anchors based on virtual stiffness iteration. This method simplifies the coupling calculation between prestressing application and the actual stiffness of the anchors. By iteratively optimizing the virtual stiffness and arrangement nodes of the prestressed anchors, it achieves a reasonable arrangement of prestressed anchors while meeting the requirements of deformation coordination and vertical stress of the superstructure, thereby improving the safety and economy of the anti-buoyancy design of underground structures.

[0008] One of the objectives of this invention is achieved through the following technical solution: A prestressed anchor placement method based on virtual stiffness iteration is applied to the anti-buoyancy design of the foundation slab of underground structures subjected to groundwater buoyancy, and includes the following steps: S1. Collect the basic design parameters and calculate the number of prestressed anchor bolts based on the basic design parameters. The basic design parameters include the parameters of the underground structure slab, hydrogeological parameters, superstructure parameters, and the design parameters of the prestressed anchor bolts. S2. Calculate the displacement distribution of the bottom plate under buoyancy conditions based on the basic design parameters to obtain the initial displacement field of the bottom plate. Determine the initial arrangement nodes of the prestressed anchors and the initial virtual stiffness of the prestressed anchors based on the initial displacement field of the bottom plate. Based on the basic design parameters, the initial arrangement nodes of the prestressed anchors and the initial virtual stiffness, establish a collaborative mechanical model of soil-bottom plate-anchor-superstructure. S3. Based on the aforementioned soil-base plate-anchor rod-superstructure collaborative mechanical model, deformation coordination calculations are performed. The relative deviation between the standard value of the internal force of the prestressed anchor rod and its design pull-out bearing capacity characteristic value is not greater than the preset allowable deviation is used as the stiffness convergence condition. The virtual stiffness of each prestressed anchor rod is iterated to obtain the converged virtual stiffness and the converged displacement field of the base plate under the corresponding arrangement node of each prestressed anchor rod. S4. Calculate the standard values ​​of internal forces of the vertical members of the superstructure based on the convergent displacement field of the base plate, and use the fact that the standard values ​​of internal forces of the vertical members of the superstructure are not greater than the corresponding standard values ​​of vertical resistance as the position convergence condition, and perform position optimization iteration on the arrangement nodes of the prestressed anchor rods; based on the arrangement nodes of the prestressed anchor rods after position optimization iteration, repeat step S3 until each prestressed anchor rod satisfies the stiffness convergence condition and the standard values ​​of internal forces of each vertical member of the superstructure satisfies the position convergence condition, thereby obtaining the convergent arrangement nodes of the prestressed anchor rods; S5. Based on the convergence arrangement nodes of each prestressed anchor rod, and the corresponding convergence virtual stiffness and bottom plate convergence displacement field obtained under the convergence arrangement nodes, the tensioning prestress value of each prestressed anchor rod is calculated by inversion, and the prestressed anchor rod arrangement scheme is determined.

[0009] The second objective of this invention is achieved through the following technical solution: A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the steps of a prestressed anchor bolt arrangement method based on virtual stiffness iteration.

[0010] The third objective of this invention is achieved through the following technical solution: A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a prestressed anchor bolt arrangement method based on virtual stiffness iteration.

[0011] Compared with the prior art, the advantages of the present invention are as follows: 1. By introducing an adjustable virtual stiffness into the prestressed anchor rod in the deformation coordination calculation, the complex coupling relationship between the prestressing application and the actual stiffness of the anchor rod is transformed into an iterative adjustment of the virtual stiffness. This eliminates the need to directly simulate the actual prestressing application process in each iteration, thereby simplifying the calculation model, reducing the amount of calculation, improving the convergence efficiency of iterative calculation, and reducing the difficulty of engineering applications.

[0012] 2. By incorporating the base slab, soil, prestressed anchor rods, and superstructure into a co-mechanical model, the internal forces of the prestressed anchor rods and the internal forces of the vertical members of the superstructure are controlled while meeting the deformation coordination requirements. This makes the overall stress on the underground structure more balanced, thereby reducing the risk of base slab cracking, punching shear failure at the junction of the base slab and vertical members, and overload failure of the prestressed anchor rods, and improving the long-term service safety of the underground structure. 3. By iteratively adjusting the virtual stiffness and arrangement nodes of the prestressed anchor rods, the prestressed anchor rods can be arranged differently according to the displacement distribution of the base plate and the vertical internal force distribution of the superstructure. This improves the problem of uneven stress on the prestressed anchor rods. Compared with the traditional uniform full-span arrangement method, this invention is beneficial to reduce the number of prestressed anchor rods, reduce material consumption and construction costs, and improve the rationality and economy of the prestressed anchor rod arrangement. Attached Figure Description

