A soft soil settlement prediction method considering nonlinear seepage

Abstract

The application discloses a soft soil settlement prediction method considering nonlinear penetration, and comprises the following steps: firstly, collecting soil samples of a target soft soil area to be predicted, and performing large-scale consolidation-permeation tests; measuring the permeability coefficient of the soil body under different consolidation stresses when the settlement is stable k and the void ratio e ; fitting a relationship model between the permeability coefficient k and the void ratio e and a relationship model between the permeability coefficient k and the consolidation stress; according to the relationship model between the permeability coefficient k and the void ratio e and the relationship model between the permeability coefficient k and the consolidation stress, a consolidation control model of the soil body under the influence of loads in a solid phase coordinate system is constructed, and a difference equation is determined; finally, the difference equation is used to solve and calculate the consolidation settlement of the soil body according to the load conditions of the target soft soil area to be predicted.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of soft soil settlement calculation, and particularly relates to a soft soil settlement prediction method considering nonlinear permeation. BACKGROUND

[0002] Soft soil usually exhibits high compressibility and low permeability, which makes its settlement behavior a key issue in engineering design and construction. Traditional soft soil settlement prediction methods are usually based on the linear permeation assumption, however, this assumption is often not accurate enough in actual engineering, especially in cases where the nonlinear characteristics of the soil are significant, the permeability of the soil changes with the stress state and void ratio of the soil, significantly affecting the settlement of the soil. There are currently several methods for calculating soft soil settlement: specification method, nonlinear consolidation settlement analytical solution method, and numerical simulation method. Among them, the specification method is simple to calculate and is more commonly used in engineering, but it cannot consider the nonlinear permeation characteristics of soft soil, and the calculated settlement has certain errors; while the nonlinear consolidation settlement analytical solution method or numerical simulation method can consider the nonlinear permeation characteristics of soft soil, but has the following shortcomings: ① the permeability coefficient is obtained from traditional indoor permeation test or consolidation-permeation combined instrument, as the soil sample is only 2cm thick, the influence of size effect on the permeability coefficient cannot be considered, especially the deep soft soil primary consolidation settlement is usually accompanied by creep, and the 2cm thick soil sample is difficult to reproduce the size effect and complexity in actual engineering; ② in actual engineering, soft soil settlement is usually affected by multi-stage loading, while traditional settlement prediction methods often assume single loading condition, making it difficult to accurately calculate the settlement behavior under multi-stage loading. Therefore, it is urgent to develop a new method to accurately and efficiently predict soft soil settlement. SUMMARY

[0003] The purpose of the present application is to solve the problems of the prior art, and to provide a soft soil settlement prediction method considering nonlinear permeation.

[0004] The present application is realized by the following technical solutions:

[0005] A soft soil settlement prediction method considering nonlinear permeation, comprising the following steps:

[0006] Step 1: For the target soft soil area to be predicted, collect its soil sample, perform large-scale consolidation-permeation test, measure the permeability coefficient of the soil under different consolidation stresses and the void ratio k of the soil at the time of settlement stabilization e data;

[0007] Step 2: According to the test data obtained in step 1, fit the relationship model between the permeability coefficient k and the void ratio e and the relationship model between the permeability coefficient k and the consolidation stress Relationship model;

[0008] Step 3: Based on the permeability coefficient obtained in Step 2 k and porosity e Relationship model and permeability coefficient k and consolidation stress The relationship model is used to construct a soil consolidation control model under load in a solid coordinate system.

[0009] Step 4: Determine the difference equations of the soil consolidation control model under load in the solid coordinate system obtained in Step 3;

[0010] Step 5: For the target soft soil area to be predicted, use the difference equation obtained in Step 4, and calculate the soil consolidation settlement according to the load conditions.

[0011] In the above technical solutions, the permeability coefficient k and porosity e The relationship model is as follows:

[0012] ;

[0013] In the formula, k —Permeability coefficient, unit: m / s; e —Porosity; A, B, and C are fitting parameters.

