A method and system for analyzing the ultimate bearing capacity of karst foundation

Abstract

The present invention relates to the field of karst analysis technology, and in particular to a method and system for analyzing the ultimate bearing capacity of a karst foundation, the method comprising the following steps: obtaining a three-dimensional numerical simulation model of the ultimate bearing capacity of a karst foundation; obtaining numerical simulation results of the ultimate bearing capacity of the karst foundation based on the three-dimensional numerical simulation model; obtaining a similar model test of the ultimate bearing capacity of the karst foundation; analyzing the ultimate bearing capacity of the karst foundation according to the similar model test to obtain a model test result; and analyzing the ultimate bearing capacity of the karst foundation in combination with the numerical simulation result and the model test result. The present invention analyzes the ultimate bearing capacity of the karst foundation in combination with the three-dimensional numerical simulation model and the similar model test, respectively. The comparative analysis of the two methods improves the accuracy of the assessment of the ultimate bearing capacity of the karst foundation, provides a reference for further evaluating the stability of the karst foundation, and provides a scientific basis for engineering applications.

Description

Technical Field

[0001] The invention relates to the technical field of karst analysis, and in particular to a method and system for analyzing the ultimate bearing capacity of a karst foundation. Background Art

[0002] As a special geological phenomenon, karst development has obvious regional characteristics; especially in the southwest region of my country, karst is relatively developed; karst can lead to major problems such as rock structure collapse and building engineering collapse; with the development of high-speed railways, highways and airports to the west, many projects need to be built on karst areas; at present, although a variety of geophysical methods can be used to detect karst structures, there are still major technical difficulties in the exploration of spatial structures in karst areas, and there are still limitations such as poor accuracy and difficulty in detecting small-scale cavities, resulting in insufficient research on the stability of karst foundations.

[0003] Based on the ultimate bearing capacity of karst areas, a comprehensive evaluation and analysis of the stability of karst foundation is carried out. With the continuous development of numerical simulation methods, the limit analysis method has become an effective means to calculate the ultimate bearing capacity of karst foundation. However, in order to reduce the calculation cost, many scholars mostly simplify the karst foundation into a two-dimensional plane strain problem for analysis, ignoring the influence of three-dimensional space effects. It is difficult for a two-dimensional plane to simulate the actual situation of the karst foundation.

[0004] In view of this, the present invention aims to establish a reliable evaluation method for the ultimate bearing capacity of karst foundation based on a three-dimensional numerical model in combination with actual engineering conditions, and to analyze the ultimate bearing capacity of karst foundation by comprehensively considering factors such as the shape and size of the cave in combination with similar physical model tests. On the basis of a large number of numerical simulations and physical model tests, the results of the physical model tests and the numerical simulations are compared and analyzed to conduct a comprehensive analysis of the ultimate bearing capacity of the karst foundation, which is of great significance to the stability assessment of the karst foundation. Summary of the invention

[0005] In view of the defects in the prior art, the present invention provides a method and system for analyzing the ultimate bearing capacity of a karst foundation.

[0006] In order to achieve the above-mentioned purpose, in the first aspect, the present invention provides a method for analyzing the ultimate bearing capacity of a karst foundation, the method comprising the following steps: obtaining a three-dimensional numerical simulation model of the ultimate bearing capacity of a karst foundation; obtaining numerical simulation results of the ultimate bearing capacity of the karst foundation based on the three-dimensional numerical simulation model; obtaining a similar model test of the ultimate bearing capacity of the karst foundation; analyzing the ultimate bearing capacity of the karst foundation according to the similar model test to obtain a model test result; and analyzing the ultimate bearing capacity of the karst foundation by combining the numerical simulation results with the model test results. The present invention analyzes the ultimate bearing capacity of a karst foundation by combining a three-dimensional numerical simulation model with a similar model test, which not only improves the accuracy of the assessment of the ultimate bearing capacity of the karst foundation, but also enhances the reliability and scientificity of the results by comparing and verifying the analysis between numerical simulation and physical tests, thereby providing a strong scientific basis for the engineering design of karst foundations.

[0007] Optionally, the three-dimensional numerical simulation model for obtaining the ultimate bearing capacity of the karst foundation includes: obtaining the constraint conditions of the ultimate bearing capacity of the karst foundation; constructing the objective function of the ultimate bearing capacity of the karst foundation; and obtaining the three-dimensional numerical simulation model of the ultimate bearing capacity of the karst foundation based on the constraint conditions and the objective function. The present invention determines the constraint conditions of the ultimate bearing capacity of the karst foundation and constructs the objective function, and then establishes a three-dimensional numerical simulation model, comprehensively considering multiple constraint conditions, which helps to improve the accuracy and comprehensiveness of the analysis results.

[0008] Optionally, the constraint conditions for obtaining the ultimate bearing capacity of the karst foundation include:

[0009]

[0010] in, is the compatibility matrix of the tetrahedral element, represents the number of tetrahedral units, represents a tetrahedral unit, is the velocity vector of the tetrahedron element, is the non-negative plastic multiplier for the tetrahedral element, is the yield function of the tetrahedral element, The present invention effectively considers the flow law constraints of the ultimate bearing capacity of karst foundation, provides data support for the subsequent construction of a three-dimensional numerical simulation model of the ultimate bearing capacity of karst foundation, and helps to improve the accuracy of numerical simulation results.

