Consolidation analysis method for non-uniform load and semi-permeable boundary of anisotropic soil

Abstract

The invention relates to the technical field of soil improvement, in particular to an anisotropic soil non-uniform load and semi-permeable boundary consolidation analysis method which comprises the following steps: constructing a two-dimensional consolidation model under the conditions of non-uniform load and semi-permeable boundary; setting the characteristics of the soil in the two-dimensional consolidation model; setting a control equation and boundary conditions of the two-dimensional consolidation model; and analyzing the two-dimensional consolidation model to obtain an analytical solution of excess pore pressure, calculating the soil consolidation rate, and analyzing the soil consolidation behavior. According to the method, the influence of anisotropy and non-uniform load of the soil and the influence of boundary drainage capacity are considered, the two-dimensional consolidation behavior of the soil can be analyzed more reasonably and accurately, a direction is indicated for two-dimensional consolidation analysis of the anisotropic soil under the non-uniform load, and a better means is provided for engineering practice of soil improvement.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of soil improvement, in particular to a method for analyzing the consolidation of anisotropic soil under non-uniform load and semi-permeable boundary. BACKGROUND

[0002] Various drainage ditches have been used in ground improvement projects such as highways, railways, buildings, and tailings dams. Research on soil consolidation behavior is crucial for ensuring the safe construction, operation, and maintenance of infrastructure. Previous studies have shown that vertical and horizontal drainage ditches can effectively accelerate soil consolidation. Among them, drainage ditches change the drainage path and boundary, allowing pore water to flow in multiple directions. Therefore, the consolidation of horizontal and vertical drainage cannot be simply simplified as a one-dimensional problem. In recent years, multi-dimensional consolidation analysis models have emerged. However, these models usually ignore the non-uniformity of load distribution, although they are prevalent in actual engineering scenarios, such as eccentric load, discontinuous load, and building load, etc. In addition, most multi-dimensional consolidation studies assume that the drainage is limited, i.e., fully permeable or impermeable, without quantifying the impact of partially permeable boundaries on consolidation behavior. In the prior art, a virtual semi-permeable layer is used to simulate horizontal drainage in soil consolidation problems. However, the semi-permeable boundary is currently mainly applied to simplified one-dimensional models, and its exploration in two-dimensional models is limited. The study of complex consolidation behavior of soil under non-uniform load and semi-permeable boundary is still insufficient.

[0003] In addition, soil anisotropy is also usually ignored in existing consolidation models, although there is evidence that soil anisotropy also plays a key role in consolidation behavior. However, no relevant information has been found in the prior art regarding a two-dimensional consolidation model that includes non-uniform load, soil anisotropy, and semi-permeable boundary. SUMMARY

[0004] The purpose of the present application is to provide an analysis method for the consolidation behavior of anisotropic soil under arbitrary non-uniform load and semi-permeable boundary, in order to describe the consolidation behavior of anisotropic soil under non-uniform load and semi-permeable boundary conditions, in view of the deficiencies in the background art.

[0005] To achieve the above purpose, the present application provides a method for analyzing the consolidation of anisotropic soil under non-uniform load and semi-permeable boundary, comprising the following steps: S1, constructing a two-dimensional consolidation model under non-uniform load and semi-permeable boundary conditions; S2, setting the properties of the soil in the two-dimensional consolidation model; S3, setting the control equations and boundary conditions of the two-dimensional consolidation model; S4, analyzing the two-dimensional consolidation model to obtain the analytical solution of the excess pore pressure, calculating the soil consolidation rate, and analyzing the soil consolidation behavior.

[0006] Further, the two-dimensional consolidation model in S1 sets an anisotropic soil with a thickness of and a finite width of , and a non-uniform load of . The two-dimensional consolidation model has fully permeable left and right boundaries and semi-permeable upper and lower boundaries with semi-permeability coefficients of , , respectively. The vertical and horizontal permeability coefficients of the soil are and , respectively.

[0007] Further, the soil properties in the two-dimensional consolidation model in S2 include: the soil is homogeneous, anisotropic, and fully saturated, composed of incompressible particles and pore water; the soil stress-strain behavior is linear, without plasticity or creep effect; and the influence of additional stress caused by soil self-weight is ignored during consolidation.

