A method and device for predicting the consolidation bearing capacity of strip foundations in clay seabed

Abstract

The present invention provides a method and device for predicting the consolidation bearing capacity of a strip foundation in a clay seabed. The target undrained shear strength distribution function of the target soil in the clay seabed is obtained by calculation, and based on the slip line theory, the target undrained shear strength distribution function is converted into the stress characteristic line equation of the soil after consolidation, and then the equation is solved according to the finite difference method to obtain the consolidation bearing capacity of the strip foundation under preload. The present invention can quickly and accurately calculate the consolidation bearing capacity of the strip foundation, solve the problem of inaccurate consolidation bearing capacity caused by the increase of foundation bearing capacity due to soil consolidation, and improve the accuracy of calculating the consolidation bearing capacity of the strip foundation.

Description

Technical Field

[0001] The present invention relates to the field of engineering geology, and in particular to a method and a device for predicting the consolidation bearing capacity of a strip foundation in a clay seabed. Background Art

[0002] Since my country's offshore areas are mainly soft clay seabeds, shallow foundations are generally used for energy development in this type of seabed to reduce construction costs. When the shallow foundation has a large aspect ratio L / B, it can be regarded as a strip foundation for analysis. At present, the assessment of the bearing capacity of strip foundations is mainly based on the in-situ stress state of the soil, considering the unconsolidated undrained bearing capacity Vuu (hereinafter referred to as unconsolidated bearing capacity) of the strip foundation. However, during the commissioning of the strip foundation, the seabed will be subjected to preload (generally the vertical load generated by the deadweight of the foundation and superstructure) and a consolidation effect will occur, resulting in an increase in soil strength and a significant increase in the foundation bearing capacity. The foundation bearing capacity at this time can be called the consolidated undrained bearing capacity Vcu (hereinafter referred to as consolidated bearing capacity) of the strip foundation. Especially in the marine environment, continuing to use the design specifications based on the unconsolidated bearing capacity of the foundation in the onshore environment without considering the consolidation effect of the seabed will result in the estimated strip foundation bearing capacity being too conservative, resulting in a waste of construction costs. Therefore, it is necessary to study the consolidation bearing capacity of strip foundations used in clay seabeds.

[0003] In the existing technology, in the article "Solution and Error Analysis of the Ultimate Bearing Capacity of Rough Strip Foundation" published by Han Dongdong in Rock and Soil Mechanics, the ultimate bearing capacity of rough strip foundation was calculated using the slip line method and finite difference method, the combined effect of soil cohesion, internal friction angle and gravity was discussed, and the fitting formula of Nγ was given. However, most of the existing technologies focus on the unconsolidated bearing capacity of strip foundations, and the research on the consolidated bearing capacity is also mainly based on the finite element method. Different working conditions need to be modeled and analyzed separately, and the process is relatively cumbersome.

[0004] Therefore, a prediction strategy for the consolidation bearing capacity of strip foundations is urgently needed to solve the problem that the existing technology does not consider the increase in foundation bearing capacity caused by soil consolidation, resulting in waste in strip foundation construction. Summary of the invention

[0005] The embodiment of the present invention provides a method and device for predicting the consolidation bearing capacity of a strip foundation in a clay seabed, so as to improve the calculation accuracy of the consolidation bearing capacity of the strip foundation.

[0006] In order to solve the above problem, an embodiment of the present invention provides a method for predicting the consolidation bearing capacity of a strip foundation in a clay seabed, comprising:

[0007] Testing a target soil body in a clay seabed to obtain a target undrained shear strength distribution function of the target soil body; wherein the target soil body is specifically: soil body located below the strip foundation and the superstructure; and the target undrained shear strength distribution function is specifically: calculated based on the first undrained shear strength distribution function and the pore pressure response function, combined with the relationship between the undrained shear strength and the vertical effective stress of the consolidated clay layer;

[0008] According to the target undrained shear strength distribution function, a slip line method is used to calculate and obtain a stress characteristic line equation of the consolidated soil;

[0009] According to the stress characteristic line equation, the consolidation bearing capacity of the strip foundation under the preload is obtained by solving it through a preset finite difference method.

[0010] As can be seen from the above, the present invention has the following beneficial effects:

[0011] The present invention provides a method for predicting the consolidation bearing capacity of a strip foundation in a clay seabed, by calculating and obtaining the target undrained shear strength distribution function of the target soil in the clay seabed, and based on the slip line theory, converting the target undrained shear strength distribution function into the stress characteristic line equation of the soil after consolidation, and then solving the equation according to the finite difference method to obtain the consolidation bearing capacity of the strip foundation under preload. The present invention can quickly and accurately calculate the consolidation bearing capacity of the strip foundation, solves the problem of inaccurate consolidation bearing capacity caused by the increase in foundation bearing capacity due to soil consolidation, and improves the accuracy of calculating the consolidation bearing capacity of the strip foundation.

[0012] As an improvement of the above scheme, the target soil in the clay seabed is tested to obtain the target undrained shear strength distribution function of the target soil, specifically: in-situ testing is performed on the target soil in the clay seabed to obtain a first undrained shear strength distribution function of the target soil; according to a preset vertical load, a pore pressure response function of the target soil is obtained by a preset stress distribution calculation formula; wherein the vertical load is generated by the deadweight of the structure and the environmental load; and the pore pressure response function includes the pore pressure response corresponding to each coordinate position in all the target soils; according to the first undrained shear strength distribution function and the pore pressure response function, The relationship between the undrained shear strength and vertical effective stress of the consolidated clay layer is used to calculate the second undrained shear strength distribution function of the target soil; wherein the vertical effective stress is calculated according to the pore pressure response function; and the second undrained shear strength distribution function is the target undrained shear strength distribution function; the initial undrained shear strength distribution function of the target soil is obtained by in-situ testing the target soil of the clay seabed; at the same time, the pore pressure response function is solved by the preset vertical load, and finally, according to the relationship between the undrained shear strength and vertical effective stress of the consolidated clay layer, the undrained shear strength distribution function of the target soil after consolidation is obtained. By simulating the load of the strip foundation, the most accurate target undrained shear strength distribution function of the target soil is obtained, which lays the foundation for the following steps.

