CN105718735B - Soil plasticity accumulation model under high cycle cyclic load - Google Patents

Soil plasticity accumulation model under high cycle cyclic load Download PDF

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CN105718735B
CN105718735B CN201610040825.5A CN201610040825A CN105718735B CN 105718735 B CN105718735 B CN 105718735B CN 201610040825 A CN201610040825 A CN 201610040825A CN 105718735 B CN105718735 B CN 105718735B
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付饶
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China Construction Eighth Engineering Division Co Ltd
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Abstract

The soil body plastic accumulation model under the high cycle cyclic load is applied to describe the change rule of the plastic strain increment under the cyclic load effect, and the plastic body strain is used as a hardening parameter to describe the magnitude of plastic strain accumulation. The method is characterized in that: firstly, carrying out total strain decomposition, secondly, determining elastic strain, determining an overstress function, then determining the direction of accumulated plastic strain in the cyclic load action process, and finally, determining accumulated plastic strain. The effect is as follows: the precision of the plastic accumulation behavior is improved by more than 0.3 percent.

Description

Soil plasticity accumulation model under high cycle cyclic load
Technical Field
The invention relates to the technical field of geotechnical engineering, in particular to a soil plasticity accumulation model under high cycle cyclic load. The method is used for simulating the plastic strain accumulation behavior of the soil body.
Background
Obvious plastic deformation accumulation exists in the soil body under the action of millions of cyclic loads. How to build reasonable physical models to calculate and predict plastic deformation accumulation is of increasing interest to those skilled in the art of geotechnical engineering. Although the boundary constitutive model breaks through the limit of the traditional elastoplasticity theory to describe and predict the dynamic behavior of the soil body under the cyclic load, the boundary constitutive model is actually influenced by the cycle times; the compaction model is used for describing long-term accumulation behaviors in the high-cycle cyclic load action process, the expression of the double hardening function of the compaction model is obtained by test fitting, and the compaction model has no clear physical significance and is difficult to accurately determine; the magnitude of the strain amplitude must be updated by combining the cyclic compaction model adopting the tensor mode with the hysteresis model, and the model is difficult to be independently used under the existing finite element framework, so that the application of the model is limited.
Disclosure of Invention
The purpose of the invention is as follows: based on the view of critical state soil mechanics, the change rule of plastic strain increment under the action of cyclic load is described by using an overstress function, and the accumulated size of plastic strain is described by using the strain of a plastic body as a hardening parameter, so that the aim of improving the precision of plastic accumulated behavior is fulfilled.
The technical scheme adopted by the invention for solving the technical problem is as follows:
step 1: total strain decomposition
During high cycle cyclic loading, plastic strain will accumulate continuouslyTotal dependent variable εijDecomposed into recoverable elastic strain
Figure BSA0000126194640000011
And non-recoverable accumulated plastic strain
Figure BSA0000126194640000012
。
Figure BSA0000126194640000021
(1) In the formula: epsilonijTotal dependent variables, dimensionless variables;
Figure BSA0000126194640000022
recoverable elastic strain, dimensionless;
Figure BSA0000126194640000023
unrecoverable accumulated plastic strain, dimensionless; sijBias stress tensor, dimensionless quantity; n, the number of times of cyclic loading is counted;
step 2: determining elastic strain
Figure BSA0000126194640000024
(2) In the formula:
Figure BSA0000126194640000025
recoverable elastic strain, dimensionless; n, model parameters; n, the number of times of cyclic loading is counted; krefReference bulk modulus; p is a radical ofrefReference to hydrostatic pressure, usually taken at standard atmospheric pressure, pref＝100kPa；σijEffective Cauchy stress tensor in the soil mass, dimensionless; g, shear modulus, dimensionless; sijBias stress tensor, dimensionless quantity; e.g. of the typeijThe polarization strain tensor, dimensionless quantity;
and step 3: determining an overstress function
Figure BSA0000126194640000026
Figure BSA00001261946400000210
(3) And (4) in the formula:
Figure BSA0000126194640000029
an overstress function; p is a radical ofaHydrostatic pressure amplitude, MPa; q. q.saBias stress amplitude, dimensionless quantity; m, critical state stress rate;
Figure BSA0000126194640000027
plastomer strain accumulation, dimensionless; p is a radical ofsStability stress level, dimensionless, related to plastomer strain accumulation; etaaAverage bias stress level, dimensionless; e is an irrational number equal to about 2.718281828; α, β, the overstress function parameter;
and 4, step 4: determining the direction of plastic strain accumulation during cyclic loading
Figure BSA0000126194640000028
(5) In the formula: m isijDirection of plastic strain accumulation during cyclic loading; p is a radical ofavThe average hydrostatic pressure, MPa,
Figure BSA0000126194640000031
qabias stress amplitude, dimensionless quantity; m, critical state stress rate; deltaijKronecker notation, i ═ j, δij1 is ═ 1; when i is not equal to j, deltaij＝0；
Figure BSA0000126194640000032