[0014] In the above technical solutions, the permeability coefficient k and consolidation stress The relationship model is as follows:

[0015] ;

[0016] In the formula, —Consolidation stress, unit: kPa; — Yield stress, unit: kPa; D, E, F, G and H are fitting parameters.

[0017] In the above technical solution, the soil sample height for the large-scale consolidation-permeability test is not less than 20cm; the stability standard for each load level is a deformation of less than 0.02mm per hour.

[0018] In the above technical solution, step 3 includes the following steps:

[0019] Step 3.1: Establish the consolidation governing equations for large deformation soil in the flowing coordinate system:

[0020] ;

[0021] In the formula, —Flowing coordinates, ,z For solid-state coordinates, t For time; —Effective stress, unit: kPa; —Specific density of water, unit: kN / m³ 3 ; —Specific gravity of soil;

[0022] Step 3.2: Based on the flow coordinates With solid coordinates z Based on the relationship, the consolidation control equations for large deformation soil in the solid coordinate system are obtained;

[0023] ;

[0024] Step 3.3: Based on the effective stress principle and the soil stress equilibrium conditions, establish the void ratio. e Equation of relationship with depth:

[0025] ;

[0026] Step 3.4: Based on the porosity from Step 3.3 e The equation relating the permeability coefficient to depth is used to obtain the permeability coefficient. k Equation relating to consolidation:

[0027] ;

[0028] Step 3.5: Calculate the permeability coefficient obtained in Step 2. k and porosity e Relationship model and permeability coefficient k and consolidation stress The relationship model between the porosity obtained in step 3.3 e The equation relating depth and the permeability coefficient obtained in step 3.4 k Substituting the equation relating to consolidation changes into the consolidation governing equations for large deformation soil in the solid coordinate system from step 3.2, we obtain the soil consolidation governing equations in the solid coordinate system:

[0029] ;

[0030] Loads during soil consolidation q For a time-varying uniformly distributed load, based on the effective stress principle, the soil consolidation control equations in the solid coordinate system are transformed to obtain a soil consolidation control model under load in the solid coordinate system:

[0031] ;

[0032] In the formula, u Indicates pore pressure;

[0033] ;

[0034] ;

[0035] .

[0036] In the above technical scheme, step 4 comprises the following steps:

[0037] Step 4.1: Dimensionless processing is performed on the soil consolidation control model affected by the load in the solid phase coordinate system obtained in step 3:

[0038] ;

[0039] In the formula, , wherein, u is the pore pressure, is the final value of the load, z is the depth of the soil, is the height of the soil, is the initial permeability coefficient, is the initial compression modulus;

[0040] ;

[0041] ;

[0042] ;

[0043] Step 4.2: Difference processing is performed on the model after the dimensionless processing in step 4.1 to obtain the difference equation thereof:

[0044] ;

[0045] In the formula, is the spatial step length; is the time step length; is the spatial node, , is the total number of spatial grids; is the time node.

[0046] In the above technical scheme, in step 5, the difference equation is solved by using the chasing method according to the solving condition to obtain the calculation formula of the soil settlement amount .

[0047] ;

[0048] In the formula, m represents the slope of the compression curve.

[0049] The advantages and beneficial effects of the present application are:

[0050] ①By adopting large-scale consolidation-permeability test soil samples (only 2 cm in traditional method) with a height of not less than 20 cm, the boundary effect interference caused by small-size samples is significantly reduced, and the change characteristics of the permeability coefficient of deep soft soil layer in the consolidation process and the creep effect of the consolidation process can be truly reflected; ②The dynamic correlation model of the permeability coefficient-pore ratio and the permeability coefficient-stress is simultaneously established, which breaks through the limitation of the traditional single permeability model; ③The consolidation control equation constructed by the difference equation can dynamically couple the application process of multi-stage load, accurately reflects the change of the soil permeation path and the drainage boundary condition caused by the staged loading in the actual engineering, and solves the settlement prediction lag problem caused by the single loading assumption of the traditional method. BRIEF DESCRIPTION OF DRAWINGS

[0051] Figure 1 is a step flow chart of the present application.