[0013] As an improvement of the above scheme, the pore pressure response function of the target soil is obtained according to the preset vertical load and the preset stress distribution calculation formula, specifically: the vertical load is obtained according to the deadweight of the strip foundation, the deadweight of the superstructure and the environmental load; according to the vertical load, the pore pressure response function in the target soil under the action of the strip uniformly distributed load is calculated by the preset stress distribution calculation formula, and the calculation formula is:

[0014]

[0015] Among them, Δu w is the pore pressure response function, V p is the vertical load, B is the foundation width, and the coordinates of any point in the soil are expressed as (x, z), where x is the horizontal distance from the calculation point to the left edge of the uniformly distributed load, and z is the vertical distance from the calculation point to the left edge of the load. The air pressure response function is calculated using the stress distribution calculation formula, which can improve the accuracy of the pore pressure response function of the target soil, thereby being closer to the actual clay seabed load situation.

[0016] As an improvement of the above scheme, according to the first undrained shear strength distribution function and the pore pressure response function, the second undrained shear strength distribution function of the target soil is calculated through the relationship between the undrained shear strength and the vertical effective stress of the consolidated clay layer. Specifically, the vertical effective stress function is calculated according to the pore pressure response function; the undrained shear strength function of the consolidated clay layer is calculated through the relationship between the undrained shear strength and the vertical effective stress of the consolidated clay layer. The specific formula is:

[0017]

[0018] Among them, S u is the undrained shear strength of the consolidated clay layer, σ′ v is the vertical effective stress; is the effective internal friction angle, the ratio of K to λ is about 0.2, And when the effective internal friction angle is determined, S u and σ′ v The ratio is a constant R, and the specific formula is: The first undrained shear strength distribution function and the undrained shear strength function of the consolidated clay layer are subjected to a preset weighted calculation to obtain a second undrained shear strength distribution function of the target soil body; the vertical effective stress function is derived from the pore pressure function, and the vertical effective stress function is calculated according to the pore pressure function. The relationship between the first undrained shear strength and the undrained shear strength function of the consolidated clay layer is used to calculate the undrained shear strength function of the consolidated clay layer, and finally the first undrained shear strength and the undrained shear strength function of the consolidated clay layer are combined for calculation, which further improves the accuracy of the target undrained shear strength distribution function.

[0019] As an improvement of the above scheme, the target undrained shear strength distribution function is calculated by the sliding line method to obtain the stress characteristic line equation of the consolidated soil, specifically: according to the target undrained shear strength distribution function, the normal stress equation in the x direction, the normal stress equation in the z direction and the shear stress equation in the plane are obtained; according to the normal stress equation in the x direction, the normal stress equation in the z direction and the shear stress equation in the plane, they are substituted into the equilibrium equation preset in the sliding line method to obtain the stress characteristic line equation of the consolidated soil; wherein, the stress characteristic line equation of the consolidated soil includes: the stress characteristic line equation of the α line and the stress characteristic line equation of the β line; the target undrained shear strength distribution function is transformed by the sliding line method, and the stress characteristic line equation of the consolidated soil is obtained according to the equilibrium equation, which lays a foundation for the calculation of each point in the target soil.

[0020] As an improvement of the above scheme, the stress characteristic line equation is solved by a preset finite difference method, specifically: according to the form of the known point parameters and the undrained shear strength of the consolidated soil at the known points, the stress characteristic line equation of the consolidated soil is converted into a finite difference equation; wherein the form of the known point parameters includes: x-coordinate, z-coordinate, characteristic stress, and the angle between the direction of the major principal stress and the Z-axis; in each calculation of the second known point parameters, the second known point parameters obtained in the previous calculation are added to the first known point parameter set, and in the updated first known point parameter set, two points that are not simultaneously substituted into the equation calculation are selected Parameters are substituted into the finite difference equation to calculate the parameters of the second known point; wherein, before the iteration starts, the first known point parameter set already includes two known point parameters; the second known point parameters obtained by each calculation are compared with the second known point parameters obtained by the previous calculation, and when the preset conditions are met, the iteration is stopped to obtain the second known point parameter set; when the preset conditions are not met, the iteration is continued; starting from the known boundary, the stress characteristic line equation is iteratively solved according to the parameters of the two known points through the finite difference method to obtain the parameters of each point in the target soil on the slip line network, so as to quickly obtain the results of the unknown point parameters in the target soil.

[0021] As an improvement of the above-mentioned scheme, the consolidation bearing capacity of the strip foundation under preload is obtained by: obtaining the consolidation bearing capacity of the strip foundation based on the obtained second known point parameter set, the x-coordinate of each point on the slip line network, the z-coordinate of each point, the characteristic stress of each point, and the angle between the major principal stress direction of each point and the Z-axis; and obtaining the consolidation bearing capacity of the strip foundation based on the obtained parameters of each point of the target soil on the slip line network, thereby improving the accuracy of the consolidation bearing capacity of the strip foundation.

[0022] As an improvement of the above scheme, the finite difference equation is discretized, and the parameters of the second known point are iteratively calculated through a numerical program; calculation through a numerical program can speed up the solution of the finite difference method, improve the calculation efficiency, and also avoid errors caused by manual calculations.

[0023] As an improvement of the above scheme, after obtaining the consolidation bearing capacity of the strip foundation after the preload, it also includes: according to the consolidation bearing capacity of the strip foundation after the preload, readjusting the design parameters of the first strip foundation to obtain a new vertical load, and calculating the consolidation bearing capacity according to the new vertical load, so as to obtain the design parameters of the second strip foundation according to the recalculated consolidation bearing capacity; wherein the design parameters of the second strip foundation tend to stable values; according to the obtained consolidation bearing capacity, adjusting the design parameters of the strip foundation, and recalculating the consolidation bearing capacity according to the consolidation bearing capacity prediction method of the strip foundation in the clay seabed, thereby improving the accuracy of parameter calculation and making the design parameters of the strip foundation more practical.

