Earthwork standard room reinforced fine-grained soil model and three-dimensional numerical calculation development method thereof

Abstract

The invention provides an earthwork standard room reinforced fine-grained soil model and a three-dimensional numerical calculation development method thereof. The method comprises the steps that filler parameters and earthwork standard room parameters are determined; calculating the equivalent tangent modulus and the equivalent Poisson's ratio of the geocell filler complex according to the filler parameters and the geocell parameters; according to the equivalent tangent modulus and the equivalent Poisson's ratio, the tentative stress and the yield stress of the geocell filler complex are calculated; judging whether the yield stress meets a yield function; if yield occurs, a stress result is output; and if not, calculating a Jacobian stiffness matrix, and continuing to update and calculate the stress. According to the method, required calculation parameters are simple and can be determined only by adopting a conventional triaxial compression test of the filler; the method solves the problem that the failure axial strain of the reinforced soil of the geocell cannot be determined in the prior art, and meanwhile, the strength nonlinear mechanical property that the strength parameter of the filler changes along with the confining pressure is considered.

Description

Technical Field

[0001] The invention belongs to the field of civil engineering, and in particular relates to a geocell reinforced fine-grained soil model and a three-dimensional numerical calculation development method thereof. Background Art

[0002] Due to its good mechanical properties, significant economic and ecological value, geocell reinforced structure has been widely used in the construction of transportation infrastructure such as highways, railways, water transport and airports, especially in the field of reinforced slopes, reinforced earth retaining walls and reinforced foundations. Geocell is a three-dimensional mesh structure material formed by ultrasonic welding, riveting or plugging of wide strips of high molecular polymer (such as high-density polyethylene, polypropylene or polyester). It is usually folded during transportation and opened and filled with soil or concrete during use. Geocell increases the cohesive strength of the soil through the mutual friction between the strips and the fill and provides a strong lateral constraint force to the filler, thereby improving the strength and stability of the soil. Due to its excellent reinforcement effect, geocell has been widely used in the construction of reinforced foundations, reinforced slopes and reinforced retaining walls. However, there is still no mature design method and design specification for geocell reinforced soil structure. Theoretical research lags behind engineering practice, which restricts the design calculation of geocell reinforced soil structure and its application in engineering practice. Summary of the invention

[0003] The purpose of the present invention is to provide a geocell reinforced fine-grained soil model and a three-dimensional numerical calculation development method thereof.

[0004] The technical solution of the present invention is as follows:

[0005] A geocell reinforced fine-grained soil model and a three-dimensional numerical calculation development method thereof, comprising:

[0006] Determine fill parameters and geocell parameters;

[0007] The equivalent tangent modulus E of the geocell filler composite is calculated based on the filler parameters and geocell parameters. tc and the equivalent Poisson's ratio v tc ;

[0008] According to the equivalent tangent modulus E tc and the equivalent Poisson's ratio v tc Calculate the test stress and yield stress of geocell fill composites;

[0009] According to whether the yield stress satisfies the yield function; if yield occurs, the stress result is output; if not, the Jacobian stiffness matrix is ​​calculated and the calculated stress is continued to be updated.

[0010] Furthermore, the method for determining the filler parameters is:

[0011] The parameters in the hyperbolic model tangent modulus expression are determined by conventional triaxial compression tests of fillers under at least three different confining pressures: elastic modulus base k, elastic modulus index n, and failure ratio R. f , cohesion c and internal friction angle And the parameters in the bulk modulus expression: volume modulus K b and volume modulus index m.

[0012] Furthermore, the method for determining the geocell parameters is:

[0013] The stress-strain relationship of geocell strips was determined by tensile test, and the tangent modulus M at different strain levels was fitted by high-order polynomials. t The initial equivalent circle diameter D0 is obtained by calculating the equivalent area according to the size of the geocell grid.

