CN105911258A - Marine soft soil stress strain model modeling method based on high-order hyperbolic mapping - Google Patents
Marine soft soil stress strain model modeling method based on high-order hyperbolic mapping Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N33/00—Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00
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- G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
Abstract
The invention relates to a marine soft soil stress strain model modeling method based on high-order hyperbolic mapping. A three-axis mechanics test of marine soft soil under a plurality of confining pressure is carried out to obtain stress strain data corresponding to each confining pressure; first-grade mathematical characteristics and second-grade mathematical characteristics of actually measured data are concluded and a model core function is selected; then, a dependent variable mapping function and an independent variable mapping function are established and independent variables and dependent variables in the core function and the actually measured data correspond one by one; a curve parameter corresponding of a basic formula under each confining pressure is determined through single stress strain curve fitting; and a mathematical relation between each model parameter and the confining pressure is analyzed to obtain a model parameter expressed by the confining pressure, and a stress strain model of a marine soil body is established. The defect that an existing soft soil stress strain model is not suitable for the marine soft soil is overcome and a stress strain curve of the marine soft soil can be accurately simulated.
Description
Technical field
The invention belongs to civil engineering material test and the technical field of numerical analysis, be specifically related to
A kind of littoral soft soil strees strain model modeling method based on high-order Hyperbolic Mapping.
Background technology
Along with economic develops rapidly, skyscraper that China's Coastal Areas is built, highway,
Urban Underground railway, enclose and cultivate code most important civil engineering infrastructure and gradually increase.Due to ground
The particularity of matter condition, these engineerings are the most all built on deep littoral soft soil ground, very
To being to build on the super soft weak soil ground of bottom silt hydraulic reclamation or polder.This kind of weak soil ground
The engineering properties of base is the most poor, first has to set up the deviatoric stress examined (following during engineering design
Be called for short " stress ") q with change axial strain (hereinafter referred to as " straining ") ε between mathematics
Model (hereinafter referred to as " strees strain model "), then carries out computational analysis, optimizes and determine
Each generic design parameter, it is ensured that superstructure or the normal usage function of structures.
At present, the hyperbolic model that the strees strain model of weak soil proposes with Duncan-Chang most represents
Property, this model assumption soil body is nonlinear elastic body, and parameter determination is simple, many in China
Geotechnical Engineering is widely used.But the experimental data of many littoral soft soil shows, with
Hyperbolic model is that the analog result of the conventional model of representative is not the same with measured data, causes
There is bigger matching in conventional model, logarithm value calculates and engineering design bring very important not
Profit impact." marine soft soil load-deformation curve complex indexes-hyperbolic model " (Wang Wei,
Song Xinjiang, Ling Hua, Lu Tinghao, Zhou Ganwu. marine soft soil load-deformation curve complex indexes-
Hyperbolic model. Geotechnical Engineering journal, 2010,32 (9): 1455-1459), " clay non-thread
The improved tangent modulus of property model " (Wang Wei, Lu Tinghao, Zhou Ganwu. clay nonlinear model
Improved tangent modulus [J]. Geotechnical Engineering journal, 2007,29 (3): 458-462.) etc. document
Although improvement project is proposed, but modeling approach indefinite, total to measured data feature in
It is the most careful to tie, and owing to lacking the key links such as mapping function, causes pattern function requirement harsh,
And model still suffers from bigger error.Therefore, it is soft that traditional strees strain model is not suitable for strand
Soil, is required for littoral soft soil, proposes new modeling method and sets up new strees strain model,
Guarantee safe construction and the operational management of building or the structures built on littoral soft soil ground.
The present invention thus produces.
Summary of the invention
The present invention is not suitable for lacking of littoral soft soil to overcome existing weak soil strees strain model
Fall into, it is provided that a kind of littoral soft soil strees strain model modeling method based on high-order Hyperbolic Mapping,
Can the stress-strain diagram of accurate simulation littoral soft soil.