[0024] Accordingly, an embodiment of the present invention further provides a device for predicting the consolidation bearing capacity of a strip foundation in a clay seabed, comprising: a first calculation module, a second calculation module and a third calculation module;

[0025] The first calculation module is used to test the target soil in the clay seabed to obtain the target undrained shear strength distribution function of the target soil; wherein the target soil is specifically: the soil located below the strip foundation and the superstructure; and the target undrained shear strength distribution function is: calculated based on the first undrained shear strength distribution function and the pore pressure response function, combined with the relationship between the undrained shear strength and the vertical effective stress of the consolidated clay layer;

[0026] The second calculation module is used to calculate the target undrained shear strength distribution function by a slip line method to obtain a stress characteristic line equation of the consolidated soil;

[0027] The third calculation module is used to solve the stress characteristic line equation through a preset finite difference method to obtain the consolidation bearing capacity of the strip foundation under preload.

[0028] As an improvement of the above solution, the first calculation module includes: a test unit, a pore pressure response unit and a combined operation unit;

[0029] The testing unit is used to: perform in-situ testing on a target soil body in a clay seabed to obtain a first undrained shear strength distribution function of the target soil body;

[0030] The pore pressure response unit is used to obtain the pore pressure response function of the target soil body according to a preset vertical load and a preset stress distribution calculation formula; wherein the vertical load is generated by the deadweight of the structure and the environmental load; and the pore pressure response function includes the pore pressure response corresponding to each coordinate position in all the target soil bodies;

[0031] The combined operation unit is used to: calculate the second undrained shear strength distribution function of the target soil body according to the first undrained shear strength distribution function and the pore pressure response function, through the relationship between the undrained shear strength and the vertical effective stress of the consolidated clay layer; wherein the vertical effective stress is calculated according to the pore pressure response function; and the second undrained shear strength distribution function is the target undrained shear strength distribution function.

[0032] As an improvement of the above scheme, the pore pressure response function of the target soil is obtained according to the preset vertical load and the preset stress distribution calculation formula, specifically: the vertical load is obtained according to the deadweight of the strip foundation, the deadweight of the superstructure and the environmental load; according to the vertical load, the pore pressure response function in the target soil under the action of the strip uniformly distributed load is calculated by the preset stress distribution calculation formula, and the calculation formula is:

[0033]

[0034] Among them, Δu w is the pore pressure response function, V p is the vertical load, B is the foundation width, and the coordinates of any point in the soil are expressed as (x, z), where x is the horizontal distance from the calculation point to the left edge of the uniformly distributed load, and z is the vertical distance from the calculation point to the left edge of the load.

[0035] As an improvement of the above scheme, according to the first undrained shear strength distribution function and the pore pressure response function, the second undrained shear strength distribution function of the target soil is calculated through the relationship between the undrained shear strength and the vertical effective stress of the consolidated clay layer. Specifically, the vertical effective stress function is calculated according to the pore pressure response function; the undrained shear strength function of the consolidated clay layer is calculated through the relationship between the undrained shear strength and the vertical effective stress of the consolidated clay layer. The specific formula is:

[0036]

[0037] Among them, S u is the undrained shear strength of the consolidated clay layer, σ′ v is the vertical effective stress; is the effective internal friction angle, the ratio of K to λ is about 0.2, And when the effective internal friction angle is determined, S u and σ′ v The ratio is a constant R, and the specific formula is: The first undrained shear strength distribution function and the consolidated clay layer undrained shear strength function are subjected to a preset weighted calculation to obtain a second undrained shear strength distribution function of the target soil body.

[0038] As an improvement of the above solution, the second calculation module includes: a decomposition unit and a stress characteristic line unit

[0039] The decomposition unit is used to obtain a normal stress equation in the x direction, a normal stress equation in the z direction and a shear stress equation in the plane according to the target undrained shear strength distribution function;

[0040] The stress characteristic line unit is used to substitute the normal stress equation in the x-direction, the normal stress equation in the z-direction and the shear stress equation in the plane into the preset equilibrium equation in the slip line method to obtain the stress characteristic line equation of the consolidated soil; wherein the stress characteristic line equation of the consolidated soil includes: the stress characteristic line equation of the α line and the stress characteristic line equation of the β line.

[0041] As an improvement of the above solution, the stress characteristic line equation is solved by a preset finite difference method, specifically:

[0042] According to the form of known point parameters and the undrained shear strength of the consolidated soil at the known points, the stress characteristic line equation of the consolidated soil is converted into a finite difference equation; wherein the form of the known point parameters includes: x-coordinate, z-coordinate, characteristic stress, and the angle between the direction of the major principal stress and the Z-axis; in each calculation of the second known point parameter, the second known point parameter obtained in the previous calculation is added to the first known point parameter set, and in the updated first known point parameter set, two point parameters that are not simultaneously substituted into the equation calculation are selected and substituted into the finite difference equation to calculate the second known point parameter; wherein the first known point parameter set already contains two known point parameters before the iteration starts; the second known point parameter obtained in each calculation is compared with the second known point parameter obtained in the previous calculation, and when the preset condition is met, the iteration is stopped to obtain the second known point parameter set; when the preset condition is not met, the iteration is continued.

[0043] As an improvement of the above-mentioned scheme, the consolidation bearing capacity of the strip foundation under preload is obtained by, specifically: according to the obtained second known point parameter set, the x-coordinate of each point on the slip line network, the z-coordinate of each point, the characteristic stress of each point, and the angle between the major principal stress direction of each point and the Z-axis, thereby obtaining the consolidation bearing capacity of the strip foundation.

[0044] As an improvement of the above solution, the finite difference equation is discretized, and the iterative calculation of the parameters of the second known point is performed through a numerical program.

[0045] As an improvement of the above scheme, after obtaining the consolidation bearing capacity of the strip foundation after the preload, it also includes: according to the consolidation bearing capacity of the strip foundation after the preload, readjusting the design parameters of the first strip foundation to obtain a new vertical load, and calculating the consolidation bearing capacity according to the new vertical load, so as to obtain the design parameters of the second strip foundation according to the recalculated consolidation bearing capacity; wherein the design parameters of the second strip foundation tend to stable values.

[0046] Correspondingly, an embodiment of the present invention further provides a computer terminal device, comprising a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein when the processor executes the computer program, a method for predicting the consolidation bearing capacity of a strip foundation in a clay seabed as described in the present invention is implemented.