[0013] Figure 1 This is an engineering example of the prestressed anchor bolt arrangement method based on virtual stiffness iteration of the present invention, showing the initial displacement field of the bottom plate under buoyancy conditions. Figure 2 This is a diagram showing the convergence virtual stiffness and convergence arrangement nodes of the prestressed anchor bolts in an engineering example of the prestressed anchor bolt arrangement method based on virtual stiffness iteration according to the present invention. Figure 3 This is the base plate convergence displacement field of an engineering example of the prestressed anchor bolt arrangement method based on virtual stiffness iteration of this invention; Figure 4 This is a diagram showing the internal force calculation results of the prestressed anchor rods and vertical members of the superstructure in an engineering example of the prestressed anchor rod arrangement method based on virtual stiffness iteration of this invention. Figure 5 This is a diagram showing the tensioning prestress values ​​of each prestressed anchor in an engineering example of the prestressed anchor arrangement method based on virtual stiffness iteration according to the present invention. Detailed Implementation

[0014] The present invention will now be described in detail with reference to the accompanying drawings and embodiments: A prestressed anchor placement method based on virtual stiffness iteration is applied to the anti-buoyancy design of the foundation slab of underground structures subjected to groundwater buoyancy, and includes the following steps: S1. Collect the basic design parameters and calculate the number of prestressed anchor bolts based on the basic design parameters. The basic design parameters include the parameters of the underground structure slab, hydrogeological parameters, superstructure parameters, and the design parameters of the prestressed anchor bolts. Specifically, the parameters of the underground structure's foundation slab include the slab's geometric dimensions, thickness, concrete strength grade, and standard value of its self-weight; the hydrogeological parameters include the groundwater design level, standard value of the total buoyancy of the foundation slab, soil physical and mechanical properties, and soil subgrade coefficient; the parameters of the superstructure include the column grid layout, standard value of the superstructure's self-weight, limit of punching shear capacity at the junction of the foundation slab and vertical members, and vertical constraint stiffness matrix of the superstructure; the design parameters of the prestressed anchor rods include the anchor rod specifications, elastic modulus, effective bearing length, characteristic value of design pull-out bearing capacity, limit of tension control stress, and true axial stiffness of the anchor rod, etc.; all of the above parameters are determined based on the actual project's design documents, geological survey data, and prestressed anchor rod design requirements.

[0015] Specifically, the anti-buoyancy design is based on the vertical resistance provided by the self-weight of the superstructure (which may be locally controlled by the punching shear capacity of the base plate and the superstructure). Considering the overall anti-buoyancy safety factor, the required number of anchor bolts is calculated. The number of anchor bolts is calculated using the following formula: ; In the formula: This refers to the number of prestressed anchor bolts arranged. The safety factor for buoyancy resistance; This represents the standard value of the total buoyancy of the base plate. The sum of the standard values ​​of vertical resistance provided for the superstructure and its own weight; The characteristic value of pull-out bearing capacity is designed for a single prestressed anchor rod.

[0016] It should be noted that, The value (i.e. the number of prestressed anchor bolts) also needs to be fine-tuned to take into account the rationality of the specific structural layout. For example, since most structures have symmetrical anchor bolt arrangements, an even number of anchor bolts is more reasonable. For the anti-buoyancy safety factor, the value should be taken according to the current specifications based on the actual project. For ordinary projects such as conventional underground garages and water tanks, a value of 1.05 can be taken, while for important projects, special projects such as high water levels and soft soil geology, a value of 1.1 to 1.2 can be taken. S2. Calculate the displacement distribution of the bottom plate under buoyancy conditions based on the basic design parameters to obtain the initial displacement field of the bottom plate. Determine the initial arrangement nodes of the prestressed anchors and the initial virtual stiffness of the prestressed anchors based on the initial displacement field of the bottom plate. Based on the basic design parameters, the initial arrangement nodes of the prestressed anchors and the initial virtual stiffness, establish a collaborative mechanical model of soil-bottom plate-anchor-superstructure. Furthermore, the initial arrangement nodes of each prestressed anchor are evenly set on the median contour line of the initial displacement field of the base plate.

[0017] Furthermore, the initial virtual stiffness of each prestressed anchor rod is the ratio of its design pull-out bearing capacity characteristic value to the median value of the initial displacement field of the base plate.

[0018] S3. Based on the aforementioned soil-base plate-anchor rod-superstructure collaborative mechanical model, deformation coordination calculations are performed. The relative deviation between the standard value of the internal force of the prestressed anchor rod and its design pull-out bearing capacity characteristic value is not greater than the preset allowable deviation is used as the stiffness convergence condition. The virtual stiffness of each prestressed anchor rod is iterated to obtain the converged virtual stiffness and the converged displacement field of the base plate under the corresponding arrangement node of each prestressed anchor rod. Furthermore, the deformation coordination calculation is determined by the following formula: ; ; In the formula: This is the overall vertical stiffness matrix; This is the vertical displacement vector of the node; It is the vertical equivalent nodal force vector of the combination of buoyancy and the self-weight of the bottom plate; Here is the vertical stiffness matrix of the base plate; This represents the vertical virtual stiffness matrix of the prestressed anchor bolt. Here is the vertical stiffness matrix of the soil subgrade. This is the vertical constraint stiffness matrix of the superstructure.