[0011] Optionally, the constraint conditions for obtaining the ultimate bearing capacity of the karst foundation include:

[0012]

[0013] in, is the coordinate transformation matrix between the global coordinate system and the local coordinate system, is the velocity distribution specified in the global coordinate system, The present invention effectively considers the velocity field boundary conditions, takes the velocity field boundary as one of the constraints of the ultimate bearing capacity of the karst foundation, provides data support for building a three-dimensional numerical simulation model, and enhances the accuracy and reliability of the numerical simulation results of the three-dimensional numerical simulation model.

[0014] Optionally, constructing the objective function of the ultimate bearing capacity of the karst foundation includes:

[0015]

[0016] in, Indicates the minimum value of the external load. is the external load acting on the unit, is the stress vector, represents transpose, is the compatibility matrix of the unit, is a continuous velocity vector, is a continuous coefficient vector, is a discontinuous coefficient vector, The present invention establishes an objective function of the ultimate bearing capacity of karst foundation, provides support for the construction of a three-dimensional numerical simulation model, and improves the comprehensiveness and accuracy of the analysis results.

[0017] Optionally, the numerical simulation result of the ultimate bearing capacity of the karst foundation obtained based on the three-dimensional numerical simulation model includes: obtaining the changing relationship between the ultimate bearing capacity of the karst foundation and the thickness of the top plate based on the three-dimensional numerical simulation model; constructing the changing relationship between the ultimate bearing capacity of the karst foundation and the size of the cave of the karst foundation according to the three-dimensional numerical simulation model; obtaining the changing relationship between the ultimate bearing capacity of the karst foundation and the cohesion of the rock mass according to the three-dimensional numerical simulation model; and obtaining the changing relationship between the ultimate bearing capacity of the karst foundation and the internal friction angle of the rock mass of the karst foundation using the three-dimensional numerical simulation model. The present invention uses a three-dimensional numerical simulation model to systematically analyze the changing relationship between the ultimate bearing capacity of the karst foundation and the thickness of the top plate, the size of the cave, the cohesion of the rock mass and the internal friction angle of the rock mass, thereby improving the accuracy of analyzing the ultimate bearing capacity of the karst foundation, providing a scientific basis for evaluating the stability of the karst foundation, and facilitating the optimization design of the engineering construction of the karst foundation.

[0018] Optionally, the similarity model test for obtaining the ultimate bearing capacity of the karst foundation includes: obtaining similar test materials with similar performance to the prototype rock mass of the karst foundation; proportioning the similar test materials to obtain simulation test samples with similar performance to the prototype rock mass of the karst foundation; constructing a karst foundation physical model of the karst foundation based on the simulation test samples; and establishing a similarity model test for analyzing the ultimate bearing capacity of the karst foundation based on the karst foundation physical model. The present invention constructs a karst foundation physical model with similar performance to the prototype rock mass of the karst foundation by obtaining similar test materials and accurately proportioning simulation test samples. The similarity model test conducted based on the karst foundation physical model provides intuitive and reliable experimental data for analyzing the ultimate bearing capacity of the karst foundation, effectively reduces risks and costs, and improves the accuracy and reliability of research results.

[0019] Optionally, the analysis of the ultimate bearing capacity of the karst foundation according to the similar model test to obtain the model test results includes: obtaining the changing relationship between the load and the top plate displacement of the physical model of the karst foundation according to the similar model test; obtaining the changing relationship between the load and the strain of the physical model of the karst foundation according to the similar model test. The present invention accurately obtains the changing relationship between the load and the top plate displacement, and the load and the strain of the physical model of the karst foundation through the similar model test, which provides effective data support for in-depth understanding and analysis of the mechanical response of the physical model of the karst foundation.

[0020] Optionally, the analysis of the ultimate bearing capacity of the karst foundation by combining the numerical simulation results with the model test results includes: comparing the numerical simulation results with the model test results to obtain a comparison result; and analyzing the ultimate bearing capacity of the karst foundation based on the comparison result. The present invention compares and analyzes the numerical simulation results with the model test results, which can comprehensively verify the calculation accuracy of the ultimate bearing capacity of the karst foundation, improve the credibility of the analysis results, ensure the comprehensiveness and scientificity of the analysis results, and provide a theoretical basis for analyzing the ultimate bearing capacity of the karst foundation.

[0021] In the second aspect, the present invention provides a karst foundation ultimate bearing capacity analysis system, the system executes a karst foundation ultimate bearing capacity analysis method provided by the present invention, the system includes an input device, an output device, a processor and a memory, and its gain lies in: the hardware facilities integrated by the present invention have excellent performance, the input device, the output device, the processor and the memory are interconnected, the information transmission between the various components is smooth, and an efficient information processing system is constructed through the interaction of multiple hardware facilities. The present invention combines a three-dimensional numerical simulation model with a similar model test to effectively analyze the ultimate bearing capacity of the karst foundation. The comparison and verification of the two methods improves the accuracy of the assessment of the ultimate bearing capacity of the karst foundation, enhances the reliability and scientificity of the analysis results, and provides a scientific basis for the engineering design of the karst foundation. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 A flow chart of a method for analyzing the ultimate bearing capacity of a karst foundation according to an embodiment of the present invention;

[0023] Figure 2 A curve diagram showing the variation of the ultimate bearing capacity of the karst foundation and the thickness of the top plate according to an embodiment of the present invention;