[0047] Correspondingly, an embodiment of the present invention further provides a computer-readable storage medium, which includes a stored computer program, wherein when the computer program is running, the device where the computer-readable storage medium is located is controlled to execute a method for predicting the consolidation bearing capacity of a strip foundation in a clay seabed as described in the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a schematic flow chart of a method for predicting the consolidation bearing capacity of a strip foundation in a clay seabed provided by an embodiment of the present invention;

[0049] Figure 2 It is a schematic structural diagram of a device for predicting the consolidation bearing capacity of a strip foundation in a clay seabed provided by an embodiment of the present invention;

[0050] Figure 3 is a simulation diagram of the preload effect provided by an embodiment of the present invention;

[0051] Figure 4 It is a schematic diagram of the structure of a terminal device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0052] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0053] Embodiment 1

[0054] See also Figure 1 , Figure 1FIG. 1 is a flow chart of a method for predicting the consolidation bearing capacity of a strip foundation in a clay seabed provided by an embodiment of the present invention. Figure 1 As shown, this embodiment includes steps 101 to 103, and each step is specifically as follows:

[0055] Step 101: testing a target soil in a clay seabed to obtain a target undrained shear strength distribution function of the target soil; wherein the target soil is specifically: soil located below a strip foundation and an upper structure; and the target undrained shear strength distribution function is calculated based on a first undrained shear strength distribution function and a pore pressure response function, combined with a relationship between an undrained shear strength of a consolidated clay layer and vertical effective stress.

[0056] In this embodiment, the target soil in the clay seabed is tested to obtain the target undrained shear strength distribution function of the target soil, which is specifically:

[0057] An in-situ test is performed on the target soil in the clay seabed to obtain the first undrained shear strength distribution function of the target soil; wherein, the initial undrained shear strength distribution can be obtained by performing an in-situ test on the target soil in the clay seabed. The in-situ test refers to a cross-plate shear test, a CPT test, etc. conducted on the clay seabed. Based on the experimental data, the undrained shear strength and the rate at which the undrained shear strength of the soil increases with depth can be obtained; the first undrained shear strength distribution function S u , including: undrained shear strength S of the soil at the mud surface uo , the rate at which the undrained shear strength of soil increases with depth k su , the specific formula is:

[0058] S u =S uo +k su z

[0059] Where z is the depth of the target soil;

[0060] According to the preset vertical load, the pore pressure response function of the target soil is obtained by a preset stress distribution calculation formula; wherein the vertical load is generated by the deadweight of the structure and the environmental load; and the pore pressure response function includes the pore pressure response corresponding to each coordinate position in all the target soils;

[0061] According to the first undrained shear strength distribution function and the pore pressure response function, the second undrained shear strength distribution function of the target soil body is calculated through the relationship between the undrained shear strength and the vertical effective stress of the consolidated clay layer; wherein the vertical effective stress is calculated according to the pore pressure response function; and the second undrained shear strength distribution function is the target undrained shear strength distribution function.

[0062] In this embodiment, according to the preset vertical load, the pore pressure response function of the target soil is obtained by a preset stress distribution calculation formula, which is specifically:

[0063] The vertical loads are obtained from the self-weight of the strip foundation, the self-weight of the superstructure and the environmental loads; for a better explanation, see Figure 3 , Figure 3 A simulation diagram of the preload effect provided by an embodiment of the present invention.

[0064] According to the vertical load, the pore pressure response function in the target soil under the strip uniformly distributed load is calculated by a preset stress distribution calculation formula, and the calculation formula is:

[0065]

[0066] Among them, Δu w is the pore pressure response function, V p is the vertical load, B is the foundation width, and the coordinates of any point in the soil are expressed as (x, z), where x is the horizontal distance from the calculation point to the left edge of the uniformly distributed load, and z is the vertical distance from the calculation point to the left edge of the load;

[0067] The preset stress distribution calculation formula is specifically: It is calculated through the Boussinesq solution and is a calculation formula obtained by the additional stress distribution in the foundation under the action of concentrated vertical load.

[0068] In this embodiment, according to the first undrained shear strength distribution function and the pore pressure response function, the second undrained shear strength distribution function of the target soil is calculated through the relationship between the undrained shear strength and the vertical effective stress of the consolidated clay layer, which is specifically:

[0069] According to the pore pressure response function, a vertical effective stress function is calculated;

[0070] The undrained shear strength function of the consolidated clay layer is calculated based on the relationship between the undrained shear strength of the consolidated clay layer and the vertical effective stress. The specific formula is:

[0071]

[0072] Among them, S u is the undrained shear strength of the consolidated clay layer, σ′ v is the vertical effective stress; is the effective internal friction angle, the ratio of K to λ is about 0.2, And when the effective internal friction angle is determined, S u and σ′ v The ratio is a constant R, and the specific formula is:

[0073] The relationship between the undrained shear strength and vertical effective stress of a consolidated clay layer refers to the relationship between the undrained shear strength and vertical effective stress of a normally consolidated clay layer under the conditions of plane strain and K0 consolidation based on the critical state theory.

[0074] The first undrained shear strength distribution function and the consolidated clay layer undrained shear strength function are subjected to a preset weighted calculation to obtain a second undrained shear strength distribution function of the target soil body; the specific formula is as follows:

[0075] Δσ′ v =Δu w ;

[0076] ΔS u =RΔσ′ v ;

[0077] S u (x,z)=S uo +k su z+RΔσ′ v ;

[0078] Among them, v′ v is the vertical effective stress function, u w is the effective function of air pressure response, S u is the undrained shear strength of the consolidated clay layer, S u (x,z) is the second undrained shear strength distribution function.

[0079] Step 102: According to the target undrained shear strength distribution function, a slip line method is used to calculate and obtain a stress characteristic line equation of the consolidated soil.