For reaching above-mentioned purpose, the present invention is achieved by the following technical solutions:
A kind of littoral soft soil strees strain model modeling method based on high-order Hyperbolic Mapping, including
Following steps:
(1) three-axis force test is carried out, it is thus achieved that experimental data;
(2) mathematical feature of measured data is excavated: include one-level mathematical feature and two grades of mathematics spies
Levying, wherein one-level mathematical feature includes the theoretical interval [x of strain stress1, x2] and stress q
Theoretical interval [y1, y2], two grades of mathematical features include initial value, incremental, concavity and convexity
With stress maximum;
(3) Selection Model core function: according to one-level mathematical feature, chooses suitable model core
Heart function f (ε), and determine that the interval of its independent variable is [X1, X2], the value of dependent variable
Interval is [Y1, Y2];
(4) dependent variable mapping function is built: described dependent variable mapping function F (ε) can keep
The interval of independent variable is constant, and is mapped as one by one by the interval of strain stress: [Y1,
Y2]→[y1, y2];
(5) independent variable mapping function is built: described independent variable mapping function g (ε) contains speed
Mapping parameters and shape map parameter;The interval that simultaneously can keep dependent variable is constant, and
The interval of independent variable is mapped as one by one: [X1, X2] it is mapped as [x one by one1, x2];Guarantee
After mapping, two grades of mathematical features of model mate with measured stress strain data;
(6) ess-strain fundamental formular is set up: by dependent variable mapping function F (ε), independent variable
Mapping function g (ε) brings model core function f (ε) into, sets up the fundamental formular containing undetermined parameter
Q=F (f (g (ε)));
(7) mathematical feature of fundamental formular is verified: check a progression of ess-strain fundamental formular
Learn feature and two grades of mathematical features, check it the most identical with the mathematical feature of measured data;
(8) stress-strain diagram matching: use ess-strain fundamental formular that single confined pressure stress is answered
Varied curve matching, determines the parameter in the fundamental formular that each confined pressure is corresponding;
(9) littoral soft soil strees strain model is determined: analyze each parameter and confined pressure in fundamental formular
Mathematical relationship, obtain with confined pressure express model parameter, set up the ess-strain of the strand soil body
Model.
The three-axis force carrying out the littoral soft soil under 3 to 5 confined pressures in described step (1) is surveyed
Examination, it is thus achieved that the stress-strain data that each confined pressure is corresponding;Described confined pressure is to execute in triaxial test
The horizontal pressure force around sample added, uses σ3Represent.
Described stress is the deviatoric stress in triaxial test, and described strain is in triaxial test
Axial strain.
Described model core function is trigonometric tangential function, and described dependent variable mapping function is
Linear function, described independent variable mapping function is high-order hyperbolic functions.
The mathematical property of described model core function is not by two grades of mathematical features of measured data
Constraint.
The mapping rates that described Rate mapping state modulator independent variable is interval, the mapping i.e. strained
Speed.
In described shape map state modulator mapping process, the shape of core function, makes core letter
Number more mates the secondary characteristics of measured data, or makes unmatched core function and actual measurement originally
Two grades of mathematics characteristic matching of data.
Described ess-strain fundamental formular meets one-level mathematical feature and two grades of mathematical features and contains
Having the mathematic(al) representation of undetermined parameter, its undetermined parameter can be by the measured stress under single confined pressure
Strain data determines.
Described strees strain model is set up based on ess-strain fundamental formular, containing model
Parameter;Its model parameter is obtained by the matching of the fundamental formular parameter obtained under each confined pressure, is all
The function of confined pressure, and be only the function of confined pressure.
Present invention littoral soft soil based on high-order Hyperbolic Mapping strees strain model modeling method, enters
The three-axis force test of the littoral soft soil under the multiple confined pressures of row, it is thus achieved that the stress that each confined pressure is corresponding
Strain data;Sum up one-level mathematical feature and two grades of mathematical features, the Selection Model of measured data
Core function;Then by setting up dependent variable mapping function and independent variable mapping function, the most real
Independent variable in existing model core function and measured data, dependent variable one_to_one corresponding, obtain stress
Strain fundamental formular;By single stress-strain diagram matching, determine under each confined pressure substantially public
The parameter of curve that formula is corresponding;Analyze the mathematical relationship of each model parameter and confined pressure, obtain with confined pressure
The model parameter expressed, sets up the strees strain model of the strand soil body.