[0014] Furthermore, the equivalent tangent modulus E tc The calculation formula is:

[0015]

[0016] In the formula, E t is the tangent modulus of the soil; v t is the tangent Poisson's ratio of the soil; M t is the tangent modulus of the geocell strip; A is the equivalent model parameter; D ε It is the deformed diameter of the geocell grid corresponding to the axial strain ε1 of the specimen.

[0017] Furthermore, the equivalent Poisson's ratio v tc The calculation formula is:

[0018]

[0019] In the formula, v t is the tangent Poisson's ratio of the soil; M t is the tangent modulus of the geocell strip; A is the equivalent model parameter; D ε It is the deformed diameter of the geocell grid corresponding to the axial strain ε1 of the specimen.

[0020] Furthermore, the yield function is expressed as:

[0021]

[0022] In the formula, σ c is the initial confining pressure applied, is the internal friction angle of the soil, c c Determined by the following formula:

[0023] c c =c+c r

[0024] Where c is the cohesion of the soil, c r is the apparent cohesion generated by the confining pressure of the geocell,

[0025] Its expression is:

[0026]

[0027] In the formula, σ g The additional confining pressure is caused by the restraint of the geocell on the soil; is the internal friction angle of the soil.

[0028] Furthermore, the method is performed by the UMAT subroutine in ABAQUS software.

[0029] Compared with the prior art, the present invention has the following advantages:

[0030] Compared with the prior art, the calculation parameters required by the present invention are simple and can be determined by only using the conventional triaxial compression test of the filler; the present invention overcomes the major problem that the prior art cannot determine the axial strain of the failure of geocell reinforced soil, while taking into account the nonlinear mechanical properties of the filler's strength parameters changing with the confining pressure; the theoretical model determination formula proposed by the present invention is derived based on the nonlinear elastic theory, without empirical parameters and empirical components; in addition, the present invention also uses the UMAT subroutine of the ABAQUS software to expand the finite element model calculation based on the proposed theoretical model of geocell reinforced fine-grained soil, which can be used to directly calculate engineering structures, and has the advantages of high calculation efficiency and good reliability; at the same time, the geocell reinforced fine-grained soil model proposed by the present invention has a wide range of applications, and is applicable to a variety of fine-grained materials and a variety of types of geocells. The present invention provides a theoretical basis for the design of geocell reinforced foundations, reinforced slopes and reinforced retaining walls in engineering practice, and provides a new way for engineering numerical simulation calculations. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The accompanying drawings generally illustrate various embodiments by way of example and not limitation, and together with the description and claims, serve to illustrate the embodiments of the invention. Where appropriate, the same reference numerals are used throughout the drawings to refer to the same or similar parts. Such embodiments are illustrative and are not intended to be exhaustive or exclusive embodiments of the present apparatus or method.

[0032] Figure 1 A schematic diagram of additional confining pressure of geocell reinforcement of the present invention is shown;

[0033] Figure 2A schematic diagram of a specific implementation process of the technical solution of the present invention is shown;

[0034] Figure 3 The stress-strain response diagrams of silty clays of different densities of the present invention are shown;

[0035] Figure 4 The tensile force-strain relationship diagram of the geocell strip of the present invention is shown;

[0036] Figure 5 A schematic diagram of experimental verification of the technical solution of the present invention is shown;

[0037] Figure 6 A schematic diagram of a model test device of the present invention is shown;

[0038] Figure 7 A schematic diagram comparing the model calculation and experimental measurement of the present invention is shown. DETAILED DESCRIPTION

[0039] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0040] The embodiment of the present invention provides a geocell reinforced fine-grained soil model and a three-dimensional numerical calculation development method thereof, including:

[0041] (1) The parameters k, n, and R in the tangent modulus expression of the hyperbolic model are determined by conventional triaxial compression tests of the filler under at least three different confining pressures. f , c and And the parameter K in the bulk modulus expression b , m, the stress-strain relationship of the geocell strip is determined by tensile test, and the tangent modulus M at different strain levels is fitted by high-order polynomials t The initial equivalent circle diameter D0 is obtained by calculating the equivalent area according to the size of the geocell grid.