[0080] In this embodiment, according to the target undrained shear strength distribution function, the slip line method is used to calculate and obtain the stress characteristic line equation of the consolidated soil, which is specifically:

[0081] According to the target undrained shear strength distribution function, the normal stress equation in the x direction, the normal stress equation in the z direction and the shear stress equation in the plane are obtained; the specific formula is:

[0082]

[0083] σ x and σ z are the normal stresses in the x and z directions, τ xz is the in-plane shear stress, γ is the total weight of the soil, σ is the characteristic stress, σ1 is the major principal stress, σ3 is the minor principal stress, and θ is the angle between the major principal stress and the Z axis;

[0084] According to the normal stress equation in the x direction, the normal stress equation in the z direction and the shear stress equation in the plane, the preset equilibrium equation in the slip line method is substituted to obtain the stress characteristic line equation of the consolidated soil; wherein the stress characteristic line equation of the consolidated soil includes: the stress characteristic line equation of the α line and the stress characteristic line equation of the β line; the specific formula of the equilibrium equation is as follows:

[0085]

[0086] The stress characteristic line equation formula is as follows:

[0087]

[0088]

[0089] in, is the angle between the direction of the major principal stress and the direction of the characteristic line.

[0090] Step 103: solving the stress characteristic line equation by a preset finite difference method to obtain the consolidation bearing capacity of the strip foundation under the preload;

[0091] In this embodiment, according to the form of known point parameters and the undrained shear strength of the consolidated soil at the known points, the stress characteristic line equation of the consolidated soil is converted into a finite difference equation; wherein the form of the known point parameters includes: x-coordinate, z-coordinate, characteristic stress, and the angle between the major principal stress direction and the Z-axis; wherein the finite difference equation is specifically:

[0092]

[0093]

[0094] Among them, S uA , S uB , S uc are the undrained shear strength of the consolidated soil at points A, B, and C, respectively, c The initial iteration value is θ A or θ B ;

[0095] In each calculation of the second known point parameter, the second known point parameter obtained in the previous calculation is added to the first known point parameter set, and in the updated first known point parameter set, two point parameters that are not simultaneously substituted into the equation calculation are selected and substituted into the finite difference equation to calculate the second known point parameter; wherein the first known point parameter set already contains two known point parameters before the iteration starts;

[0096] The parameters of the two known points are: point A (x A ,z A ,σ A ,θ A ) and point B (x B ,z B ,σ B ,θ B ), point A is a known point on line α, and point B is a known point on line β;

[0097] Compare the second known point parameters obtained by each calculation with the second known point parameters obtained by the previous calculation. When the preset conditions are met, stop the iteration and obtain the second known point parameter set; when the preset conditions are not met, continue the iteration; wherein the preset conditions are specifically:

[0098] |x c -x c old |≤Tol·B

[0099] |z c -z c old |≤Tol·B

[0100] |θ c -θ c old |≤Tol

[0101] |σ c -σ c old |≤Tol·|σ c |

[0102] Where Tol is the allowable error in calculation, which is set to 10 -10 .

[0103] In this embodiment, the consolidation bearing capacity of the strip foundation under preload is obtained, specifically: based on the obtained second known point parameter set, the x-coordinate of each point on the slip line network, the z-coordinate of each point, the characteristic stress of each point, and the angle between the major principal stress direction of each point and the Z-axis, the consolidation bearing capacity of the strip foundation is obtained.

[0104] In this embodiment, the finite difference equation is discretized, and the iterative calculation of the second known point parameter is performed in the form of a numerical program; the numerical program can be run through Matlab, Fortran, C++ or Python.

[0105] In this embodiment, after obtaining the consolidation bearing capacity of the strip foundation after the preload, it also includes: according to the consolidation bearing capacity of the strip foundation after the preload, readjusting the design parameters of the first strip foundation to obtain a new vertical load, and calculating the consolidation bearing capacity according to the new vertical load, so as to obtain the design parameters of the second strip foundation according to the recalculated consolidation bearing capacity; wherein the design parameters of the second strip foundation tend to stable values.

[0106] This embodiment obtains the target undrained shear strength distribution function of the target soil in the clay seabed by calculation, and based on the slip line theory, converts the target undrained shear strength distribution function into the stress characteristic line equation of the soil after consolidation, and then solves the equation according to the finite difference method to obtain the consolidation bearing capacity of the strip foundation under preload. This embodiment can quickly predict the consolidation bearing capacity of the strip foundation after preload in saturated clay, has a simple principle, high calculation accuracy, and strong practicality. By adjusting the original design of the strip foundation through the calculated high-precision consolidation bearing capacity, the existing shallow foundation design specifications can be further improved to avoid wasting construction costs.

[0107] Embodiment 2

[0108] See also Figure 2 , Figure 2 It is a structural schematic diagram of a device for predicting the consolidation bearing capacity of a strip foundation in a clay seabed provided by an embodiment of the present invention, comprising: a first calculation module 201, a second calculation module 202 and a third calculation module 203;

[0109] The first calculation module 201 is used to obtain a target undrained shear strength distribution function of a target soil body in a clay seabed; wherein the target soil body is specifically: a soil body located below a strip foundation and an upper structure;

[0110] The second calculation module 202 is used to test the target soil in the clay seabed to obtain the target undrained shear strength distribution function of the target soil; wherein the target soil is specifically: the soil located below the strip foundation and the superstructure; and the target undrained shear strength distribution function is: calculated based on the first undrained shear strength distribution function and the pore pressure response function, combined with the relationship between the undrained shear strength and the vertical effective stress of the consolidated clay layer;

[0111] The third calculation module 203 is used to solve the stress characteristic line equation by a preset finite difference method to obtain the consolidation bearing capacity of the strip foundation under the preload.

[0112] As an improvement of the above solution, the first calculation module 201 includes: a test unit, a pore pressure response unit and a combined operation unit;

[0113] The testing unit is used to: perform in-situ testing on a target soil body in a clay seabed to obtain a first undrained shear strength distribution function of the target soil body;

[0114] The pore pressure response unit is used to obtain the pore pressure response function of the target soil body according to a preset vertical load and a preset stress distribution calculation formula; wherein the vertical load is generated by the deadweight of the structure and the environmental load; and the pore pressure response function includes the pore pressure response corresponding to each coordinate position in all the target soil bodies;

[0115] The combined operation unit is used to: calculate the second undrained shear strength distribution function of the target soil body according to the first undrained shear strength distribution function and the pore pressure response function, through the relationship between the undrained shear strength and the vertical effective stress of the consolidated clay layer; wherein the vertical effective stress is calculated according to the pore pressure response function; and the second undrained shear strength distribution function is the target undrained shear strength distribution function.