Beneficial effects of the present invention is as follows:
1, the present invention is that the strees strain model accurately building littoral soft soil provides a kind of new side
Method, this model, based on ordinary triaxial test, has higher accuracy and the suitability, Ke Yiwei
The Operation, Administration and Maintenance of strand Geotechnical Engineering provides reliable reference frame;
2, the mathematical feature of measured data is classified, i.e. one-level mathematical feature and two grades of mathematical features,
Only consider to meet one-level mathematical feature when building model core function, overcome tradition modeling side
Method requires excessively harsh shortcoming to the pattern function of primary election;
3, by the mapping in the Rate mapping state modulator independent variable interval in independent variable mapping function
Speed, overcomes in tradition modeling method in modeling initial stage necessary mutually the same deficiency;
4, by the shape map parameter in independent variable mapping function, core in mapping process is controlled
The shape of function, it is achieved core function is mated with two grades of mathematical features of measured data, overcomes
Its deficiency must being mutually matched at the modeling initial stage in tradition modeling method.
Accompanying drawing explanation
Fig. 1 is the modeling procedure figure of the present invention;
Fig. 2 is the measured stress strain curve of the embodiment of the present invention;
Fig. 3 is the core function schematic diagram of the embodiment of the present invention;
The ess-strain fundamental formular mathematical feature schematic diagram of Fig. 4 embodiment of the present invention.
Detailed description of the invention
Below in conjunction with specific embodiment, the present invention is further illustrated, but the protection of the present invention
Scope is not limited to this.
Southeastern coast road engineering, for Soft Ground of Shore Deposit, design early stage needs by often
Rule triaxial test, sets up accurate strees strain model, for numerical simulation and engineering design
Time reference.
Present invention littoral soft soil based on high-order Hyperbolic Mapping strees strain model modeling method, enters
The three-axis force test of the littoral soft soil under the multiple confined pressures of row, it is thus achieved that the stress that each confined pressure is corresponding
Strain data;Sum up one-level mathematical feature and two grades of mathematical features, the Selection Model of measured data
Core function;Then by setting up dependent variable mapping function and independent variable mapping function, the most real
Independent variable in existing model core function and measured data, dependent variable one_to_one corresponding, obtain stress
Strain fundamental formular;By single stress-strain diagram matching, determine under each confined pressure substantially public
The parameter of curve that formula is corresponding;Analyze the mathematical relationship of each model parameter and confined pressure, obtain with confined pressure
The model parameter expressed, sets up the strees strain model of the strand soil body.Modeling procedure is shown in Fig. 1.
Stress in the present invention, for the deviatoric stress in triaxial test, represents with q.Strain, for
Axial strain in triaxial test, represents with ε.Confined pressure, for the sample applied in triaxial test
Horizontal pressure force around, uses σ3Represent.
The one-level mathematical feature of the measured data in the present invention, including the theoretical value district of strain stress
Between [x1, x2] and the theoretical interval [y of deviatoric stress q1, y2].Two grades of mathematics of measured data
Feature, including initial value, incremental, concavity and convexity and stress maximum etc..
The interval of the model core function argument in the present invention is [X1, X2], dependent variable
Interval is [Y1, Y2], two intervals all can be corresponding with measured data by mapping function
Two interval one_to_one corresponding.Preferably, trigonometric tangential function is taken.
The mathematical property of the model core function in the present invention can not be by two progression of measured data
Learn the constraint of feature.
Dependent variable mapping function in the present invention, it is possible to by the dependent variable value of model core function
Interval [Y1, Y2] it is mapped as [y one by one1, y2], accurately reflect stress maximum.Preferably, take
Linear function.
Independent variable mapping function in the present invention, it is possible to accurately reflect the Rate mapping ginseng of independent variable
Number and shape map parameter, by model core argument of function interval [X1, X2] reflect one by one
Penetrate as [x1, x2].Preferably, high-order hyperbolic functions are taken.