Mean bias stress tensor, dimensionless quantity;
Figure BSA0000126194640000033
mean partial strain tensor, dimensionless quantity; e is an irrational number equal to about 2.718281828;
and 5: determination of cumulative plastic strain
Figure BSA0000126194640000034
(6) In the formula:
Figure BSA0000126194640000035
unrecoverable accumulated plastic strain, dimensionless; n, the number of times of cyclic loading is counted;<>represents Macauley brackets; is defined as:
Figure BSA0000126194640000036
substituting the expressions (3) and (5) into the expression (6) to obtain:
Figure BSA0000126194640000037
(1) the variables in the formulas (1) to (7) are implicitly related, and the Newton-Raphson iterative method is adopted for solving, and the iterative solving method is well known technical content in the same line and is not detailed here.
(1) The parameters in the formulae (1) to (7) can be determined by measuring the average hydrostatic pressure pavAnd average bias stress level ηaThe results of the drainage circulation triaxial test are verified, and the verification method is the same well-known technical content and is not detailed here.
The invention has the beneficial effects that: the change rule of the plastic strain increment under the action of cyclic load is described by using an overstress function, the plastic strain is used as a hardening parameter to describe the accumulated size of the plastic strain, and the precision of the plastic accumulated behavior is improved by more than 0.3 percent.
DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION
The soil body plastic accumulation model is explained by the railway track subgrade under the action of high cycle load.
Step 1: total strain decomposition
During the high cycle cyclic load action, the plastic strain will be accumulated continuously, and the total strain amount epsilonijDecomposed into recoverable elastic strain
Figure BSA0000126194640000041
And non-recoverable accumulated plastic strain
Figure BSA0000126194640000042
。
Figure BSA0000126194640000043
(1) In the formula: epsilonijTotal dependent variables, dimensionless variables;
Figure BSA0000126194640000044
recoverable elastic strain, dimensionless;
Figure BSA0000126194640000045
unrecoverable accumulated plastic strain, dimensionless; sijBias stress tensor, dimensionless quantity; n, the number of times of cyclic loading is counted;
step 2: determining elastic strain
Figure BSA0000126194640000046
(2) In the formula:
Figure BSA0000126194640000047
recoverable elastic strain, dimensionless; n, model parameters; n, the number of times of cyclic loading is counted; krefReference bulk modulus; p is a radical ofrefReference to hydrostatic pressure, usually taken at standard atmospheric pressure, pref＝100kPa；σijEffective Cauchy stress tensor in the soil mass, dimensionless; g, shear modulus, dimensionless; sijBias stress tensor, dimensionless quantity; e.g. of the typeijThe magnitude of the bias strain tensor,dimensionless quantities;
and step 3: determining an overstress function
Figure BSA0000126194640000048
Figure BSA00001261946400000411
(3) And (4) in the formula:
Figure BSA00001261946400000410
an overstress function; p is a radical ofaHydrostatic pressure amplitude, MPa; q. q.saBias stress amplitude, dimensionless quantity; m, critical state stress rate;
Figure BSA0000126194640000049
plastomer strain accumulation, dimensionless; p is a radical ofsStability stress level, dimensionless, related to plastomer strain accumulation; etaaAverage bias stress level, dimensionless; e is an irrational number equal to about 2.718281828; α, β, the overstress function parameter;
and 4, step 4: determining the direction of plastic strain accumulation during cyclic loading
Figure BSA0000126194640000051
(5) In the formula: m isijDirection of plastic strain accumulation during cyclic loading; p is a radical ofavThe average hydrostatic pressure, MPa,
Figure BSA0000126194640000052
qabias stress amplitude, dimensionless quantity; m, critical state stress rate; deltaijKronecker notation, i ═ j, δij1 is ═ 1; when i is not equal to j, deltaij＝0；
Figure BSA0000126194640000053
Mean bias stress tensor, dimensionless quantity;
Figure BSA0000126194640000054
mean partial strain tensor, dimensionless quantity; e is an irrational number equal to about 2.718281828;
and 5: determination of cumulative plastic strain
Figure BSA0000126194640000055
(6) In the formula:
Figure BSA0000126194640000056
unrecoverable accumulated plastic strain, dimensionless; n, the number of times of cyclic loading is counted;<>represents Macauley brackets; is defined as:
Figure BSA0000126194640000057
substituting the expressions (3) and (5) into the expression (6) to obtain:
Figure BSA0000126194640000058
(1) the variables in the formulas (1) to (7) are implicitly related, and the Newton-Raphson iterative method is adopted for solving, and the iterative solving method is well known technical content in the same line and is not detailed here.
(1) The parameters in the formulae (1) to (7) can be determined by measuring the average hydrostatic pressure pavAnd average bias stress level ηaThe results of the drainage circulation triaxial test are verified, and the verification method is the same well-known technical content and is not detailed here.
The application effect is as follows: the change rule of the plastic strain increment under the action of cyclic load is described by using an overstress function, the plastic strain is used as a hardening parameter to describe the accumulated size of the plastic strain, and the precision of the plastic accumulated behavior is improved by 0.32 percent.
The above description is only for facilitating the understanding of the technical solutions of the present invention by those skilled in the art, and is not intended to limit the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (3)