[0116] As an improvement of the above scheme, the pore pressure response function of the target soil is obtained according to the preset vertical load and the preset stress distribution calculation formula, specifically: the vertical load is obtained according to the deadweight of the strip foundation, the deadweight of the superstructure and the environmental load; according to the vertical load, the pore pressure response function in the target soil under the action of the strip uniformly distributed load is calculated by the preset stress distribution calculation formula, and the calculation formula is:

[0117]

[0118] Among them, Δu w is the pore pressure response function, V p is the vertical load, B is the foundation width, and the coordinates of any point in the soil are expressed as (x, z), where x is the horizontal distance from the calculation point to the left edge of the uniformly distributed load, and z is the vertical distance from the calculation point to the left edge of the load.

[0119] As an improvement of the above scheme, according to the first undrained shear strength distribution function and the pore pressure response function, the second undrained shear strength distribution function of the target soil is calculated through the relationship between the undrained shear strength and the vertical effective stress of the consolidated clay layer. Specifically, the vertical effective stress function is calculated according to the pore pressure response function; the undrained shear strength function of the consolidated clay layer is calculated through the relationship between the undrained shear strength and the vertical effective stress of the consolidated clay layer. The specific formula is:

[0120]

[0121] Among them, S uis the undrained shear strength of the consolidated clay layer, σ v ′ is the vertical effective stress; is the effective internal friction angle, the ratio of K to λ is about 0.2, And when the effective internal friction angle is determined, S u The ratio of σv′ is a constant R, and the specific formula is: The first undrained shear strength distribution function and the consolidated clay layer undrained shear strength function are subjected to a preset weighted calculation to obtain a second undrained shear strength distribution function of the target soil body.

[0122] As an improvement of the above solution, the second calculation module 202 includes: a decomposition unit and a stress characteristic line unit

[0123] The decomposition unit is used to obtain a normal stress equation in the x direction, a normal stress equation in the z direction and a shear stress equation in the plane according to the target undrained shear strength distribution function;

[0124] The stress characteristic line unit is used to substitute the normal stress equation in the x-direction, the normal stress equation in the z-direction and the shear stress equation in the plane into the preset equilibrium equation in the slip line method to obtain the stress characteristic line equation of the consolidated soil; wherein the stress characteristic line equation of the consolidated soil includes: the stress characteristic line equation of the α line and the stress characteristic line equation of the β line.

[0125] As an improvement of the above solution, the stress characteristic line equation is solved by a preset finite difference method, specifically:

[0126] According to the form of known point parameters and the undrained shear strength of the consolidated soil at the known points, the stress characteristic line equation of the consolidated soil is converted into a finite difference equation; wherein the form of the known point parameters includes: x-coordinate, z-coordinate, characteristic stress, and the angle between the direction of the major principal stress and the Z-axis; in each calculation of the second known point parameter, the second known point parameter obtained in the previous calculation is added to the first known point parameter set, and in the updated first known point parameter set, two point parameters that are not simultaneously substituted into the equation calculation are selected and substituted into the finite difference equation to calculate the second known point parameter; wherein the first known point parameter set already contains two known point parameters before the iteration starts; the second known point parameter obtained in each calculation is compared with the second known point parameter obtained in the previous calculation, and when the preset condition is met, the iteration is stopped to obtain the second known point parameter set; when the preset condition is not met, the iteration is continued.

[0127] As an improvement of the above-mentioned scheme, the consolidation bearing capacity of the strip foundation under preload is obtained by, specifically: according to the obtained second known point parameter set, the x-coordinate of each point on the slip line network, the z-coordinate of each point, the characteristic stress of each point, and the angle between the major principal stress direction of each point and the Z-axis, thereby obtaining the consolidation bearing capacity of the strip foundation.

[0128] As an improvement of the above solution, the finite difference equation is discretized, and the iterative calculation of the parameters of the second known point is performed through a numerical program.

[0129] As an improvement of the above scheme, after obtaining the consolidation bearing capacity of the strip foundation after the preload, it also includes: according to the consolidation bearing capacity of the strip foundation after the preload, readjusting the design parameters of the first strip foundation to obtain a new vertical load, and calculating the consolidation bearing capacity according to the new vertical load, so as to obtain the design parameters of the second strip foundation according to the recalculated consolidation bearing capacity; wherein the design parameters of the second strip foundation tend to stable values.

[0130] In this embodiment, the target undrained shear strength distribution function of the consolidated soil generated after the target soil of the clay seabed is consolidated under the action of preload is solved by the first calculation module, and the obtained target undrained shear strength distribution function is input into the second calculation module to transform the stress characteristic line equation of the soil after consolidation, and finally solved by the third calculation module to obtain the consolidation bearing capacity of the strip foundation under the action of preload. The implementation of this embodiment can improve the calculation efficiency of the consolidation bearing capacity of the strip foundation, and has the advantages of high calculation accuracy and strong practicality.

[0131] Embodiment 3

[0132] See also Figure 4 , Figure 4 It is a schematic diagram of the structure of a terminal device provided in one embodiment of the present invention.

[0133] A terminal device of this embodiment includes: a processor 401, a memory 402, and a computer program stored in the memory 402 and executable on the processor 401. When the processor 401 executes the computer program, the steps of the above-mentioned method for predicting the consolidation bearing capacity of a strip foundation in a clay seabed in the embodiment are implemented, for example Figure 1 Alternatively, when the processor executes the computer program, the functions of each module in the above-mentioned device embodiments are realized, for example: Figure 2 All modules of the device for predicting the consolidation bearing capacity of strip foundations in clay seabed are shown.

[0134] In addition, an embodiment of the present invention further provides a computer-readable storage medium, which includes a stored computer program, wherein when the computer program is running, the device where the computer-readable storage medium is located is controlled to execute the method for predicting the consolidation bearing capacity of a strip foundation in a clay seabed as described in any of the above embodiments.

[0135] Those skilled in the art will understand that the schematic diagram is merely an example of a terminal device and does not constitute a limitation on the terminal device. The terminal device may include more or fewer components than shown in the diagram, or a combination of certain components, or different components. For example, the terminal device may also include input and output devices, network access devices, buses, etc.