[0052] Figure 2 is e - k v Model fitting curve.

[0053] Figure 3 is σ - k v Model fitting curve.

[0054] Figure 4 is the calculation of the settlement and the test settlement time curve.

[0055] For those skilled in the art, other related drawings can be obtained according to the above drawings without creative labor. DETAILED DESCRIPTION

[0056] In order for those skilled in the art to better understand the present application, the technical solutions of the present application will be further described below in combination with specific embodiments.

[0057] A soft soil settlement prediction method considering nonlinear permeation, see attached Figure 1 , comprising the following steps:

[0058] Step 1: For the target soft soil area to be predicted, collect the soil sample thereof, and perform large-scale consolidation-permeability test to collect test data.

[0059] Through large-scale consolidation-permeability test, the permeability coefficient and the pore ratio k of the soil body at the time of settlement stabilization under the action of different consolidation stresses e are measured.

[0060] Step 2: Based on the experimental data obtained in Step 1, fit the permeability coefficient. k and porosity e Relationship model (i.e.) k - e (model) and permeability coefficient k and consolidation stress Relationship model (i.e.) k - σ Model).

[0061] k - e Model:

[0062] (1);

[0063] In the formula, k —Permeability coefficient, unit: m / s; e —Porosity; A, B, and C are fitting parameters.

[0064] Model:

[0065] (2);

[0066] In the formula, σ —Consolidation stress, unit: kPa; σ c — Yield stress, unit: kPa; D, E, F, G and H are fitting parameters.

[0067] It should be noted that the soil sample height for large-scale consolidation-permeability tests must be no less than 20 cm, so that... k - e Model and k - σ The model takes into account the influence of soil sample size on consolidation. The permeability coefficient varies during consolidation, meaning the consolidation process is a large-strain consolidation. The stability criterion for each load level is a deformation of less than 0.02 mm per hour.

[0068] Step 3: Based on the permeability coefficient obtained in Step 2 k and porosity e Relationship model and permeability coefficient k and consolidation stress σ Based on the relationship model, a soil consolidation control model under load is constructed in a solid coordinate system.

[0069] Step 3.1: Establish the consolidation control equations for large deformation soil in the flowing coordinate system.

[0070] The consolidation control equation for large deformation soil in the fluid coordinate system is given by equation (3):

[0071] (3);

[0072] wherein, flow coordinate, , z solid phase coordinate, t time; effective stress, unit: kPa; water bulk density, unit: kN / m 3 ; soil specific gravity;

[0073] Step 3.2: According to the relationship between the flow coordinate and the solid phase coordinate z , the consolidation control equation of the large deformation soil body under the solid phase coordinate system is obtained.

[0074] The relationship between the flow coordinate and the solid phase coordinate z is as follows:

[0075] (4);

[0076] By substituting equation (4) into equation (3), the consolidation control equation of the large deformation soil body under the solid phase coordinate system is obtained as follows:

[0077] (5);

[0078] Step 3.3: According to the effective stress principle and the force balance condition of the soil body, the equation of the relationship between the void ratio e and the depth is established.

[0079] According to the effective stress principle and the force balance condition of the soil body, it is known that:

[0080] (6);

[0081] According to equation (6) above, the equation of the relationship between the void ratio e and the depth is obtained as follows:

[0082] (7);

[0083] Step 3.4: According to the equation of the relationship between the void ratio e and the depth in step 3.3, the equation of the relationship between the permeability coefficient k and the soil body consolidation is obtained as follows:

[0084] (8);

[0085] Step 3.5: The permeability coefficient k and the void ratio ethe relationship model between the coefficient of permeability and the consolidation stress (i.e. k - e the relationship model between the coefficient of permeability and the consolidation stress (i.e. k - σ the relationship model between the coefficient of permeability and the consolidation stress (i.e. k - σ the relationship model between the coefficient of permeability and the consolidation stress (i.e. e the relationship model between the coefficient of permeability and the consolidation stress (i.e. k the relationship model between the coefficient of permeability and the consolidation stress (i.e.