[0042] (2) Tangent modulus E of EB model filler using Duncan-Chang model t and Poisson's ratio v t :

[0043]

[0044] (4.1) is based on the packing k, n, R f , c and Determine the tangent modulus E t , the parameter B in formula (4.2) is determined by formula (4.3), and formula (4.3) is the parameter K of the filler b , m confirmed.

[0045] (3) When the geocell reinforced soil structure is subjected to axial stress σ1, the soil inside it will generate an extrusion hoop stress σ'3 toward the inner wall of the geocell in order to reach a new equilibrium state. At the same time, the geocell uses its own structural strength to apply an additional hoop confining pressure σ to the soil. g The reinforcement mechanism is as follows: Figure 3 According to the thin-walled cylinder tension theory, the additional confining pressure σ is determined g :

[0046]

[0047] The cell circumferential strain ε corresponding to the current step axial strain ε1 c It can be determined by the following formula:

[0048]

[0049] The cell diameter corresponding to the current step axial strain ε1 can be determined by the following formula:

[0050]

[0051] Corresponding to the circumferential strain ε c Cell tangent modulus M t Calculated by the following formula:

[0052]

[0053] Where A, B and C are determined by the stress-strain relationship curve obtained from the tensile test of the geocell strip, and M ref is the reference modulus, equal to 1kN / m.

[0054] (4) Under the triaxial stress state, the relationship between the horizontal strain increment and the stress increment can be obtained from the generalized Hooke's law:

[0055]

[0056] After geocell reinforcement, the constraint of geocell in the horizontal direction will generate additional confining pressure dσ g , therefore, the horizontal stress increment after geocell reinforcement is

[0057] dσ3=dσ c +dσ g (4.9)

[0058] (4.9) c is the initial confining pressure increment applied in the test, dσ g Expand (4.4) into incremental form:

[0059]

[0060] Assuming that the deformation of the specimen in the circumferential direction is uniform, then dε in equation (4.10) is c It can be approximately expressed as:

[0061] dε c =-dε3 (4.11)

[0062] Combining equations (4.8), (4.9) and (4.10), we can obtain the relationship between the horizontal strain increment and the stress increment of the generalized Hooke's law after geocell reinforcement:

[0063]

[0064] (4.11) where the parameters

[0065] By substituting equations (4.11) and (4.9) into equation (4.10), we can obtain the additional confining pressure dσ g for

[0066]

[0067] (5) Under triaxial stress conditions, by solving the inverse expression of equation (4.8), the expression of the axial stress increment can be obtained:

[0068] dσ1=E t dε1+2v t dσ3 (4.14)

[0069] Combining equations (4.9), (4.13) and (4.14), we can obtain the expression of the axial stress increment of the geocell reinforced soil composite:

[0070] dσ1=E tc dε1+2v tc dσ c (4.15)

[0071] The equivalent tangent modulus E of the geocell reinforced soil composite in (4.15) tc and the equivalent Poisson's ratio v tc By solving equations (4.9), (4.13) and (4.14), we get the expression that is the focus of this invention. The specific expression is as follows:

[0072] The equivalent tangent modulus E given by the present invention is tc The parameter calculation formula is as follows:

[0073]

[0074] The equivalent Poisson's ratio v given by the present invention is tc The calculation formula is as follows:

[0075]

[0076] (6) The Mohr-Coulomb yield function is used as the model failure criterion. Due to the additional restraint confining pressure of geocell reinforcement, the Mohr-Coulomb yield function needs to be corrected. The expression of the corrected Mohr-Coulomb yield function given by the present invention is:

[0077]

[0078] In the formula, σ c is the initial confining pressure applied, c c Determined by the following formula:

[0079] c c =c+c r (4.19)

[0080] Among them, c r is the apparent cohesion generated by the confining pressure of the geocell, and its expression is:

[0081]

[0082] (7) The geocell reinforced fine-grained soil model was redeveloped using the UMAT subroutine of ABAQUS software. During the development process, two key tasks need to be completed: First, the tangent stiffness matrix of the reinforced soil constitutive model, namely the Jacobian matrix, is derived. As shown in the following formula, it is used to continuously update the stress state.