Rate mapping parameter in the present invention, controls the mapping rates that independent variable is interval, i.e. strains
Mapping rates.
Shape map parameter in the present invention, controls the shape of core function in mapping process, makes
Core function more mates the secondary characteristics of measured data, or makes unmatched core function originally
Two grades of mathematics characteristic matching with measured data.
Ess-strain fundamental formular in the present invention, it is possible to meet one-level mathematical feature and two progression
Learning feature and the mathematic(al) representation containing undetermined parameter, its undetermined parameter can be by under single confined pressure
Measured stress strain data determine.
Strees strain model in the present invention, sets up based on ess-strain fundamental formular, contains
There is model parameter;Its model parameter is obtained by the matching of the fundamental formular parameter obtained under each confined pressure,
It is all the function of confined pressure, and is only the function of confined pressure.
Present invention littoral soft soil based on high-order Hyperbolic Mapping strees strain model modeling method, bag
Include following steps:
(1) mechanical test is carried out, it is thus achieved that experimental data.Carry out the strand under 3 to 5 confined pressures
The three-axis force test of weak soil, it is thus achieved that the stress-strain data that each confined pressure is corresponding.
This time test takes 4 different confined pressures, respectively 100kPa, 200kPa, 300kPa
And 400kPa, the different stress numerical that typically strain value is corresponding recorded under each confined pressure, see figure
2。
(2) mathematical feature of measured data is excavated.Including one-level mathematical feature and two grades of mathematics spies
Levying, wherein one-level mathematical feature includes the theoretical interval [x of strain stress1, x2] and stress q
Theoretical interval [y1, y2], two grades of mathematical features include initial value, incremental, concavity and convexity,
Stress maximum.
According to Fig. 1, in the present embodiment, the theoretical interval of independent variable strain stress is [0, ∞],
The theoretical interval of stress q is [0, A].Wherein, A is one and positive treats rational method,
Correspond to stress maximum;Initial value is (0,0), and dependent variable strain stress is with independent variable stress
The increase monotonic increase of q, and away from axis of abscissas direction evagination, deviatoric stress q has asymptotic value (to answer
Power maximum) and its numerical value corresponding to constant A.
(3) Selection Model core function.According to one-level mathematical feature, choose suitable model core
Heart function f (ε), and determine that the interval of its independent variable is [X1, X2], the value of dependent variable
Interval is [Y1, Y2]。
In the present embodiment, employing trigonometric tangential function:
F (ε)=tan (ε) (1)
Interval [the X of its independent variable1, X2] it is [0, π/4], the interval [Y of dependent variable1,
Y2] it is [0,1], see Fig. 3.
(4) dependent variable mapping function is built.This dependent variable mapping function F (ε) can keep certainly
The interval of variable is constant, and is mapped as one by one by the interval of strain stress: [Y1,
Y2]→[y1, y2]。
In the present embodiment, employing linear function:
F (ε)=A* ε (2)
Now, the interval keeping independent variable is constant, and the interval of dependent variable is mapped as one by one:
[0,1] → [0, A].
(5) independent variable mapping function is built.This independent variable mapping function g (ε) reflects containing speed
Penetrate parameter and shape map parameter;The interval that simultaneously can keep dependent variable is constant, and will
Interval [the X of independent variable1, X2] it is mapped as [x one by one1, x2];Guarantee map after model two
Level mathematical feature mates with stress-strain diagram.
In the present embodiment, employing high-order Hyperbolic Mapping:
Now, keep dependent variable interval [0, A] constant, the interval of independent variable [0,
π/4] it is mapped as [0, ∞] one by one.Wherein, B is a positive rational method for the treatment of, corresponding
For Rate mapping parameter;K is also one and positive treats rational method, corresponds to shape map ginseng
Number.
(6) ess-strain fundamental formular is set up.By dependent variable mapping function F (ε), independent variable
Mapping function g (ε) brings model core function f (ε) into, sets up the fundamental formular containing undetermined parameter
Q=F (f (g (ε))).