[0019] It should be noted that establishing a collaborative mechanical model of soil-base slab-anchor bolt-superstructure and introducing the concept of virtual stiffness of prestressed anchor bolts is to simplify the complex calculation of coupling between actual prestressing and real stiffness of anchor bolts, and to prepare for refined iterative calculations. This can effectively reduce the actual amount of calculation. The model features are: the foundation soil, base slab and superstructure all adopt real stiffness, and the anchor bolt position and virtual stiffness of anchor bolts are variables.

[0020] The "virtual stiffness" described in this invention is an adjustable numerical parameter introduced in deformation compatibility calculations. It is assigned to each node containing an anchor rod, has a definite physical dimension (kN / m), but does not correspond to any actual physical stiffness of the anchor rod. Its function is to decouple the complex coupling effect between prestress and the actual stiffness of the anchor rod during the calculation process. By iteratively adjusting its value, the internal force of the anchor rod is precisely controlled to the target value; it is a purely internal force control variable. In subsequent steps, the actual prestress application value will be derived from the converged virtual stiffness value.

[0021] Specifically, The (i.e., the vertical virtual stiffness matrix of the prestressed anchor) is a diagonal matrix, with values ​​assigned only at nodes where the anchor is located, and elements at non-anchor locations being 0; it has no actual physical stiffness correspondence, and is only used as an internal force control variable to decouple the prestress from the actual stiffness coupling.

[0022] This model is strictly based on the fundamental principles of the displacement method in structural mechanics. The vertical displacement vector of the node is the only fundamental unknown. All stiffness terms are defined as the vertical stiffness of the corresponding node's vertical displacement, with unified physical meaning, consistent dimensions (kN / m), and a unified coordinate system (global vertical coordinate system). According to the principle of superposition of small deformations in linear elasticity: when multiple linear elastic springs act on the same node in the same displacement direction, the total stiffness of the node is equal to the algebraic sum of the stiffnesses of each spring. The physical meaning of each stiffness matrix is ​​as follows: The vertical stiffness matrix of the base plate, in physical terms, is "the vertical force required to produce a unit vertical displacement at a node of the base plate"; The vertical virtual stiffness matrix of a prestressed anchor bolt, physically defined as "the anchor bolt tension required to produce a unit vertical displacement at the corresponding node of the anchor bolt"; : Soil vertical subgrade stiffness matrix, physically meaning "the internal force of the foundation required to produce a unit vertical displacement at a certain node of the soil"; The vertical constraint stiffness matrix of the superstructure is physically defined as "the vertical internal force of the superstructure required to produce a unit vertical displacement at the column / wall node".

[0023] in, The first stiffness matrix is ​​not a diagonal matrix; it describes the interactions between nodes. The other stiffness matrices are diagonal matrices (assigned only to the corresponding nodes), describing locally independent behavior. All the above stiffness matrices correspond to the same vertical degree of freedom of the nodes. Based on the principle of linear elastic superposition and the standard operation of finite element normal matrix integration, Provides contributions to inter-node coupling. , , Each element contributes independent stiffness to the vertical degree of freedom of its corresponding node in the form of diagonal elements. These elements can be directly algebraically added together in their respective degrees of freedom to form the overall stiffness matrix. ; It should be noted that the initial displacement field of the base plate is obtained by setting the virtual stiffness of each prestressed anchor rod to 0, i.e., in the simultaneous calculation for deformation compatibility, , =0.

[0024] The construction of the overall stiffness matrix in the above deformation compatibility calculation equation strictly follows the matrix integration principle of the finite element method. A full-array or strip matrix is ​​used to characterize the coupling effect between base plate elements, while , , This is a diagonal matrix with non-zero terms only in the vertical degrees of freedom at this node. Adding them algebraically over their corresponding degrees of freedom is a standard assembly operation commonly used in structural analysis, moving from elements to the whole. It has a rigorous physical and mathematical foundation. This method simplifies the complex problem of a spatial continuum into a clear and universally applicable parallel spring-plate combination model, ensuring the stability and convergence of the iterative solution.

[0025] Further, in step S3, the standard value of the internal force of the prestressed anchor rod is calculated using the following formula: ; In the formula: For the first i Standard values ​​of internal forces in a prestressed anchor bolt; For the first i Virtual stiffness of a prestressed anchor rod; For the first i Displacement of the bottom plate node corresponding to the prestressed anchor rod.