[0008] Further, the control equation for two-dimensional consolidation in S3 is: ; where is the excess pore pressure, , are the vertical and horizontal consolidation coefficients of the soil, , are the vertical and horizontal coordinates in the Cartesian coordinate system, is time; The initial conditions for two-dimensional consolidation are: ; where is the non-uniform load distribution; In the two-dimensional consolidation model, vertical drainage pipes are set, and the left and right boundaries are designated as fully permeable boundaries, so that water can pass through the left and right boundary conditions: ; ; The upper and lower boundaries are designated as semi-permeable boundaries, and the upper and lower boundary conditions are: ; .

[0009] Further, the Fourier finite sine transform is introduced in S4: ; where is the Fourier transform parameter and is a positive integer. Combined with the control equation for two-dimensional consolidation and the left and right boundary conditions, we have: ; The initial condition of two-dimensional consolidation is rewritten as: ; The upper boundary condition and the lower boundary condition are rewritten as: ; ; Further, in S4 is further decomposed into a steady-state solution and a transient solution : ; According to the variable separation method, the transient solution is further decomposed into a spatial function and a time function : ; Thus, we obtain: ; where is an eigenvalue, so that the time function satisfies: ; The spatial function satisfies: ; Combining the obtained ; where, when : ; When : ; where, ; ; Thus, we obtain: ; ; Thus, we obtain: ; ; where, and , , , about, and ; ; ; Combining steady-state solution , the inverse finite sine transform is applied to the solution process to obtain the two-dimensional consolidation of the excess pore pressure: .

[0010] Further, the variable is and and the ratio of and : ; then is expressed as: ; wherein, is any non-zero constant.

[0011] Further, the calculation formula of the consolidation rate : ; wherein, is the length range of the non-uniform load.

[0012] The above scheme of the present application has the following beneficial effects: The anisotropic soil non-uniform load and semi-transparent boundary consolidation analysis method provided by the present application can more reasonably and accurately analyze the two-dimensional consolidation behavior of soil by establishing a two-dimensional consolidation model, considering the anisotropy of soil, the influence of non-uniform load, and the influence of boundary drainage capacity, and points out the direction for the two-dimensional consolidation analysis of anisotropic soil under non-uniform load, and provides a better means for soil improvement engineering practice. Other beneficial effects of the present application will be described in detail in the subsequent specific embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 is the step flow chart of the present application; Figure 2 is the comparison chart of the present application and the field test results; Figure 3 is the comparison chart of the present application and the two-dimensional numerical simulation results, wherein (a) is the result of different depths, and (b) is the result of different times. DETAILED DESCRIPTION

[0014] The present disclosure is described in detail by way of specific specific examples. As will be obvious to one of skill in the art, the examples can not cover the only ways of practicing the present disclosure. The present disclosure can be implemented or carried out in other ways without departing from the spirit and essential characteristics of the disclosure. Various modifications can be made to the details of the disclosure without departing from the essential characteristics of the disclosure. Therefore, the specific examples described herein are to be construed as merely illustrative, and not limiting of the scope of the disclosure, as defined by the appended claims, along with the full scope of equivalents to which such claims are entitled. It will be apparent that aspects, overlapping aspects, and / or embodiments of the present disclosure can be combined and / or used in various ways.

[0015] It is to be understood that the following description is based on certain specific examples that fall within the scope of the appended claims. The description is intended to be illustrative, but not to limit the scope of the application, as defined by the appended claims. It will be apparent to one of ordinary skill in the art that aspects, overlapping aspects, and / or embodiments of the present disclosure can be combined and / or used in various ways. For example, one can practice a device and / or practice a method using any number of the aspects set forth herein. In addition, one can practice an apparatus and / or practice a method using other structure and / or functionality in place of or in addition to those described herein.

[0016] It is also to be understood that the following description is based on certain specific examples that fall within the scope of the appended claims. The description is intended to be illustrative, but not to limit the scope of the application, as defined by the appended claims. It will be apparent to one of ordinary skill in the art that aspects, overlapping aspects, and / or embodiments of the present disclosure can be combined and / or used in various ways. For example, one can practice a device and / or practice a method using any number of the aspects set forth herein. In addition, one can practice an apparatus and / or practice a method using other structure and / or functionality in place of or in addition to those described herein.