[0086] (9);

[0087] When the load during the consolidation process of the soil body is a time-varying uniform load q , according to the effective stress principle, formula (9) is transformed to obtain the soil body consolidation control model under the influence of the load in the solid phase coordinate system:

[0088] (10);

[0089] In the formula, u represents the pore pressure;

[0090] (11);

[0091] (12);

[0092] (13);

[0093] Step 4: Determine the difference equation of the soil body consolidation control model under the influence of the load in the solid phase coordinate system obtained in step 3.

[0094] Step 4.1: Perform dimensionless processing on the soil body consolidation control model under the influence of the load in the solid phase coordinate system obtained in step 3 (i.e., formula 10):

[0095] (14);

[0096] In the formula, wherein, u is the pore pressure, is the final value of the load, z is the depth of the soil body, is the height of the soil body, is the initial coefficient of permeability,​ Ei is the initial compression modulus;

[0097] (15);

[0098] (16);

[0099] (17);

[0100] Step 4.2: Difference processing is performed on the model after the dimensionless processing of step 4.1 to obtain the difference equation thereof:

[0101] (18);

[0102] In the formula, is the spatial step length; is the time step length; is the spatial node, , is the total number of spatial grids; is the time node.

[0103] Step 5: For the target soft soil area to be predicted, the difference equation obtained in step 4 is adopted, and the consolidation settlement of the soil is solved and calculated according to the load condition.

[0104] The solving conditions are set as follows:

[0105] Initial condition: ;

[0106] Boundary condition: .

[0107] According to the solving conditions, the difference equation is solved by using the chasing method to obtain the calculation formula of the soil settlement .

[0108] ;

[0109] In the formula, m represents the compression curve slope, m which is obtained from the compression curve.

[0110] Verification example:

[0111] A remolded soil sample is prepared, and the density is 1.56 kg / cm 3The water content is 68.3%, the initial porosity ratio is 1.812, the specific gravity is 2.71, the sample size is 20cm*Φ25cm, the large-scale consolidation permeability test is carried out, the load levels are 6kPa, 21kpa, 36kPa, 67kPa, 83kpa, 98kPa, 128kPa and 160kPa, and the deformation is less than 0.02mm per hour.

[0112] According to the test results, the following is obtained: k - e The model fitting curve is as follows: Figure 2 , k - σ The model fitting curve is as follows: Figure 3 ;

[0113] k - e Model: ;

[0114] k - σ Model: .

[0115] The parameters of the model and the model are brought into formula (10), and the following is obtained: k - e The parameters of the model and the model are brought into formula (10), and the following is obtained: k - σ The parameters of the model and the model are brought into formula (10), and the following is obtained:

[0116] ;

[0117] In the formula:

[0118] ;

[0119] ;

[0120] ;

[0121] According to formulas (15), (16) and (17), the following is obtained:

[0122] ;

[0123] ;

[0124] ;

[0125] Finally, the difference equation is solved, and the soil consolidation settlement of 2487 hours is calculated as 75.71mm, the soil settlement obtained by the test is 73.63mm, and the calculation error is 1.4%. The time history curve of the calculated settlement and the test settlement is as follows: Figure 4 .

[0126] It should be noted that the above-mentioned embodiments illustrate rather than limit the application, and that those skilled in the art will be able to design many alternative embodiments without departing from the scope of the application. Accordingly, the legal scope of the application is defined only by the appended claims.