[0026] It should be noted that the first i Standard value of internal force of prestressed anchor rod The virtual stiffness of the prestressed anchor during the current iteration process The displacement of the bottom plate nodes at the corresponding arrangement nodes Determined jointly. The virtual stiffness of the prestressed anchor bolt is adjusted each time. Subsequently, the vertical virtual stiffness matrix of the prestressed anchor rod The system is then updated, and deformation compatibility calculations are performed again to obtain the updated base plate displacement field and the corresponding base plate node displacements at the arranged nodes. And then recalculate the first i Standard value of internal force of prestressed anchor rod .

[0027] Further, in step S3, the relative deviation between the standard value of the internal force of the prestressed anchor rod and its designed pull-out bearing capacity characteristic value does not exceed a preset allowable deviation as the stiffness convergence condition. The preset allowable deviation can be selected from 0.01 to 0.08 according to the actual engineering situation, and can be calculated by the following formula: ; In the formula: For the first i Standard values ​​of internal forces in a prestressed anchor bolt; Design the characteristic value of pull-out bearing capacity for a single prestressed anchor rod; This is the preset allowable deviation.

[0028] Specifically, when the i The prestressed anchor rod does not meet the stiffness convergence condition, and Less than At that time, increase the number of times. i Virtual stiffness of prestressed anchor rods When the first i The prestressed anchor rod does not meet the stiffness convergence condition, and Greater than When, decrease the first i Virtual stiffness of prestressed anchor rods When the first i When a prestressed anchor rod satisfies the aforementioned stiffness convergence condition, its virtual stiffness is maintained. constant.

[0029] S4. Calculate the standard values ​​of internal forces of the vertical members of the superstructure based on the convergent displacement field of the base plate, and use the fact that the standard values ​​of internal forces of the vertical members of the superstructure are not greater than the corresponding standard values ​​of vertical resistance as the position convergence condition, and perform position optimization iteration on the arrangement nodes of the prestressed anchor rods; based on the arrangement nodes of the prestressed anchor rods after position optimization iteration, repeat step S3 until each prestressed anchor rod satisfies the stiffness convergence condition and the standard values ​​of internal forces of each vertical member of the superstructure satisfies the position convergence condition, thereby obtaining the convergent arrangement nodes of the prestressed anchor rods; Further, in step S4, the standard value of the internal force of the vertical members of the superstructure is calculated using the following formula: ; In the formula: Let j be the standard value of the internal force of the j-th vertical member of the superstructure; Let J be the vertical constraint stiffness of the j-th vertical member of the superstructure. Let be the displacement of the bottom plate node corresponding to the j-th vertical member of the superstructure.

[0030] It should be noted that the vertical constraint stiffness of the j-th vertical member of the superstructure... The parameters of the vertical members of the superstructure are determined based on the cross-sectional parameters, material elastic modulus, member length, connection relationship, and boundary constraint conditions.

[0031] Furthermore, in step S4, the standard value of the internal force of the j-th vertical member of the superstructure is used. Not greater than its corresponding standard value of vertical resistance As a condition for location convergence, that is: ≤ ; The standard value of vertical resistance The vertical resistance is determined based on the permanent vertical load within the influence range of the j-th vertical member of the superstructure that provides anti-buoyancy. This permanent vertical load includes the self-weight of the superstructure, the self-weight of the foundation, the weight of the soil cover at the base, and other permanent vertical loads that can be included in the anti-buoyancy calculation, excluding live loads. The standard value of the vertical resistance... The shear resistance limit at the junction of the base plate and the j-th vertical member of the superstructure shall not exceed the limit value of the punching shear capacity.

[0032] Further, in step S4, the position optimization iteration specifically involves: when the standard value of the internal force of the j-th vertical member of the superstructure... Greater than its corresponding vertical resistance standard value At that time, the arrangement nodes of the prestressed anchor rods associated with the vertical members of the superstructure will be adjusted to be closer to the vertical members of the superstructure.

[0033] Furthermore, since the number of prestressed anchor rods is limited, the standard value of the internal force of the vertical members of the superstructure needs to be as close as possible to the standard value of its vertical resistance. Therefore, when the j-th vertical member of the superstructure satisfies the aforementioned position convergence condition and has a large vertical resistance margin, the arrangement node of the prestressed anchor rod associated with the vertical member of the superstructure can be adjusted to a direction away from the vertical member of the superstructure, thereby improving the rationality of the arrangement node.

[0034] Furthermore, in step S4, based on the prestressed anchor bolt arrangement nodes after position optimization iteration, the virtual stiffness obtained by each prestressed anchor bolt in the previous stiffness iteration is used again, and step S3 is returned as the initial virtual stiffness to re-perform virtual stiffness iteration and deformation coordination calculation until each prestressed anchor bolt satisfies the stiffness convergence condition and each vertical component of the superstructure satisfies the position convergence condition, thereby obtaining the convergence arrangement nodes of the prestressed anchor bolts.