[0017] As Figure 1 shown, the embodiments of the present application provide an analysis method for anisotropic soil bearing arbitrary non-uniform load and semi-permeable boundary, comprising the following steps: S1, constructing a two-dimensional consolidation model under non-uniform load and semi-permeable boundary conditions.

[0018] In this embodiment, the two-dimensional consolidation model constructed adopts anisotropic soil, the thickness of which is limited, the width of which is limited, and the distribution of non-uniform load is is expressed. The two-dimensional consolidation model is fully permeable at the left and right boundaries, and semi-permeable at the upper and lower boundaries, with semi-permeability coefficients of , Due to the anisotropy of the soil, the vertical and horizontal permeability coefficients of the soil are represented by and , respectively.

[0019] S2, the following assumptions and settings are made for the two-dimensional consolidation model: the soil is homogeneous, anisotropic, and fully saturated, composed of incompressible particles and pore water; the stress-strain behavior is linear, small-strain, and has no plastic or creep effect; the influence of additional stress caused by soil self-weight is ignored during consolidation.

[0020] S3, the control equations and boundary conditions of the two-dimensional consolidation model are set.

[0021] According to the Terzaghi-Rendulic law, the control equation of two-dimensional consolidation can be written as: (1) where is the excess pore pressure, , are the vertical and horizontal consolidation coefficients of the soil, , are the vertical and horizontal coordinates in the Cartesian coordinate system, is the time.

[0022] The initial conditions of two-dimensional consolidation are: (2) where is the non-uniform load distribution, which varies with .

[0023] In the two-dimensional consolidation model, vertical drainage pipes are set, and the left and right boundaries are designated as fully permeable boundaries, so that the water can pass through the boundary conditions as follows: (3) (4) The upper and lower boundaries are designated as semi-permeable boundaries, and the boundary conditions are as follows: (5) (6) It should be noted that for the boundary semi-permeability coefficients , , when = 0, the above two equations can be simplified to impermeable boundaries to describe the places where water is difficult to penetrate in the underlying bedrock: (7) (8) When approaching positive infinity, it can be simplified as a full permeable boundary to simulate the lower sand bed with free water seepage: (9) (10) S4, Analyze the two-dimensional consolidation model to obtain the analytical solution of the excess pore pressure, calculate the soil consolidation rate, and analyze the consolidation behavior.

[0024] In this embodiment, the specific formula of the Fourier finite sine transform is as follows: (11) Wherein is the Fourier transform parameter, and is a positive integer. Apply equation (11) to the control equation (1) of two-dimensional consolidation, and combine the left and right boundary conditions (3) and (4) to obtain: (12) The initial condition (2) can be rewritten as: (13) The upper and lower boundary conditions (5) and (6) can be rewritten as: (14) (15) Wherein, can be further decomposed into steady-state solution and transient solution , as follows: (16) According to the variable separation method, the transient solution is further decomposed into spatial function and time function : (17) Combine equation (17) with equation (12) and simplify to obtain: (18) Wherein is the characteristic value, so that the time function satisfies: (19) The spatial function satisfies: (20)​ By combining equations (19) and (20), we can obtain the following: (twenty one) Among them, when hour: (twenty two) when hour: (twenty three) in, (twenty four) (25) Combining equation (21) with equation (14), we get: (26) (27) Combining equation (21) with equation (15), we get: (28) (29) in, and , , , Related, and (30) (31) To further simplify the solution, variables are used. for and The ratio and and The ratio: (32) It can be represented as: (33) in, It is any non-zero constant.

[0025] The following can be obtained through the initial condition (13): (34) Consider steady-state solution The final result is 0. Applying the inverse finite sine transform to the solution process yields the excess pore pressure of the two-dimensional consolidation: (35) consolidation ratio is a key indicator to measure the average consolidation degree of soil, which is calculated by , and the specific calculation formula is as follows: (36) wherein, is the length range of the non-uniform load.