[0024] Figure 3 A curve diagram showing the change of the ultimate bearing capacity of the karst foundation and the size of the karst cave according to an embodiment of the present invention;

[0025] Figure 4 A curve diagram showing the change of the ultimate bearing capacity of the karst foundation and the rock mass cohesion in an embodiment of the present invention;

[0026] Figure 5 is a curve diagram showing the variation of the ultimate bearing capacity of the karst foundation and the friction angle in the rock mass according to an embodiment of the present invention;

[0027] Figure 6 A curve diagram showing changes in load and top plate displacement of a karst foundation physical model according to an embodiment of the present invention;

[0028] Figure 7 The present invention is a framework diagram of a karst foundation ultimate bearing capacity analysis system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0029] The specific embodiments of the present invention will be described in detail below. It should be noted that the embodiments described herein are only for illustration and are not intended to limit the present invention. In the following description, a large number of specific details are set forth in order to provide a thorough understanding of the present invention. However, it is obvious to those of ordinary skill in the art that these specific details do not need to be adopted to implement the present invention. In other examples, in order to avoid confusing the present invention, known circuits, software or methods are not specifically described.

[0030] Throughout the specification, references to "one embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in conjunction with the embodiment or example is included in at least one embodiment of the present invention. Therefore, the phrases "in one embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily all refer to the same embodiment or example. In addition, particular features, structures, or characteristics may be combined in one or more embodiments or examples in any suitable combination and / or subcombination. In addition, it should be understood by those of ordinary skill in the art that the figures provided herein are for illustrative purposes and that the figures are not necessarily drawn to scale.

[0031] See also Figure 1 An embodiment of the present invention provides a method for analyzing the ultimate bearing capacity of a karst foundation, the method comprising the following steps:

[0032] S1. Obtain a three-dimensional numerical simulation model of the ultimate bearing capacity of karst foundation.

[0033] Among them, S1 specifically includes the following steps:

[0034] S11. Obtaining the constraint conditions of the ultimate bearing capacity of the karst foundation.

[0035] Among them, S11 specifically includes the following steps:

[0036] S111. Discretize various parts of the karst foundation.

[0037] Specifically, in this embodiment, in order to construct the maneuverable allowable velocity field of the karst foundation, finite elements are used to discretize various parts of the karst foundation, the rock mass of the karst foundation is discretized using tetrahedral elements, and for weak structural surfaces with a certain thickness, low-strength eight-node joint elements are used for simulation.

[0038] It should be noted that it is assumed that the stress component of the joint unit is constant along the thickness direction and changes linearly in the length direction.

[0039] More specifically, the tetrahedral unit has 6 stress components and 3 velocity components; assuming that the velocity in the tetrahedral unit changes linearly, the velocity of each tetrahedral unit satisfies the following relationship:

[0040]

[0041] in, is the velocity of the tetrahedral element, represents the number of tetrahedral units, represents a tetrahedral unit, are the nodes of the tetrahedral element, is the shape function associated with the nodal coordinates of the tetrahedral element, is the velocity of the tetrahedral element node.

[0042] The shape function associated with the node coordinates of the tetrahedral element satisfies the following relationship:

[0043]

[0044]

[0045] in, is the shape function related to the node coordinates of the tetrahedral element, is the volume of the tetrahedral unit, represents the number of tetrahedral units, represents the joint unit, , , and is the coefficient related to the geometric position of the tetrahedral element node, are the nodes of the tetrahedral element, is the horizontal coordinate of the node, is the ordinate of the node, is the vertical coordinate of the node.

[0046] Furthermore, each of the joint units has 6 stress components and 8 velocity components, and the velocity of the joint unit satisfies the following relationship:

[0047]

[0048] in, is the velocity of the joint unit, represents the number of tetrahedral units, represents the joint unit, is the node of the joint unit, is the shape function related to the nodal coordinates of the joint element, is the velocity of the joint unit node.

[0049] The shape function associated with the node coordinates of the joint unit satisfies the following relationship:

[0050]

[0051]

[0052] in, is the shape function related to the nodal coordinates of the joint element, are the local coordinates of the joint element nodes, The nodes of the joint unit.

[0053] S112. Obtaining the nonlinear yield condition of the ultimate bearing capacity of the karst foundation.

[0054] Specifically, when the combination of shear stress and normal stress in the tetrahedral unit on any plane reaches a critical condition, the rock mass begins to yield; the stress state in the tetrahedral unit is described using the Mohr-Coulomb strength criterion, which satisfies the following relationship:

[0055]

[0056]

[0057] in, is the yield function of the tetrahedral element, represents the number of tetrahedral units, represents a tetrahedral unit, is the stress vector, is the first invariant of the stress deviator tensor, is the internal friction angle of rock material, is the second invariant of the stress deviator tensor, is the stress Lode angle, The cohesion of rock material.

[0058] Furthermore, the stress state in the joint unit needs to satisfy the Mohr-Coulomb strength criterion and the no-tensile stress condition, satisfying the following relationship:

[0059]

[0060] in, is the yield function of the joint element, represents the number of joint units, represents the joint unit, is the stress vector, is the first invariant of the stress deviator tensor, is the internal friction angle of rock material, is the second invariant of the stress deviator tensor, is the stress Lode angle, is the cohesion of the rock mass material, is the first principal stress of the joint element.