[0035] S5. Based on the convergence arrangement nodes of each prestressed anchor rod, and the corresponding convergence virtual stiffness and bottom plate convergence displacement field obtained under the convergence arrangement nodes, the tensioning prestress value of each prestressed anchor rod is calculated by inversion, and the prestressed anchor rod arrangement scheme is determined.

[0036] Furthermore, the inversion calculation formula for the tensioning prestress value of the prestressed anchor in step S5 is as follows: ; In the formula: For the first i The tensioning prestress value of the prestressed anchor rod; For the first i The convergence virtual stiffness of a prestressed anchor rod; For the first i The convergence displacement of the bottom plate node corresponding to the prestressed anchor rod; For the first i The actual axial stiffness of the prestressed anchor rod; When applying prestress, the first i The equivalent stiffness component of the foundation at the location corresponding to the prestressed anchor rod.

[0037] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the above-described method for arranging prestressed anchor bolts based on virtual stiffness iteration.

[0038] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method for arranging prestressed anchor bolts based on virtual stiffness iteration.

[0039] Furthermore, the above-mentioned method for arranging prestressed anchor bolts based on virtual stiffness iteration also includes the following steps: S6. Verify the bearing capacity of the prestressed anchor bolt arrangement scheme, and after construction according to the prestressed anchor bolt arrangement scheme, monitor and verify the stress of each prestressed anchor bolt and the vertical internal force of the superstructure.

[0040] The bearing capacity check specifically requires that the sum of the total pull-out bearing capacity of the prestressed anchor rods and the vertical resistance that can be taken into account for anti-buoyancy effect should not be less than the total buoyancy of the bottom plate after considering the anti-buoyancy safety factor.

[0041] Furthermore, based on the above-mentioned prestressed anchor arrangement method, the prestressed anchors can be arranged differently. Specifically, for areas with large base plate displacement and high anti-buoyancy requirements, the anchors can be arranged more densely; for areas with strong superstructure self-weight constraints and large vertical resistance margins, the prestressed anchors in these areas can be arranged more sparsely. It should be noted that the number of prestressed anchors calculated in this invention is the minimum number of anchors. After the prestressed anchor arrangement nodes are determined, additional prestressed anchors can be added for local densification.

[0042] The following engineering examples further illustrate the prestressed anchor bolt arrangement method based on virtual stiffness iteration of this invention: like Figure 1-5 The diagram shown is an engineering example of the prestressed anchor bolt arrangement method based on virtual stiffness iteration provided by this invention: I. Collect foundation design parameters and determine the number of anchor bolts. This project example is applied to the anti-buoyancy engineering of an existing underground parking garage in a city. The bearing layer of the independent foundation and the anti-buoyancy raft is a dense gravel layer, and the subgrade coefficient is taken as 6.5×10. 4 kN / m 3 The project has two underground floors, with a standard column grid layout of 7.5m × 8.0m (large columns are 15m × 16m, with the height of the large columns covering the second underground floor and the fifth floor above ground; the smaller columns in the middle only extend to the first basement floor). It is a multi-span frame structure with a base slab thickness of 400mm, concrete strength grade C40, and concrete unit weight of 25kN / m³. 3 The groundwater design water level is located 5.0m above the bottom surface of the foundation slab, and the standard value of buoyancy is... =50kN / m 2 The control value for the buoyancy bearing capacity of the main column is 1600kN at the junction of the base plate and the column, and the control value for the buoyancy bearing capacity of the secondary column is 600kN based on its own weight; the standard value for the ultimate tensile strength of the four columns is 1860N / mm². 2 S15.2 has bonded steel strand prestressed anchor bolts with a free section length of 5m and an anchor bolt stiffness k=2.15×10. 4 kN / m, the characteristic value of the design pull-out bearing capacity of the anchor is 350kN.

[0043] The minimum number of anchor bolts is calculated based on the parameters of the underground structure's base plate, hydrogeological parameters, superstructure parameters, and the design parameters of the prestressed anchor bolts.

[0044] Calculation of the number of anchor bolts: ; n = (1.05×15×16×50-15×16×0.4×25-1×1600-3×600) / 350 = 19.4, take 20 roots.

[0045] II. Establishing a co-mechanical model and calculating the initial displacement field of the base plate This engineering example uses PKPM software to establish a collaborative mechanical model of soil-base slab-prestressed anchor rod-superstructure. The foundation soil, base slab and superstructure are included in the calculation according to their actual stiffness, and the arrangement nodes and virtual stiffness of the prestressed anchor rods are used as subsequent iteration variables.

[0046] When calculating the initial displacement field of the base plate, the vertical virtual stiffness matrix of the prestressed anchor rod is used. The value is set to zero, meaning the vertical constraint effect of the prestressed anchor rods on the base plate is not considered, and deformation compatibility calculations are performed according to the following formula: ; ; Thus, the initial displacement field of the bottom plate under buoyancy conditions and the corresponding displacement contour curves are obtained, as shown in the attached figure. Figure 1 As shown.