[0136] The processor 401 may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor, etc. The processor 401 is the control center of the terminal device, and uses various interfaces and lines to connect various parts of the entire terminal device.

[0137] The memory 402 can be used to store the computer program and / or module, and the processor 401 realizes various functions of the terminal device by running or executing the computer program and / or module stored in the memory, and calling the data stored in the memory 402. The memory 402 can mainly include a program storage area and a data storage area, wherein the program storage area can store an operating system, an application required for at least one function (such as a sound playback function, an image playback function, etc.), etc.; the data storage area can store data created according to the use of the mobile phone (such as audio data, a phone book, etc.), etc. In addition, the memory can include a high-speed random access memory, and can also include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), at least one disk storage device, a flash memory device, or other volatile solid-state storage devices.

[0138] Wherein, if the module / unit integrated in the terminal device is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, the present invention implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of the above-mentioned various method embodiments when executed by the processor. Wherein, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form, etc. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), electric carrier signal, telecommunication signal and software distribution medium, etc.

[0139] It should be noted that the device embodiments described above are merely schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. In addition, in the accompanying drawings of the device embodiments provided by the present invention, the connection relationship between the modules indicates that there is a communication connection between them, which may be specifically implemented as one or more communication buses or signal lines. A person of ordinary skill in the art may understand and implement it without paying any creative effort.

[0140] The above is a preferred embodiment of the present invention. It should be pointed out that a person skilled in the art can make several improvements and modifications without departing from the principle of the present invention. These improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A method for predicting the consolidation bearing capacity of a strip foundation in a clay seabed, characterized in that: include: A target soil body in a clay seabed is tested to obtain a target undrained shear strength distribution function of the target soil body; wherein the target soil body is specifically: a soil body located below a strip foundation and an upper structure; and the target undrained shear strength distribution function is calculated based on the first undrained shear strength distribution function and the pore pressure response function, combined with the relationship between the undrained shear strength and the vertical effective stress of the consolidated clay layer; According to the target undrained shear strength distribution function, the slip line method is used to calculate and obtain the stress characteristic line equation of the consolidated soil; wherein, according to the target undrained shear strength distribution function, the slip line method is used to calculate and obtain the stress characteristic line equation of the consolidated soil, specifically: according to the target undrained shear strength distribution function, the normal stress equation in the x direction, the normal stress equation in the z direction and the shear stress equation in the plane are obtained; the specific formula is: S u is the undrained shear strength of the consolidated clay layer, σ x and σ z are the normal stresses in the x and z directions, τ xz is the in-plane shear stress, γ is the total weight of the soil, σ is the characteristic stress, σ1 is the major principal stress, σ3 is the minor principal stress, and θ is the angle between the major principal stress and the Z axis; According to the normal stress equation in the x direction, the normal stress equation in the z direction and the shear stress equation in the plane, the preset equilibrium equation in the slip line method is substituted to obtain the stress characteristic line equation of the consolidated soil; wherein the stress characteristic line equation of the consolidated soil includes: the stress characteristic line equation of the α line and the stress characteristic line equation of the β line; the specific formula of the equilibrium equation is as follows: The obtained stress characteristic line equation formula is as follows: in, is the angle between the direction of the major principal stress and the direction of the characteristic line; According to the stress characteristic line equation, the consolidation bearing capacity of the strip foundation under preload is obtained by solving it through a preset finite difference method; wherein, according to the form of the known point parameters and the undrained shear strength of the consolidated soil at the known points, the stress characteristic line equation of the consolidated soil is converted into a finite difference equation; wherein, the form of the known point parameters includes: x-coordinate, z-coordinate, characteristic stress, and the angle between the major principal stress direction and the Z-axis; wherein, the finite difference equation is specifically: Among them, S uA , S uB , S uc are the undrained shear strength of the consolidated soil at points A, B, and C, respectively, c The initial iteration value is θ A or θ B ; In each calculation of the second known point parameter, the second known point parameter obtained in the previous calculation is added to the first known point parameter set, and in the updated first known point parameter set, two point parameters that are not simultaneously substituted into the equation calculation are selected and substituted into the finite difference equation to calculate the second known point parameter; wherein the first known point parameter set already contains two known point parameters before the iteration starts; The parameters of the two known points are: point A (x A , z A , σ A ,θ A ) and point B (x B , z B , σ B ,θ B ), point A is a known point on line α, and point B is a known point on line β; Compare the second known point parameters obtained by each calculation with the second known point parameters obtained by the previous calculation. When the preset conditions are met, stop the iteration and obtain the second known point parameter set; when the preset conditions are not met, continue the iteration; wherein the preset conditions are specifically: |x c -x c old |≤Tol·B |z c -z c old |≤Tol·B |θ c -θ c old |≤Tol |s c -s c old |≤Tol·|σ c | Where Tol is the allowable error in calculation, which is set to 10 -10 .

2. The method for predicting the consolidation bearing capacity of strip foundations in clay seabed according to claim 1, characterized in that: The target soil in the clay seabed is tested to obtain the target undrained shear strength distribution function of the target soil, which is specifically: Performing in-situ testing on a target soil body in a clay seabed to obtain a first undrained shear strength distribution function of the target soil body; According to the preset vertical load, the pore pressure response function of the target soil is obtained by a preset stress distribution calculation formula; wherein the vertical load is generated by the deadweight of the structure and the environmental load; and the pore pressure response function includes the pore pressure response corresponding to each coordinate position in all the target soils; According to the first undrained shear strength distribution function and the pore pressure response function, the second undrained shear strength distribution function of the target soil body is calculated through the relationship between the undrained shear strength and the vertical effective stress of the consolidated clay layer; wherein the vertical effective stress is calculated according to the pore pressure response function; and the second undrained shear strength distribution function is the target undrained shear strength distribution function.