[0061] S113, obtaining the flow law constraint of the ultimate bearing capacity of the karst foundation.

[0062] Specifically, for a rock mass of an ideal rigid-plastic material, the strain component obtained from the deformation compatibility condition should be equal to the plastic strain rate component obtained from the relevant flow rule and yield condition; since the strain in the tetrahedral unit is continuous, the flow law constraint of the tetrahedral unit satisfies the following relationship:

[0063]

[0064] in, is the compatibility matrix of the tetrahedral element, represents the number of tetrahedral units, represents a tetrahedral unit, is the velocity vector of the tetrahedron element, is the non-negative plastic multiplier for the tetrahedral element, is the yield function of the tetrahedral element, is the stress vector.

[0065] More specifically, the flow law constraints of the joint unit satisfy the following relationship:

[0066]

[0067] in, is the compatibility matrix of the joint unit, represents the number of joint units, represents the joint unit, is the velocity vector of the joint unit, is the non-negative plastic multiplier of the joint element, is the yield function of the joint element, is the stress vector.

[0068] Furthermore, the flow law constraint on the velocity discontinuity surface in the mobile allowable velocity field of the karst foundation satisfies the following relationship:

[0069]

[0070]

[0071]

[0072] in, and is the coefficient matrix associated with the velocity components, and is the velocity component, Represents the number of common faces of tetrahedral elements.

[0073] S114. Obtaining velocity boundary conditions of the ultimate bearing capacity of the karst foundation.

[0074] Specifically, the velocity boundary condition of the maneuverable permissible velocity field of the karst foundation satisfies the following relationship:

[0075]

[0076]

[0077] in, is the coordinate transformation matrix between the global coordinate system and the local coordinate system, is the velocity distribution specified in the global coordinate system, are the known components of velocity in different directions, Represents the number of boundary cells whose velocities are known.

[0078] S12, constructing an objective function of the ultimate bearing capacity of the karst foundation.

[0079] Specifically, the objective function of the ultimate bearing capacity of the karst foundation satisfies the following relationship:

[0080]

[0081] in, Indicates the minimum value of the external load. is the external load acting on the unit, is the stress vector, represents transpose, is the compatibility matrix of the unit, is a continuous velocity vector, is a continuous coefficient vector, is a discontinuous coefficient vector, is a discontinuous velocity vector.

[0082] S13. Obtaining a three-dimensional numerical simulation model of the ultimate bearing capacity of the karst foundation based on the constraint conditions and the objective function.

[0083] Specifically, the calculation process of the ultimate bearing capacity of the karst foundation is reduced to an optimization problem, and a nonlinear mathematical programming model of the ultimate bearing capacity of the karst foundation is constructed as a three-dimensional numerical simulation model to satisfy the following relationship:

[0084]

[0085]

[0086] in, Indicates the minimum value of the external load. is the external load acting on the unit, is the stress vector, represents transpose, is the compatibility matrix of the unit, is a continuous velocity vector, is a continuous coefficient vector, is a discontinuous coefficient vector, is a discontinuous velocity vector, is the compatibility matrix of the tetrahedral element, represents the number of tetrahedral units, represents a tetrahedral unit, is the velocity vector of the tetrahedron element, is the non-negative plastic multiplier for the tetrahedral element, is the yield function of the tetrahedral element, is the compatibility matrix of the joint unit, represents the number of joint units, represents the joint unit, is the velocity vector of the joint unit, is the non-negative plastic multiplier of the joint element, is the yield function of the joint element, and is the coefficient matrix associated with the velocity components, and is the velocity component, represents the number of common faces of tetrahedral units, is the coordinate transformation matrix between the global coordinate system and the local coordinate system, is the velocity distribution specified in the global coordinate system, are the known components of velocity in different directions, Represents the number of boundary cells whose velocity is known.

[0087] S2. Obtaining numerical simulation results of the ultimate bearing capacity of the karst foundation based on the three-dimensional numerical simulation model.

[0088] It should be noted that the fitting objects of the three-dimensional numerical simulation model are circular through-hole karst foundation, spherical karst cave karst foundation and rectangular karst cave karst foundation, and the changing relationships between the ultimate bearing capacity of the circular through-hole karst foundation, spherical karst cave foundation and rectangular karst cave karst foundation and the thickness of the roof, cave size, rock cohesion and friction angle within the rock mass are obtained respectively.

[0089] Among them, different interlayer inclination angles were used as variable control groups.

[0090] Among them, S2 specifically includes the following steps:

[0091] S21. Obtaining the changing relationship between the ultimate bearing capacity of the karst foundation and the thickness of the top plate based on the three-dimensional numerical simulation model.

[0092] For details, see Figure 2 The figure shows the changing curves of the ultimate bearing capacity of karst foundation and the thickness of the top plate, which respectively show the changing curves of the ultimate bearing capacity of karst foundation and the thickness of the top plate of circular through-hole cave, the changing curves of the ultimate bearing capacity of karst foundation and the thickness of the top plate of spherical cave and the changing curves of the ultimate bearing capacity of karst foundation and the thickness of the top plate of rectangular cave.

[0093] S22. Constructing the relationship between the ultimate bearing capacity of the karst foundation and the size of the caves of the karst foundation based on the three-dimensional numerical simulation model.