[0047] The median of the initial displacement field of the base slab is approximately 2.0 mm. The initial arrangement nodes of the 20 prestressed anchor rods are evenly distributed along the contour line of the median of the initial displacement field of the base slab, while also considering symmetry. The initial virtual stiffness of each prestressed anchor rod is: 350kN ÷ 2.0mm = 17.5 × 10 4 kN / m.

[0048] III. Performing Virtual Stiffness Iteration Assign the initial arrangement nodes and initial virtual stiffness of each prestressed anchor to the co-mechanical model, and perform deformation coordination calculations according to the following formula: ; ; Obtain the displacement of the bottom plate nodes, and calculate the standard value of the internal force of each prestressed anchor rod according to the following formula: ; Preset tolerance in this project example Take 0.08, when the first i The prestressed anchor rod does not meet the stiffness convergence condition, and Less than When this is done, increase the virtual stiffness of the prestressed anchor rod. ;when Greater than When this is done, the virtual stiffness of the prestressed anchor rod is reduced. ; When it satisfies the following formula, the corresponding virtual stiffness remains unchanged: ; After each adjustment of the virtual stiffness of the prestressed anchor, update the vertical virtual stiffness matrix of the prestressed anchor. Then, the deformation coordination calculation was re-performed, and the standard value of the internal force of each prestressed anchor was re-determined until each prestressed anchor met the stiffness convergence condition.

[0049] IV. Iterative optimization of anchor bolt positions Based on the convergent displacement field of the base plate obtained by virtual stiffness iteration, the standard values ​​of the internal forces of the vertical members of the superstructure are calculated according to the following formula: ; in, The parameters are determined based on the cross-sectional parameters, material elastic modulus, member length, connection relationships, and boundary constraints of the j-th vertical member of the superstructure. This represents the displacement of the bottom plate node corresponding to the vertical member of the superstructure.

[0050] The standard value of the internal force of the vertical members of the superstructure is not greater than the standard value of its corresponding vertical resistance, which is taken as the location convergence condition. ≤ ; When the standard value of the internal force of a vertical member of the superstructure is greater than the standard value of its corresponding vertical resistance, the arrangement nodes of the prestressed anchors associated with the vertical member of the superstructure will be adjusted to be closer to the vertical member of the superstructure. When a vertical member of the superstructure meets the position convergence condition and has a large vertical resistance margin, the prestressed anchors associated with it can be adjusted to be farther away from the vertical member of the superstructure, so that the prestressed anchors are redistributed to the area with larger vertical internal forces.

[0051] Based on the prestressed anchor bolt arrangement nodes after position optimization iteration, the virtual stiffness of each prestressed anchor bolt obtained in the previous stiffness iteration is reused, and the vertical virtual stiffness matrix of the prestressed anchor bolts is updated according to the adjusted arrangement nodes. Then, the virtual stiffness iteration and deformation compatibility calculations are re-executed.

[0052] This project example uses manually controlled iterative parameters and PKPM software to complete multiple rounds of virtual stiffness iteration and position optimization iteration. The virtual stiffness and convergence arrangement nodes of the prestressed anchor bolts are shown in the attached figure. Figure 2 As shown, the corresponding convergent displacement field of the base plate is attached. Figure 3 As shown in the attached figure, the internal force calculation results for each prestressed anchor rod and the vertical members of the superstructure are as follows. Figure 4 As shown.

[0053] V. Determine the convergence criteria After the final iteration calculation, the standard values ​​of the internal forces of each prestressed anchor rod were 329–344 kN, with the maximum relative deviation being: (350 - 329) ÷ 350 = 0.06.

[0054] Since 0.06 is less than the preset relative tolerance of 0.08 used in this project example, all prestressed anchor rods meet the stiffness convergence condition.

[0055] The calculated standard value of the maximum vertical internal force of the large column is 1435kN, which is less than the corresponding standard value of vertical resistance of 1600kN; the standard value of the maximum vertical internal force of the small column is 514kN, which is less than the corresponding standard value of vertical resistance of 600kN.

[0056] Therefore, all vertical components of the superstructure satisfy the position convergence condition. The anchor bolt arrangement node obtained in this iteration is determined as the convergence arrangement node. The virtual stiffness of each anchor bolt corresponding to the convergence arrangement node is the convergence virtual stiffness, and the displacement field of the bottom plate corresponding to the convergence arrangement node is the bottom plate convergence displacement field.

[0057] VI. Inversion Calculation of Tension Prestress Values ​​for Prestressed Anchor Bolts Based on the convergence arrangement nodes, convergence virtual stiffness, and corresponding bottom plate node convergence displacement of each prestressed anchor, the tensioning prestress value of each prestressed anchor is determined according to the following formula: ; In this engineering example, the equivalent vertical stiffness component of the foundation at the corresponding location is estimated based on the equivalent grid area shared by each prestressed anchor rod: =6.5×10 4 ×15×16÷20=7.8×10 5 kN / m.