Claims

1. A method for predicting settlement of soft soil considering nonlinear permeability, characterized in that, Includes the following steps: Step 1: For the target soft soil area to be predicted, collect soil samples and conduct large-scale consolidation-permeability tests to measure the permeability coefficient k and void ratio e of the soil when the settlement is stable under different consolidation stresses σ. Step 2: Based on the experimental data obtained in Step 1, fit the relationship model between the permeability coefficient k and the void ratio e, and the relationship model between the permeability coefficient k and the consolidation stress σ. The relationship between the permeability coefficient k and the void ratio e is modeled as follows: In the formula, k is the permeability coefficient, in m / s; e is the void ratio; and A, B, and C are fitting parameters. The relationship model between the permeability coefficient k and the consolidation stress σ is as follows: In the formula, σ—consolidation stress, unit: kPa; σ c — Yield stress, unit: kPa; D, E, F, G and H are fitting parameters; Step 3: Based on the relationship models between the permeability coefficient k and the void ratio e, and the relationship model between the permeability coefficient k and the consolidation stress σ obtained in Step 2, construct a soil consolidation control model under load in a solid coordinate system; Step 3 includes the following steps: Step 3.1: Establish the consolidation governing equations for large deformation soil in the flowing coordinate system: In the formula, ξ—flow coordinate, ξ=f(z,t), z is the solid coordinate, t is time; σ′—effective stress, unit: kPa; γ w —Specific density of water, unit: kN / m³ 3 G s —Specific gravity of soil; Step 3.2: Based on the relationship between the flowing coordinate ξ and the solid coordinate z, the consolidation control equations for large deformation soil in the solid coordinate system are obtained; Step 3.3: Based on the effective stress principle and the soil stress equilibrium conditions, establish the equation relating void ratio e to depth: Step 3.4: Based on the equation relating porosity e to depth from Step 3.3, obtain the equation relating permeability coefficient k to consolidation: Step 3.5: Substitute the relationship models between permeability coefficient k and void ratio e, and between permeability coefficient k and consolidation stress σ obtained in Step 2, the equations relating void ratio e to depth obtained in Step 3.3, and the equations relating permeability coefficient k to consolidation obtained in Step 3.4, into the consolidation control equations for large deformation soil in the solid coordinate system obtained in Step 3.2, to obtain the soil consolidation control equations in the solid coordinate system: When the load q on the soil during the consolidation process is a uniformly distributed load that varies with time, according to the effective stress principle, the soil consolidation control equations in the solid coordinate system described above can be transformed to obtain the soil consolidation control model under load in the solid coordinate system: In the formula, u represents the pore pressure; Step 4: Determine the difference equations of the soil consolidation control model under load in the solid coordinate system obtained in Step 3; Step 5: For the target soft soil area to be predicted, use the difference equation obtained in Step 4, and calculate the soil consolidation settlement according to the load conditions.

2. The method for predicting soft soil settlement considering nonlinear permeability according to claim 1, characterized in that: For large-scale consolidation-permeability tests, the soil sample height should be no less than 20 cm; the stability standard for each load level is a deformation of less than 0.02 mm per hour.

3. The method for predicting soft soil settlement considering nonlinear permeability according to claim 1, characterized in that: Step 4 includes the following steps: Step 4.1: Perform dimensionless processing on the soil consolidation control model under load in the solid coordinate system obtained in Step 3: In the formula, Where u is the pore pressure, q u denoted as the final load value, z as the soil depth, h as the soil height, k0 as the initial permeability coefficient, and E0 as the initial compression modulus. Step 4.2: Perform finite difference processing on the model after dimensionless processing in Step 4.1 to obtain its difference equation: In the formula, ΔZ is the spatial step size; ΔT v is the time step; i is the spatial node, i = 1, 2, 3, ..., n, where n is the total number of spatial grids; j is the time node.

4. The method for predicting soft soil settlement considering nonlinear permeability according to claim 3, characterized in that: In step 5, based on the solution conditions, the difference equation is solved using the chasing method, and the calculation formula for soil settlement s(t) is obtained as follows: In the formula, m represents the slope of the compression curve.

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