[0026] Therefore, by the consolidation analysis method of anisotropic soil under non-uniform load and semi-permeable boundary provided by the embodiment, a two-dimensional consolidation model is established, and the anisotropy of soil, the influence of non-uniform load, and the influence of boundary drainage capacity are considered, so that the two-dimensional consolidation behavior of soil can be more reasonably and accurately analyzed, which indicates the direction for the two-dimensional consolidation analysis of anisotropic soil under non-uniform load, and provides a better means for the engineering practice of soil improvement.

[0027] The two-dimensional consolidation model provided by the embodiment is verified by specific cases as follows. First, the on-site test is compared and verified: The on-site test case is the excessive pore pressure under the load generated by a certain dam, which is measured on the seventy-fourth day and the nine hundred and fifty-eighth day, and the measurement focus is the silty clay layer of 22m. The upper boundary is mainly silt sand, and the lower boundary is a full permeable boundary. The method takes the vertical distribution of the seventy-fourth day excess pore pressure as the initial condition, and obtains the eight hundred and eighty-fourth day distribution through S1-S4. The related parameters are = 22m, = 100m, , = 1.8 x 10 -7 m 2 / s, = 0 (indicating that the horizontal leakage is ignored), = 7.56 x 10 -10 m / s, = 884 days, and the load is applied to simulate the dam itself. The calculation structure of the method is compared with the on-site test, as shown in FIG. 2. It can be seen that the method has good consistency with the on-site test results.

[0028] Then, the two-dimensional numerical simulation results are compared. A two-dimensional numerical model is established by using COMSOL Multiphysics 6.2, and the conditions adopted by the two-dimensional numerical model are the same as those of the method, and the parameter list is shown in Table 1. Both models are applied with a parabolic load. The two-dimensional numerical model is discretized into 7468 grid units, and a partial differential equation (PDE) module is used for solving, and the results are as follows: Figure 3The analytical solution obtained by the method is further verified to be very consistent with the two-dimensional numerical model in terms of the spatio-temporal variation, which confirms the accuracy of the method and supports the analysis of the effects of non-uniform load and boundary permeability on the anisotropic soil consolidation.

[0029] Table 1 Input geometric and physical parameters of the two-dimensional numerical model (and the method)

[0030] Based on the same inventive concept, the embodiment also provides a device, comprising: a memory for storing a computer program; and a processor for implementing the software method-related steps of the anisotropic soil non-uniform load and semi-permeable boundary consolidation analysis method as described above when executing the computer program.

[0031] The processor can include one or more processing cores, such as a 4-core processor, an 8-core processor, etc. The processor can be implemented in at least one of a hardware form of a Digital Signal Processing (DSP), a Field-Programmable Gate Array (FPGA), a Programmable Logic Array (PLA). The processor can also include a main processor and a coprocessor. The main processor is a processor for processing data in an awake state, also known as a Central Processing Unit (CPU). The coprocessor is a low-power processor for processing data in a standby state. In some specific embodiments, the processor can be integrated with a Graphics Processing Unit (GPU) for rendering and drawing the content to be displayed by the display screen. In some embodiments, the processor can also include an Artificial Intelligence (AI) processor for processing machine learning-related computing operations.

[0032] The memory can include one or more computer-readable storage media, which can be non-transitory. The memory can also include a high-speed random access memory, and a nonvolatile memory such as one or more disk storage devices, flash storage devices. In the embodiment, the memory is at least used to store the following computer program, wherein the computer program is loaded and executed by the processor, and can implement the software method-related steps described above. In addition, the resources stored by the memory can also include an operating system and data, etc., and the storage mode can be temporary storage or permanent storage. The operating system can include Windows, Unix, Linux, etc.

[0033] The embodiment also provides a computer readable storage medium, and the computer readable storage medium stores a computer program, and the computer program is executed by a processor to implement the software method related steps of the anisotropic soil non-uniform load and semi-permeable boundary consolidation analysis method.

[0034] The system, the device, the computer readable storage medium and the like provided by the embodiment have the same inventive concept and beneficial effects as the foregoing method, and will not be described here.

[0035] The technical features of the above embodiments can be combined in any manner. To make the description concise, not all possible combinations of the technical features in the above embodiments are described, but as long as the combinations of the technical features do not exist contradictions, they should be considered as the scope of the present disclosure.