[0058] By combining the equivalent vertical stiffness of the base slab at each prestressed anchor node, the equivalent vertical stiffness of the base slab and foundation at the corresponding location when prestressing is applied is obtained. Substituting this into the aforementioned inversion calculation formula, the tensioning prestress value of each prestressed anchor is obtained. The calculation results are attached. Figure 5 As shown.

[0059] VII. Determine the prestressed anchor bolt arrangement scheme Based on the convergence displacement field of the base plate and the internal force distribution of the vertical members of the superstructure, the 20 prestressed anchor rods were arranged differently. Ultimately, the prestressed anchor rods were distributed in a rhomboid pattern around the perimeter of the columns, with a relatively dense arrangement in the mid-span area where the base plate displacement is large and the anti-buoyancy requirement is high, and a relatively sparse arrangement in the column area where the superstructure self-weight constraint is strong and the vertical resistance margin is large.

[0060] At the same time, the spacing between adjacent prestressed anchor rods is checked to ensure that it meets the preset minimum spacing requirements, so as to reduce the adverse effect of the group anchor effect on the pull-out bearing capacity of a single prestressed anchor rod, and finally form a prestressed anchor rod arrangement scheme that is compatible with the requirements of bottom plate deformation coordination and overall vertical force balance.

[0061] 8. Conduct load-bearing capacity verification and construction monitoring. The sum of the characteristic values ​​of the pull-out bearing capacity of the 20 prestressed anchor rods within the 15m×16m slab is: 350 × 20 = 7000 kN.

[0062] The sum of the standard values ​​of vertical resistance provided by the three small columns is: 3 × 600 = 1800 kN.

[0063] A single column can provide a standard vertical resistance of 1600 kN, and the standard self-weight of the base plate is: 15×16×0.4×25=2400kN.

[0064] Therefore, the total standard value of the anti-buoyancy effect that this grating can provide is: 7000+1800+1600+2400=12800kN.

[0065] The buoyancy design requirements for this grating, considering the anti-buoyancy safety factor, are as follows: 1.05×15×16×50=12600kN.

[0066] Since 12800kN is greater than 12600kN, the prestressed anchor arrangement scheme meets the overall anti-buoyancy bearing capacity requirements.

[0067] The prestressed anchor bolts were installed and prestressed tensioning was completed according to the above layout plan. After completion, continuous monitoring was conducted for 6 months. The monitoring results showed that the floating displacement of the base plate remained stable, with a deviation from the calculated value of less than 10%. The prestressed anchor bolts were subjected to relatively uniform stress, and no obvious cracking occurred in the base plate, meeting the anti-buoyancy design requirements of the project.

[0068] The advantages of the prestressed anchor bolt arrangement method based on virtual stiffness iteration of the present invention are further illustrated below by comparative examples: IX. Comparative Example Using the traditional uniform full-span arrangement method, without considering the synergistic anti-buoyancy effect provided by the vertical members of the superstructure, the number of prestressed anchors required for the same 15m×16m slab is: n0=(1.05×15×16×50-15×16×0.4×25)÷350=29.1.

[0069] After rounding up, 30 prestressed anchor bolts are required. Compared with the traditional uniform full-span arrangement method, the number of prestressed anchor bolts used in the engineering example of this invention is reduced from 30 to 20, a reduction of 10 bolts, representing a decrease of approximately 33.3% in the number of anchor bolts. Conversely, the traditional uniform full-span arrangement method increases the number of anchor bolts by 50% compared to this invention. This demonstrates that this invention can reduce the amount of prestressed anchor bolts and improve the rationality of anchor bolt arrangement while meeting the requirements of base plate deformation coordination, vertical internal force control of the superstructure, and overall anti-buoyancy bearing capacity.