[0094] For details, see Figure 3 The figure shows the change curve of the ultimate bearing capacity of karst foundation and the size of cave, which includes the change curve of the ultimate bearing capacity of karst foundation and the size of circular through-hole cave, the change curve of the ultimate bearing capacity of karst foundation and the size of cave in spherical cave and the change curve of the ultimate bearing capacity of karst foundation and the size of cave in rectangular cave.

[0095] Among them, the measurement scale of the cave size in the curve diagram of the change between the ultimate bearing capacity of the karst foundation of the circular through cave and the cave size is the cross-sectional radius of the circular through cave; the measurement scale of the cave size in the curve diagram of the change between the ultimate bearing capacity of the karst foundation of the spherical cave and the cave size is the cross-sectional radius of the spherical cave; the measurement scale of the cave size in the curve diagram of the change between the ultimate bearing capacity of the karst foundation of the rectangular cave and the cave size is the cave span of the rectangular cave.

[0096] S23. Obtaining the changing relationship between the ultimate bearing capacity of the karst foundation and the cohesion of the rock mass according to the three-dimensional numerical simulation model.

[0097] For details, see Figure 4 The figure shows the changing curves of the ultimate bearing capacity of karst foundation and the cohesion of rock mass, which respectively show the changing curves of the ultimate bearing capacity of karst foundation and the cohesion of rock mass in circular through-hole cave, the changing curves of the ultimate bearing capacity of karst foundation and the cohesion of rock mass in spherical cave and the changing curves of the ultimate bearing capacity of karst foundation and the cohesion of rock mass in rectangular cave.

[0098] S24. Using the three-dimensional numerical simulation model, obtain the changing relationship between the ultimate bearing capacity of the karst foundation and the internal friction angle of the rock mass of the karst foundation.

[0099] For details, see Figure 5 The figure shows the changing curves of the ultimate bearing capacity of karst foundation and the friction angle of rock body, which respectively show the changing curves of the ultimate bearing capacity of karst foundation and the friction angle of rock body in circular through-hole cave, the changing curves of the ultimate bearing capacity of karst foundation and the friction angle of rock body in spherical cave and the changing curves of the ultimate bearing capacity of karst foundation and the friction angle of rock body in rectangular cave.

[0100] S3. A similar model test is performed to obtain the ultimate bearing capacity of the karst foundation.

[0101] Among them, S3 specifically includes the following steps:

[0102] S31. Obtain similar test materials with properties similar to those of the prototype rock mass of the karst foundation.

[0103] Specifically, the similar materials of the karst foundation are usually composed of aggregates, binders and regulators; currently, barite powder, river sand and iron powder are mainly used as aggregates, gypsum powder and cement are used as binders, and retarders are added as regulators.

[0104] Furthermore, in this embodiment, river sand, cement, gypsum powder and tap water are used as the similar test materials.

[0105] The particle size of the river sand is 0.1 mm to 0.6 mm, and the density of the river sand is about 1.71 g / cm 3 The cement is P.C42.5 composite silicate cement, the density of the cement is about 3.0g / cm³, the density of the gypsum powder is about 2.3g / cm³, the initial setting time of the gypsum powder is 4min~6min, and the final setting time is 8min~10min.

[0106] S32. The similar test materials are mixed and proportioned to obtain simulation test samples having properties similar to those of the prototype rock mass of the karst foundation.

[0107] Wherein, S32 specifically includes the following steps:

[0108] S321. Perform a ratio design on the similar test materials to obtain a similar ratio design table.

[0109] Specifically, in this embodiment, in order to better simulate the actual situation in engineering applications, important physical and mechanical parameters are made to meet the theoretical similarity ratio as much as possible. The similarity ratio is shown in Table 1:

[0110] Table 1

[0111]

[0112] More specifically, the mechanical parameters of the real values ​​of the limestone prototype in the karst area and the similarity model target values ​​of the simulated test samples are shown in Table 2 according to Table 1:

[0113] Table 2

[0114]

[0115] Furthermore, in this embodiment, the total mass of the river sand, cement and gypsum powder is determined to be 100%, the water-solid ratio is 1:6, and similar proportions are performed on the similar test materials, and 6 proportioning schemes are designed and constructed to obtain a similar proportion design table, as shown in Table 3:

[0116] Table 3

[0117]

[0118] It should be noted that the similar test materials must meet the following requirements: the main mechanical properties of the similar test materials are similar to those of the prototype rock mass; the simulated test samples obtained based on the similar test materials are similar to the prototype rock mass in material composition and structure; the physical and mechanical properties of the simulated test samples are stable and not easily affected by external conditions; when the ratios of similar test materials are different, the physical and mechanical properties of the obtained simulated test samples change accordingly to adapt to the screening requirements of similar conditions; similar test materials must be safe and non-toxic, easy to obtain, low-cost, easy to shape and convenient to manufacture.

[0119] S322. Prepare the similar test materials according to the similar proportion design table to obtain simulation test samples with different proportions.

[0120] Specifically, since the initial setting time of the used gypsum powder is relatively short, in order to prevent similar test materials from rapidly agglomerating, in this embodiment, the dry similar test materials are firstly evenly mixed, and then tap water is added and evenly stirred to prepare a simulated test sample.

[0121] Wherein, the mold used to prepare the simulation test sample is a cube mold, and the side length of the cube mold is 70.7 mm.