3. The method for predicting the consolidation bearing capacity of strip foundations in clay seabed according to claim 2, characterized in that: According to the preset vertical load, the pore pressure response function of the target soil is obtained by using the preset stress distribution calculation formula, which is specifically: The vertical load is obtained based on the self-weight of the strip foundation, the self-weight of the superstructure and the environmental load; According to the vertical load, the pore pressure response function in the target soil under the strip uniformly distributed load is calculated by a preset stress distribution calculation formula, and the calculation formula is: Among them, Δu w is the pore pressure response function, V p is the vertical load, B is the foundation width, and the coordinates of any point in the soil are expressed as (x, z), where x is the horizontal distance from the calculation point to the left edge of the uniformly distributed load, and z is the vertical distance from the calculation point to the left edge of the load.

4. The method for predicting the consolidation bearing capacity of a strip foundation in a clay seabed according to claim 2, characterized in that: The second undrained shear strength distribution function of the target soil mass is calculated based on the first undrained shear strength distribution function and the pore pressure response function through the relationship between the undrained shear strength and the vertical effective stress of the consolidated clay layer, specifically: According to the pore pressure response function, a vertical effective stress function is calculated; The undrained shear strength function of the consolidated clay layer is calculated based on the relationship between the undrained shear strength of the consolidated clay layer and the vertical effective stress. The specific formula is: Among them, S u is the undrained shear strength of the consolidated clay layer, σ′ v is the vertical effective stress; is the effective internal friction angle, the ratio of K and λ is 0.2, And when the effective internal friction angle is determined, S i and σ v ′ is a constant R, and the specific formula is: The first undrained shear strength distribution function and the consolidated clay layer undrained shear strength function are subjected to a preset weighted calculation to obtain a second undrained shear strength distribution function of the target soil body.

5. The method for predicting the consolidation bearing capacity of a strip foundation in a clay seabed according to claim 4, characterized in that: The method of obtaining the consolidation bearing capacity of the strip foundation under preload is specifically as follows: based on the obtained second known point parameter set, the x-coordinate of each point on the slip line network, the z-coordinate of each point, the characteristic stress of each point, and the angle between the major principal stress direction of each point and the Z-axis, the consolidation bearing capacity of the strip foundation is obtained.

6. The method for predicting the consolidation bearing capacity of a strip foundation in a clay seabed according to claim 5, characterized in that: The finite difference equation is discretized and the parameters of the second known point are iteratively calculated through a numerical program.

7. The method for predicting the consolidation bearing capacity of strip foundations in a clay seabed according to claim 2, characterized in that: After obtaining the consolidation bearing capacity of the strip foundation after the preload, the method also includes: according to the consolidation bearing capacity of the strip foundation after the preload, readjusting the design parameters of the first strip foundation to obtain a new vertical load, and calculating the consolidation bearing capacity according to the new vertical load, so as to obtain the design parameters of the second strip foundation according to the recalculated consolidation bearing capacity; wherein the design parameters of the second strip foundation tend to stable values.

8. A device for predicting the consolidation bearing capacity of a strip foundation in a clay seabed, characterized in that: include: A first computing module, a second computing module, and a third computing module; The first calculation module is used to test the target soil in the clay seabed to obtain the target undrained shear strength distribution function of the target soil; wherein the target soil is specifically: the soil located below the strip foundation and the superstructure; and the target undrained shear strength distribution function is: calculated based on the first undrained shear strength distribution function and the pore pressure response function, combined with the relationship between the undrained shear strength and the vertical effective stress of the consolidated clay layer; The second calculation module is used to calculate the stress characteristic line equation of the soil after consolidation by using the sliding line method according to the target undrained shear strength distribution function; wherein, the stress characteristic line equation of the soil after consolidation is obtained by calculating the target undrained shear strength distribution function by using the sliding line method, specifically: according to the target undrained shear strength distribution function, the normal stress equation in the x direction, the normal stress equation in the z direction and the shear stress equation in the plane are obtained; the specific formula is: S u is the undrained shear strength of the consolidated clay layer, σ x and σ z are the normal stresses in the x and z directions, τ xz is the in-plane shear stress, γ is the total weight of the soil, σ is the characteristic stress, σ1 is the major principal stress, σ3 is the minor principal stress, and θ is the angle between the major principal stress and the Z axis; According to the normal stress equation in the x direction, the normal stress equation in the z direction and the shear stress equation in the plane, the preset equilibrium equation in the slip line method is substituted to obtain the stress characteristic line equation of the consolidated soil; wherein the stress characteristic line equation of the consolidated soil includes: the stress characteristic line equation of the α line and the stress characteristic line equation of the β line; the specific formula of the equilibrium equation is as follows: The obtained stress characteristic line equation formula is as follows: in, is the angle between the direction of the major principal stress and the direction of the characteristic line; the third calculation module, according to the stress characteristic line equation, is solved by a preset finite difference method to obtain the consolidation bearing capacity of the strip foundation under the action of preload; wherein, according to the form of the known point parameters and the undrained shear strength of the consolidated soil at the known point, the stress characteristic line equation of the consolidated soil is converted into a finite difference equation; wherein, the form of the known point parameters includes: x-coordinate, z-coordinate, characteristic stress, and the angle between the major principal stress direction and the Z-axis; wherein, the finite difference equation is specifically: Among them, S uA , S uB , S uc are the undrained shear strength of the consolidated soil at points A, B, and C, respectively, c The initial iteration value is θ A or θ B ; In each calculation of the second known point parameter, the second known point parameter obtained in the previous calculation is added to the first known point parameter set, and in the updated first known point parameter set, two point parameters that are not simultaneously substituted into the equation calculation are selected and substituted into the finite difference equation to calculate the second known point parameter; wherein the first known point parameter set already contains two known point parameters before the iteration starts; The parameters of the two known points are: point A (x A , z A , σ A ,θ A ) and point B (x B , z B , σ B ,θ B ), point A is a known point on line α, and point B is a known point on line β; Compare the second known point parameters obtained by each calculation with the second known point parameters obtained by the previous calculation. When the preset conditions are met, stop the iteration and obtain the second known point parameter set; when the preset conditions are not met, continue the iteration; wherein the preset conditions are specifically: |x c -x c old |≤Tol·B |z c -z c old |≤Tol·B |θ c -θ c old |≤Tol |s c -s c old |≤Tol·|σ c | Where Tol is the allowable error in calculation, which is set to 10 -10 .

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