1. The soil plasticity accumulation model under the high cycle cyclic load is characterized in that: the adopted technical scheme is as follows:
step 1: total strain decomposition
Total amount of strain εijDecomposed into recoverable elastic strain
Figure FDA0003044234180000011
And non-recoverable accumulated plastic strain
Figure FDA0003044234180000012
Figure FDA0003044234180000013
(1) In the formula: epsilonijTotal dependent variables, dimensionless variables;
Figure FDA0003044234180000014
recoverable elastic strain, dimensionless;
Figure FDA0003044234180000015
non-recoverable accumulated plastic strain, dimensionless; sijBias stress tensor, dimensionless quantity; n, the number of times of cyclic loading is counted;
step 2: determining elastic strain
Figure FDA0003044234180000016
(2) In the formula:
Figure FDA0003044234180000017
recoverable elastic strain, dimensionless; n, model parameters; n, the number of times of cyclic loading is counted; krefReference bulk modulus; p is a radical ofrefReference hydrostatic pressure, taking the standard atmospheric pressure, pref ＝ 100kPa ；σ ij Effective Cauchy stress tensor in the soil mass, dimensionless; g, shear modulus, dimensionless; sijBias stress tensor, dimensionless quantity; e.g. of the typeijThe polarization strain tensor, dimensionless quantity;
and step 3: determining an overstress function
Figure FDA0003044234180000018
Figure FDA0003044234180000019
(3) And (4) in the formula:
Figure FDA00030442341800000121
an overstress function; p is a radical ofaHydrostatic pressure amplitude, MPa; q. q.saBias stress amplitude, dimensionless quantity; m, critical state stress rate;
Figure FDA00030442341800000111
plastomer strain accumulation, dimensionless; p is a radical ofsStability stress level, dimensionless, related to plastomer strain accumulation; etaaAverage bias stress level, dimensionless; e is an irrational number, 2.718281828; α, β, the overstress function parameter;
and 4, step 4: determining the direction of plastic strain accumulation during cyclic loading
Figure FDA00030442341800000112
(5) In the formula: m isijDirection of plastic strain accumulation during cyclic loading; p is a radical ofavThe average hydrostatic pressure, MPa,
Figure DEST_PATH_FSA0000126194630000023
qabias stress amplitude, dimensionless quantity; m, critical state stress rate; deltaijKronecker notation, i ═ j, δij1 is ═ 1; when i is not equal to j, deltaij＝0；
Figure FDA00030442341800000114
Mean bias stress tensor, dimensionless;
Figure FDA00030442341800000115
mean partial strain tensor, dimensionless; e is an irrational number, 2.718281828;
and 5: determination of cumulative plastic strain
Figure FDA00030442341800000116
(6) In the formula:
Figure FDA00030442341800000117
non-recoverable accumulated plastic strain, dimensionless; n, the number of times of cyclic loading is counted;<>represents Macauley brackets; is defined as:
Figure FDA00030442341800000118
substituting the expressions (3) and (5) into the expression (6) to obtain:
Figure FDA0003044234180000021
2. the model of claim 1 for the plastic accumulation of soil mass under high cyclic loading, wherein: (1) all variables in the formula (7) are implicitly related and are solved by adopting a Newton-Raphson iteration method.
3. The model of claim 1 for the plastic accumulation of soil mass under high cyclic loading, wherein: (1) the parameters in the formulae (1) to (7) can be determined by measuring the average hydrostatic pressure pavAnd average bias stress level ηaAnd verifying the lower drainage circulation three-axis test result.
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