[0122] More specifically, the preparation steps of the simulated test samples include: cleaning the cube mold and applying a thin layer of engine oil inside the cube mold; calculating the mass of river sand, cement and gypsum powder of each group of simulated test samples according to the similar proportion design table, putting them into a container and stirring them evenly; then adding tap water and stirring them evenly to obtain mortar; pouring the mortar into the cube mold and tamping from the edge to the center, and during the tamping process, adding mortar when the mortar sinks below the test mold opening of the cube mold, and after tamping and compacting, scraping and smoothing the mortar that is higher than the test mold opening of the cube mold.

[0123] Furthermore, the prepared simulation test samples are allowed to stand and are numbered, and after the standing is completed, the simulation test samples are demolded, and the demolded simulation test samples are cured in a standard curing box, and then the cured simulation test samples are naturally air-dried.

[0124] Among them, the static temperature requirement is 15℃~25℃, the static time is 24h, the temperature of the standard curing box is 20℃, the relative humidity is 90%, the curing time is 14d, and the natural air drying time is 3d.

[0125] S323, testing the simulation test samples with different proportions.

[0126] Specifically, a uniaxial compression test is performed on the simulated test samples with 6 ratios to obtain the compressive strength and elastic modulus of the simulated test samples; a direct shear test is performed on the simulated test samples with 6 ratios to obtain the internal friction angle and cohesion of the simulated test samples.

[0127] Furthermore, uniaxial compression tests and direct shear tests were performed on 6 groups of simulation test samples with different ratios to obtain the compressive strength, elastic modulus, internal friction angle and cohesion of the simulation test samples with different ratios, as shown in Table 4:

[0128] Table 4

[0129]

[0130] In this embodiment, the compressive strength of the simulated test samples is distributed between 2.90MPa and 13.07MPa, the elastic modulus is distributed between 3.19GPa and 6.72GPa, the internal friction angle is distributed between 30.1° and 57.8°, and the cohesion is distributed between 0.68MPa and 7.33MPa. According to Table 4, the physical and mechanical parameters of the simulated test samples prepared with Ratio 3 are closest to the target values ​​of the similar model, and can better simulate the mechanical properties of the limestone karst foundation.

[0131] S33. Constructing a karst foundation physical model of the karst foundation based on the simulation test samples.

[0132] In this embodiment, the physical and mechanical parameters of the simulation test sample prepared by the ratio 3 are closest to the target values ​​of the similar model, and the karst foundation physical model is produced based on the ratio 3.

[0133] Specifically, the size of the foundation mold used to prepare the karst foundation physical model is 1000mm×1000mm×800mm, and the size of the casting test block of the karst foundation physical model is 1000mm×1000mm×700mm. The molds all reserve 100mm for installing wooden tie strips to prevent deformation and cracking of the top of the foundation mold during the casting process.

[0134] More specifically, a cylindrical PVC pipe with a radius of 100 mm is arranged in the foundation mold of the circular through-hole karst cave foundation physical model, which passes through the foundation mold from front to back; a spherical foam with a radius of 100 mm is arranged in the foundation mold of the spherical karst cave foundation physical model, the spherical foam is 200 mm away from the top surface of the foundation mold, and the spherical foam is connected to a PVC pipe with a radius of 4 mm; a rectangular foam of 400 mm (length) × 400 mm (width) × 200 mm (height) is arranged in the foundation model of the rectangular karst cave foundation physical model, the rectangular foam is 200 mm away from the top surface of the foundation mold, and the rectangular foam is connected to a PVC pipe with a radius of 4 mm.

[0135] Furthermore, according to ratio 3, a circular through-hole karst cave karst foundation physical model, a spherical karst cave karst foundation physical model and a rectangular karst cave karst foundation physical model were made based on the foundation mold; because the test block volume of the karst foundation physical model is large, in order to prevent the gypsum powder from setting quickly due to the long pouring time, a retarder is added during the mixing process, and the amount of the retarder is 0.3% of the mass of the gypsum powder. Taking into account that one-time pouring may cause uneven material mixing and the capacity of the mixer, the karst foundation physical model is poured in three times, and the pouring height of each time is 1 / 3 of the entire karst foundation physical model.

[0136] The material consumption of the karst foundation physical model is shown in Table 5:

[0137] Table 5

[0138]

[0139] Furthermore, the materials are poured into a mixer for stirring according to the material dosage; water is continuously added during the stirring process, and the water adding speed is strictly controlled to prevent uneven stirring so that the mixed mortar material absorbs and condenses into a mass; the evenly stirred mixed mortar material is poured into a corresponding mold and compacted; when the pouring process reaches the embedded position of the strain gauge, the strain gauge is buried in the mortar material and compacted until it is completely fitted; and continuous pouring is continued to obtain a karst foundation physical model.

[0140] Wherein, the stirring time is 6 minutes.

[0141] In this embodiment, the cast karst foundation physical model is left to stand and then demolded, and then cured; after the demolding is completed, the cylindrical PVC pipe of the circular through-hole karst cave karst foundation physical model is extracted to obtain a circular through-hole karst cave karst foundation physical model; gasoline is injected through the PVC pipe of the spherical karst cave karst foundation physical model so that the spherical foam reacts with the gasoline and then quickly dissolves to form a spherical cavity to obtain a spherical karst foundation physical model; gasoline is injected through the PVC pipe of the rectangular karst cave karst foundation physical model so that the rectangular foam reacts with the gasoline and then quickly dissolves to form a rectangular cavity to obtain a rectangular karst cave karst foundation physical model.