[0083]

[0084] Secondly, the strain increment and Jacobian matrix in the UMAT subroutine are called by the ABAQUS main program to calculate the stress increment, update the stress, and then return it to the main program. The UMAT subroutine is called continuously to update the stress through the Newton-Raphson iteration method until the yield function is satisfied, and the entire calculation process is output. The algorithm flow chart of the UMAT subroutine for a specific model is shown in the figure below. Figure 4 shown.

[0085] When writing the UMAT subroutine for the geocell reinforced fine-grained soil model, the program header and tail follow the fixed format of the ABAQUS software, and the core task is to use the Fortran language to write the core calculation program part based on the geocell reinforced fine-grained soil model. A modular programming strategy is adopted to split the complex calculation program part into five independent subroutines. During the calculation, these five subroutines are called through the main program of the UMAT subroutine. The writing of the specific model UMAT subroutine has the following aspects:

[0086] (a) Declare model material parameters and state variables: Model material parameter numbers PROPS(1) to PROPS(7) correspond to filler parameters K, n, and R respectively. f ,c,φ,K b , m, material parameter number PROPS(8) refers specifically to the original diameter D0 of the geocell, and material parameter numbers PROPS(9) to PROPS(11) are used to define the tangent modulus M of the geocell. t The coefficients A, B and C.

[0087] (b) Declare state variables: State variable numbers STATEV(1) to STATEV(3) represent the historical maximum deviation stress, consolidation stress and stress level, respectively.

[0088] (c) Write three principal stress subroutines: Get the three principal stresses in the model calculation by calling the built-in function SPRINC (STRESS, PS, LSTR, NDI, NSHR) of ABAQUS software. It is worth noting that in ABAQUS software, stress is positive in tension, which is opposite to the sign specified in soil mechanics. Here, the three principal stresses need to be adjusted to opposite signs.

[0089] (d) Write a subroutine for the three principal strains: Obtain the three principal strains in the model calculation by calling the built-in function SPRINC (STRAN, PS2, LSTR, NDI, NSHR) of the ABAQUS software. Similarly, the three principal strains are adjusted to opposite signs.

[0090] (e) Write the modulus corresponding to the stress state: According to equations (4.1)-(4.17), write the equivalent tangent modulus E of the excavated cell reinforced fine-grained soil model tc and the equivalent Poisson's ratio v tc Calculation program. At the same time, according to formula (4.18)-(4.20), the equivalent strength c r The modified Mohr-Coulomb yield function is used to determine whether the UMAT subroutine of the model should continue to calculate.

[0091] (f) Write the Jacobian stiffness matrix subroutine: First, initialize a 6×6 order zero matrix as the framework of the Jacobian stiffness matrix, and then assign the corresponding calculation formula to each element of the Jacobian stiffness matrix according to (7).

[0092] (g) Write a stress update subroutine, based on the Jacobian stiffness matrix and strain increment, using the incremental stress-strain relationship ({dσ}=[D tc ]{dε}) calculates the stress increment, and then adds the calculated stress increment to the total stress value obtained in the previous iteration to update the total stress of the current iteration step.