[0070] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A prestressed anchor bolt arrangement method based on virtual stiffness iteration, applied to the anti-buoyancy design of the foundation slab of an underground structure subjected to groundwater buoyancy, characterized in that... Includes the following steps: S1. Collect the basic design parameters and calculate the number of prestressed anchor bolts based on the basic design parameters. The basic design parameters include the parameters of the underground structure slab, hydrogeological parameters, superstructure parameters, and the design parameters of the prestressed anchor bolts. S2. Calculate the displacement distribution of the bottom plate under buoyancy conditions based on the basic design parameters to obtain the initial displacement field of the bottom plate. Determine the initial arrangement nodes of the prestressed anchors and the initial virtual stiffness of the prestressed anchors based on the initial displacement field of the bottom plate. Based on the basic design parameters, the initial arrangement nodes of the prestressed anchors and the initial virtual stiffness, establish a collaborative mechanical model of soil-bottom plate-anchor-superstructure. S3. Based on the aforementioned soil-base plate-anchor rod-superstructure collaborative mechanical model, deformation coordination calculations are performed. The relative deviation between the standard value of the internal force of the prestressed anchor rod and its design pull-out bearing capacity characteristic value is not greater than the preset allowable deviation is used as the stiffness convergence condition. The virtual stiffness of each prestressed anchor rod is iterated to obtain the converged virtual stiffness and the converged displacement field of the base plate under the corresponding arrangement node of each prestressed anchor rod. S4. Calculate the standard values ​​of internal forces of vertical members of the superstructure based on the convergent displacement field of the base plate, and use the fact that the standard values ​​of internal forces of vertical members of the superstructure are not greater than the corresponding standard values ​​of vertical resistance as the position convergence condition, and perform position optimization iteration on the arrangement nodes of prestressed anchor rods. Based on the prestressed anchor bolt arrangement nodes after position optimization iteration, step S3 is executed again until each prestressed anchor bolt satisfies the stiffness convergence condition and the standard value of the internal force of each vertical component of the superstructure satisfies the position convergence condition, thereby obtaining the converged arrangement nodes of the prestressed anchor bolts. S5. Based on the convergence arrangement nodes of each prestressed anchor rod, and the corresponding convergence virtual stiffness and bottom plate convergence displacement field obtained under the convergence arrangement nodes, the tensioning prestress value of each prestressed anchor rod is calculated by inversion, and the prestressed anchor rod arrangement scheme is determined.

2. The method for arranging prestressed anchor bolts based on virtual stiffness iteration according to claim 1, characterized in that: In step S2, the initial arrangement nodes of each prestressed anchor are evenly set on the median contour line of the initial displacement field of the base plate.

3. The method for arranging prestressed anchor bolts based on virtual stiffness iteration according to claim 1, characterized in that: In step S2, the initial virtual stiffness of each prestressed anchor rod is the ratio of its design pull-out bearing capacity characteristic value to the median value of the initial displacement field of the base plate.

4. The method for arranging prestressed anchor bolts based on virtual stiffness iteration according to claim 1, characterized in that: In step S3, the deformation compatibility calculation is determined by the following formula: ; ; In the formula: This is the overall vertical stiffness matrix; This is the vertical displacement vector of the node; It is the vertical equivalent nodal force vector of the combination of buoyancy and the self-weight of the bottom plate; Here is the vertical stiffness matrix of the base plate; This represents the vertical virtual stiffness matrix of the prestressed anchor bolt. Here is the vertical stiffness matrix of the soil subgrade. This is the vertical constraint stiffness matrix of the superstructure.

5. The method for arranging prestressed anchor bolts based on virtual stiffness iteration according to claim 4, characterized in that, In step S3, the standard value of the internal force of the prestressed anchor rod is calculated using the following formula: ; In the formula: For the first i Standard values ​​of internal forces in a prestressed anchor bolt; For the first i Virtual stiffness of a prestressed anchor rod; For the first i Displacement of the bottom plate node corresponding to the prestressed anchor rod.

6. The method for arranging prestressed anchor bolts based on virtual stiffness iteration according to claim 5, characterized in that, In step S4, the standard value of the internal force of the vertical members of the superstructure is calculated using the following formula: ; In the formula: Let j be the standard value of the internal force of the j-th vertical member of the superstructure; Let J be the vertical constraint stiffness of the j-th vertical member of the superstructure. Let be the displacement of the bottom plate node corresponding to the j-th vertical member of the superstructure.

7. The method for arranging prestressed anchor bolts based on virtual stiffness iteration according to claim 6, characterized in that, The inversion calculation formula for the tensioning prestress value of the prestressed anchor in step S5 is as follows: ; In the formula: For the first i The tensioning prestress value of the prestressed anchor rod; For the first i The convergence virtual stiffness of a prestressed anchor rod; For the first i The convergence displacement of the bottom plate node corresponding to the prestressed anchor rod; For the first i The actual axial stiffness of the prestressed anchor rod; When applying prestress, the first i The equivalent stiffness component of the foundation at the location corresponding to the prestressed anchor rod.

8. The method for arranging prestressed anchor bolts based on virtual stiffness iteration according to claim 1, characterized in that, It also includes the following steps: S6. Verify the bearing capacity of the prestressed anchor bolt arrangement scheme, and after construction according to the prestressed anchor bolt arrangement scheme, monitor and verify the stress of each prestressed anchor bolt and the vertical internal force of the superstructure.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, it implements the steps of any one of claims 1 to 7 of the prestressed anchor bolt arrangement method based on virtual stiffness iteration.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the steps of any one of the prestressed anchor bolt arrangement methods based on virtual stiffness iteration as described in claims 1 to 7.

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