[0142] The standing time is 24 hours, the curing temperature is an average room temperature of 22° C., and the curing time is 14 days.

[0143] S34. Establishing a similarity model test for analyzing the ultimate bearing capacity of the karst foundation based on the physical model of the karst foundation.

[0144] Specifically, in this embodiment, a microcomputer-controlled electro-hydraulic servo pressure testing machine is used as a loading device for the karst foundation physical model; a displacement sensor is used to record the displacement of the measuring points of the karst foundation physical model during the loading process; strain gauges are installed at the measuring point positions, and a static strain tester is used as a stress and strain acquisition device during the loading process of the karst foundation physical model.

[0145] More specifically, in this embodiment, the pile body is replaced by a steel plate with a thickness of 20 mm and a size of 250 mm × 250 mm, and several layers of solid iron blocks are laid on the steel plate to allow the steel plate to be fully stressed; the surrounding rock pressure around the karst foundation physical model is replaced by a confinement steel plate with a thickness of 15 mm, and six 5 mm × 10 mm square steels are installed on each surface of the steel plate, and every two square steels are fixed with an anchor rod to limit the normal displacement of the rock mass around the karst foundation physical model.

[0146] Furthermore, before starting loading using the microcomputer-controlled electro-hydraulic servo pressure testing machine, connect the strain gauges at each position to the static strain tester and test whether the signal is in a normal state. Set the loading rate of the microcomputer-controlled electro-hydraulic servo pressure testing machine to a uniform loading rate of 0.5 kN / s, and stop loading immediately after the physical model of the karst foundation is damaged.

[0147] S4. Analyze the ultimate bearing capacity of the karst foundation based on the similar model test to obtain model test results.

[0148] Wherein, S4 specifically includes the following steps:

[0149] S41. Obtaining the changing relationship between the load and top plate displacement of the karst foundation physical model according to the similarity model test.

[0150] For details, see Figure 6 , the figure shows the change curve diagram of the load and top plate displacement of the karst foundation physical model, and the figure shows the change curve diagram of the load and top plate displacement of the circular through-hole karst foundation physical model, the change curve diagram of the load and top plate displacement of the spherical karst cave karst foundation physical model and the change curve diagram of the load and top plate displacement of the rectangular karst cave karst foundation physical model.

[0151] More specifically, in the similar model test, according to the change curve of the load and top plate displacement of the karst foundation physical model, the destruction process of the karst foundation physical model is divided into stage I-compaction stage, stage II-elastic stage and stage III-plastic stage.

[0152] Furthermore, according to the curve of the change of load and top plate displacement of the karst foundation physical model, the ultimate bearing capacity of the circular through-hole karst foundation physical model is 13.932Mpa, the ultimate bearing capacity of the spherical karst cave karst foundation physical model is 24.715Mpa, and the ultimate bearing capacity of the rectangular karst cave karst foundation physical model is 5.558Mpa; and the three different karst foundation physical models roughly show a rule that the top plate displacement increases with the increase of load in stage I-compaction stage, and roughly show a rule that the ultimate bearing capacity increases approximately linearly with the increase of top plate displacement in stage II-elastic stage, and roughly show a rule that the load growth rate gradually slows down until it reaches the peak value with the continuous increase of top plate displacement in stage III-plastic stage, and the load begins to decrease after exceeding the peak value, indicating that the top plate rock mass is damaged at this moment and irreversible plastic deformation occurs.

[0153] S42. Obtaining the changing relationship between the load and strain of the karst foundation physical model according to the similarity model test.

[0154] Specifically, during the similar model test, the strain gauge in the karst foundation physical model is connected to the static strain tester, and the static strain tester is used to record the strain of the karst foundation physical model during the load increase process, and further obtain the changing relationship between the load and strain of the karst foundation physical model.

[0155] S5. Analyze the ultimate bearing capacity of the karst foundation by combining the numerical simulation results with the model test results.

[0156] Among them, S5 specifically includes the following steps:

[0157] S51, comparing and analyzing the numerical simulation results with the model test results to obtain a comparison result.

[0158] Specifically, in this embodiment, by setting control groups with different variables, the ultimate bearing capacity of the karst foundation is calculated based on numerical simulation and model test, and the comparative results of the ultimate bearing capacity analysis of the karst foundation are obtained based on the comparative analysis of the numerical simulation results and the model test results.

[0159] S52. Analyze the ultimate bearing capacity of the karst foundation based on the comparison result.

[0160] Specifically, based on the comparison results of the numerical simulation and the model test, the comparison results are analyzed using a computer processor, and then the ultimate bearing capacity of the karst foundation is analyzed.

[0161] See also Figure 7 In an optional embodiment, in order to efficiently execute a karst foundation ultimate bearing capacity analysis method provided by the present invention, the present invention provides a karst foundation ultimate bearing capacity analysis system, the system includes an input device, an output device, a processor and a memory, the hardware facilities are interconnected, wherein the memory is used to store a computer program, the computer program includes program instructions, and the processor is configured to call the program instructions to execute the specific steps of the relevant embodiments of the karst foundation ultimate bearing capacity analysis method provided by the present invention. The karst foundation ultimate bearing capacity analysis system provided by the present invention has a complete structure and is objectively stable, which improves the overall applicability and practical application ability of the present invention.