[0093] The technical solution provided by the present invention has been calibrated by a small triaxial test of geocell reinforced soil. Two fillers with different relative densities were used in the test, and the geocell was made of PE material. The stress-strain response of fillers with different relative densities measured by conventional triaxial compression tests is shown in Figure 2. Figure 3 The stress-strain relationship of the geocell measured by the tensile test is shown in Figure 4 The comparison between the finite element calculation results of the model and the measured results of the triaxial test is shown in Figure 5 As shown. Figure 5 It can be seen that the stress-strain response predicted by the finite element method of the model is basically consistent with the measured results, which verifies the correctness and effectiveness of the technical solution. In order to further evaluate the performance of the reinforced soil constitutive model in actual engineering, the model test of Yang et al. was verified. The model box size of their model test was designed to be 800mm×800mm×600mm. The load was applied by adjusting the air pressure in the cylinder. The loading plate was a circular steel plate with a radius of 75mm. Kansas river sand was used as the test filler in the model box. The sand was filled and compacted in three layers (each layer was 50mm, 50mm and 20mm thick) to ensure that the relative density of each layer after compaction reached 70%, and the total filling thickness was 120mm. The entire experiment included two groups of controls: one group was a model test without reinforcement, and the other group buried a quasi-elliptical geocell with a height of 100mm in the center of the bottom of the model box (the long axis was about 240mm and the short axis was about 200mm). The test device is as follows: Figure 6 shown. Figure 7 The load-settlement curve of the geocell reinforced soil foundation model obtained by finite element calculation is compared with the load-settlement curve measured by the test. Figure 7 It can be seen that the two are very close, which verifies the correctness of the technical solution of the present invention.

[0094] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A geocell reinforced fine-grained soil model and a three-dimensional numerical calculation development method thereof, characterized in that: include: Determine fill parameters and geocell parameters; The equivalent tangent modulus E of the geocell filler composite is calculated based on the filler parameters and geocell parameters. tc and the equivalent Poisson's ratio v tc ; According to the equivalent tangent modulus E tc and the equivalent Poisson's ratio v tc Calculate the test stress and yield stress of geocell fill composites; According to whether the yield stress satisfies the yield function; if yield occurs, output the stress result; If there is no yield, the Jacobian stiffness matrix is ​​calculated and the calculated stress is continued to be updated.

2. The geocell reinforced fine-grained soil model and three-dimensional numerical calculation development method thereof according to claim 1 is characterized in that: The method for determining the filler parameters is: The parameters in the hyperbolic model tangent modulus expression are determined by conventional triaxial compression tests of fillers under at least three different confining pressures: elastic modulus base k, elastic modulus index n, and failure ratio R. f , cohesion c and internal friction angle And the parameters in the bulk modulus expression: volume modulus K b and volume modulus index m.

3. The geocell reinforced fine-grained soil model and three-dimensional numerical calculation development method thereof according to claim 1 is characterized in that: The method for determining the geocell parameters is: The stress-strain relationship of geocell strips was determined by tensile test, and the tangent modulus M at different strain levels was fitted by high-order polynomials. t The initial equivalent circle diameter D0 is obtained by calculating the equivalent area according to the size of the geocell grid.

4. The geocell reinforced fine-grained soil model and three-dimensional numerical calculation development method thereof according to claim 1 is characterized in that: The equivalent tangent modulus E tc The calculation formula is: In the formula, E t is the tangent modulus of the soil; v t is the tangent Poisson's ratio of the soil; M t is the tangent modulus of the geocell strip; A is the equivalent model parameter; D ε It is the deformed diameter of the geocell grid corresponding to the axial strain ε1 of the specimen.

5. The geocell reinforced fine-grained soil model and three-dimensional numerical calculation development method thereof according to claim 1 is characterized in that: The equivalent Poisson's ratio v tc The calculation formula is: In the formula, v t is the tangent Poisson's ratio of the soil; M t is the tangent modulus of the geocell strip; A is the equivalent model parameter; D ε It is the deformed diameter of the geocell grid corresponding to the axial strain ε1 of the specimen.

6. The geocell reinforced fine-grained soil model and three-dimensional numerical calculation development method thereof according to claim 1 is characterized in that: The yield function expression is: In the formula, σ c is the initial confining pressure applied, is the internal friction angle of the soil, c c Determined by the following formula: C c =c+c r Where c is the cohesion of the soil, c r is the apparent cohesion generated by the confining pressure of the geocell, and its expression is: In the formula, σ g The additional confining pressure is caused by the restraint effect of the geocell on the soil; is the internal friction angle of the soil.

7. The geocell reinforced fine-grained soil model and three-dimensional numerical calculation development method thereof according to claim 1 is characterized in that: The method is carried out by the UMAT subroutine in ABAQUS software.

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