[0036] The above embodiments only express several implementation manners of the present application, and the description is relatively specific and detailed, but it should not be understood as a limitation on the scope of the application. It should be pointed out that for those skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are all within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the appended claims.

Claims

1. A consolidation analysis method for anisotropic soil under non-uniform load and semi-permeable boundary, characterized in that, Includes the following steps: S1, construct a two-dimensional consolidation model under non-uniform load and semi-permeable boundary conditions; S2 sets the properties of the soil in the two-dimensional consolidation model; S3, set the governing equations and boundary conditions for the two-dimensional consolidation model; S4. The two-dimensional consolidation model is analyzed to obtain the analytical solution of excess pore pressure, calculate the soil consolidation rate, and analyze the soil consolidation behavior.

2. The consolidation analysis method for anisotropic soil under non-uniform load and semi-permeable boundary as described in claim 1, characterized in that, The two-dimensional consolidation model in S1 uses anisotropic soil with a thickness of [missing information]. And it is limited, with a width of And finite, non-uniform load is The two-dimensional consolidation model is fully permeable at the left and right boundaries and semi-permeable at the top and bottom boundaries. The semi-permeability coefficients of the top and bottom boundaries are respectively... , The vertical and horizontal permeability coefficients of the soil are respectively and .

3. The consolidation analysis method for anisotropic soil under non-uniform load and semi-permeable boundary as described in claim 2, characterized in that, The soil properties in the two-dimensional consolidation model in S2 include: the soil is homogeneous, anisotropic, and fully saturated, consisting of incompressible particles and pore water; the soil stress-strain behavior is linear, with no plastic or creep effects; and the influence of additional stress caused by the soil's own weight is ignored during the consolidation process.

4. The consolidation analysis method for anisotropic soil under non-uniform load and semi-permeable boundary as described in claim 3, characterized in that, The governing equations for the two-dimensional consolidation in S3 are: ； in, This is excess pore pressure. , These are the soil vertical consolidation coefficient and the horizontal consolidation coefficient, respectively. , These are the vertical and horizontal coordinates of the Cartesian coordinate system, respectively. For time; The initial conditions for two-position consolidation are: ； in, The load distribution is non-uniform. In the two-dimensional consolidated model, a vertical drainage pipe is set, and the left and right boundaries are designated as fully permeable boundaries, thus allowing water to pass through. The left and right boundary conditions are as follows: ； ； The upper and lower boundaries are designated as semi-permeable boundaries, with the following conditions: ； 。 5. The consolidation analysis method for anisotropic soil under non-uniform load and semi-permeable boundary according to claim 4, characterized in that, S4 introduces the Fourier finite sine transform: ； in Given the Fourier transform parameter as a positive integer, and combining it with the governing equations of the two-dimensional consolidation, as well as the left and right boundary conditions, we obtain: ； The initial conditions for the two-position consolidation can be rewritten as follows: ； The upper and lower boundary conditions are rewritten as follows: ； 。 6. The consolidation analysis method for anisotropic soil under non-uniform load and semi-permeable boundary according to claim 5, characterized in that, S4 in Further decomposition into steady-state solutions and transient solutions : ； According to the method of separation of variables, the transient solution is... Further decomposed into space functions and time function : ； Therefore, we get: ； in For eigenvalues, so that the time function satisfy: ； Space function satisfy: ； Combined to obtain ； Among them, when hour: ； when hour: ； in, ； ； Therefore, we get: ； ； Therefore, we get: ； ； in, and , , , Related, and ； ； ； Combined with steady-state solution By applying the inverse finite sine transform to the solution process, the excess pore pressure of the two-dimensional consolidation is obtained: 。 7. The consolidation analysis method for anisotropic soil under non-uniform load and semi-permeable boundary as described in claim 6, characterized in that, With variables for and The ratio and and The ratio: ； but Represented as: ； in, It is any non-zero constant.

8. The consolidation analysis method for anisotropic soil under non-uniform load and semi-permeable boundary as described in claim 6, characterized in that, Consolidation rate The calculation formula is: ； in, The length range for which a non-uniform load is applied.

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