[0162] In summary, the method of the present invention provides a karst foundation ultimate bearing capacity analysis method and system, which combines two technical methods, namely a three-dimensional numerical simulation model and a similar model test, to deeply analyze the ultimate bearing capacity of the karst foundation, improve the accuracy of the assessment of the ultimate bearing capacity of the karst foundation, and further enhance the reliability and scientificity of the research results through comparative analysis and verification of the numerical simulation results and the model test results, providing a scientific reference basis for the engineering design of karst foundations. The method of the present invention is easy to understand, simple to calculate, with a small workload, and is convenient for engineering application, providing a theoretical basis and technical support for the further development of the field of karst analysis technology.

[0163] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. These modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and specification of the present invention.

Claims

1. A method for analyzing the ultimate bearing capacity of a karst foundation, characterized in that: The steps include: Obtain a three-dimensional numerical simulation model of the ultimate bearing capacity of karst foundation; Obtaining a numerical simulation result of the ultimate bearing capacity of the karst foundation based on the three-dimensional numerical simulation model; A similar model test is performed to obtain the ultimate bearing capacity of the karst foundation; Analyzing the ultimate bearing capacity of the karst foundation according to the similar model test to obtain a model test result; Analyzing the ultimate bearing capacity of the karst foundation by combining the numerical simulation results with the model test results; The three-dimensional numerical simulation model for obtaining the ultimate bearing capacity of the karst foundation includes: Obtaining the constraint conditions of the ultimate bearing capacity of the karst foundation; Constructing an objective function of the ultimate bearing capacity of the karst foundation; Obtaining a three-dimensional numerical simulation model of the ultimate bearing capacity of the karst foundation based on the constraint conditions and the objective function; The constraint conditions for obtaining the ultimate bearing capacity of the karst foundation include: ； in, is the compatibility matrix of the tetrahedral element, represents the number of tetrahedral units, represents a tetrahedral unit, is the velocity vector of the tetrahedron element, is the non-negative plastic multiplier for the tetrahedral element, is the yield function of the tetrahedral element, is the stress vector; The constraint conditions for obtaining the ultimate bearing capacity of the karst foundation include: ； in, is the coordinate transformation matrix between the global coordinate system and the local coordinate system, is the velocity distribution specified in the global coordinate system, are the known components of velocity in different directions; The objective function of constructing the ultimate bearing capacity of the karst foundation includes: ； in, Indicates the minimum value of the external load. is the external load acting on the unit, is the stress vector, represents transpose, is the compatibility matrix of the unit, is a continuous velocity vector, is a continuous coefficient vector, is a discontinuous coefficient vector, is a discontinuous velocity vector.

2. The method for analyzing the ultimate bearing capacity of karst foundation according to claim 1, characterized in that: The numerical simulation result of the ultimate bearing capacity of the karst foundation obtained based on the three-dimensional numerical simulation model includes: Obtaining the changing relationship between the ultimate bearing capacity of the karst foundation and the thickness of the top plate based on the three-dimensional numerical simulation model; Constructing the relationship between the ultimate bearing capacity of the karst foundation and the size of the cave of the karst foundation according to the three-dimensional numerical simulation model; Obtaining the changing relationship between the ultimate bearing capacity of the karst foundation and the cohesion of the rock mass according to the three-dimensional numerical simulation model; The three-dimensional numerical simulation model is used to obtain the changing relationship between the ultimate bearing capacity of the karst foundation and the internal friction angle of the rock mass of the karst foundation.

3. The method for analyzing the ultimate bearing capacity of karst foundation according to claim 1, characterized in that: The similarity model test for obtaining the ultimate bearing capacity of the karst foundation includes: Obtaining similar test materials with similar properties to the prototype rock mass of the karst foundation; The similar test materials are mixed and proportioned to obtain simulation test samples having properties similar to those of the prototype rock mass of the karst foundation; Constructing a karst foundation physical model of the karst foundation according to the simulation test sample; A similar model test for analyzing the ultimate bearing capacity of the karst foundation is established based on the karst foundation physical model.

4. The method for analyzing the ultimate bearing capacity of karst foundation according to claim 3, characterized in that: The method of analyzing the ultimate bearing capacity of the karst foundation according to the similar model test to obtain the model test result includes: According to the similarity model test, the changing relationship between the load and the top plate displacement of the karst foundation physical model is obtained; The variation relationship between the load and strain of the karst foundation physical model is obtained according to the similarity model test.

5. The method for analyzing the ultimate bearing capacity of karst foundation according to claim 1, characterized in that: The analyzing the ultimate bearing capacity of the karst foundation by combining the numerical simulation results with the model test results includes: Comparing and analyzing the numerical simulation results with the model test results to obtain a comparison result; Based on the comparison results, the ultimate bearing capacity of the karst foundation is analyzed.

6. A karst foundation ultimate bearing capacity analysis system, characterized in that: The system includes an input device, an output device, a processor and a memory, wherein the input device, the output device, the processor and the memory are interconnected, wherein the memory is used to store a computer program, the computer program includes program instructions, and the processor is configured to call the program instructions to execute the karst foundation ultimate bearing capacity analysis method as described in any one of claims 1 to 5.

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