(7) mathematical feature of fundamental formular is verified.One progression of inspection ess-strain fundamental formular
Learn feature and two grades of mathematical features, check it the most identical with the mathematical feature of measured data.
The two grades of mathematics spies being made up of initial value, first derivative, second dervative, stress maximum
Levy for:
Initial value: q |ε=0=0
First derivative:And
Second dervative:
Asymptotic value: q |ε→∞=A
According to higher mathematics principle, this ess-strain fundamental formular can meet the institute of measured data
There are one-level mathematical feature and two grades of mathematical features, obtain this base according to the different values of A, B, K
(4) two typical schematic diagrams of this formula and relevant parameter are shown in Fig. 4.
(8) use ess-strain fundamental formular to single confined pressure stress-strain diagram matching.By list
Stress-strain diagram matching under individual confined pressure effect, determines in the fundamental formular that each confined pressure is corresponding
Parameter.
Use ess-strain fundamental formular q=F of the present invention (f (g (ε))), to Fig. 1 surveys number
According to being simulated matching, obtain each parameter value of ess-strain fundamental formular under 4 confined pressures, see
Table 1.
The parameter value that each confined pressure of table 1 is corresponding
Parameter | σ3=100kPa | σ3=200kPa | σ3=300kPa | σ3=400kPa |
A | 165.08 | 257.87 | 360.44 | 463.10 |
B(10-3) | 16.01 | 6.81 | 4.40 | 3.77 |
K | 1.20 | 1.21 | 1.18 | 1.19 |
(9) littoral soft soil strees strain model is determined.Analyze each parameter and confined pressure in fundamental formular
Mathematical relationship, obtain with confined pressure express model parameter, set up the ess-strain of the strand soil body
Model.
According to table 1, it is fitted obtaining to three parameters: parameter A and the approximately linear pass of confined pressure
System, parameter B and confined pressure are approximated to power function relationship, and the value of parameter K is little with enclosing change,
It is approximately constant k, i.e.;
A=a1+a2σ3,K=k
The strees strain model obtaining littoral soft soil further is:
This model comprises a1、a2, m, n, k totally 5 model parameters.Test in conjunction with this, mould
The matching value of shape parameter is shown in Table 2.
Table 2 Estimating The Model Coefficients value
a1 | a2 | m | n | k |
62.46 | 1.00 | 2.13 | -1.07 | 1.20 |
Further into, table 2 is brought model expression (5), obtain this test littoral soft soil
The expression of strees strain model be:
Comparative example
Contrast traditional double curve model and the inventive method, for fully proving the standard of the inventive method
Really property, uses ess-strain fundamental formular, strees strain model to answer actual measurement under 4 confined pressures
Stress-strain data are fitted, and carry out Error Calculation, the results are shown in Table 3.Obviously, the present invention
The strees strain model provided error under each operating mode is respectively less than conventional model, is more suitable for retouching
State the mechanical characteristic of littoral soft soil.
Table 3 present invention contrasts with traditional method error
Present invention littoral soft soil based on high-order Hyperbolic Mapping strees strain model modeling method, will
The mathematical feature classification of measured data, progressively meets in modeling process, overcomes tradition modeling
In method, pattern function selects to require excessively harsh shortcoming;Employing trigonometric tangential function is core
Function, in conjunction with high-order Hyperbolic Mapping function founding mathematical models, modeling method is simple;This model
Can accurate description littoral soft soil triaxial stress strain, model error is little, can be strand rock
Numerical simulation and the engineering design of geotechnique's journey provide reliable reference frame.
Above-described embodiment is only used for illustrating the inventive concept of the present invention, rather than weighs the present invention
The restriction of profit protection, all changes utilizing this design that the present invention carries out unsubstantiality, all should fall
Enter protection scope of the present invention.
Claims (9)
1. a littoral soft soil strees strain model modeling method based on high-order Hyperbolic Mapping, its feature
It is to comprise the following steps:
(1) three-axis force test is carried out, it is thus achieved that experimental data;
(2) mathematical feature of measured data is excavated: include one-level mathematical feature and two grades of mathematical features,
Wherein one-level mathematical feature includes the theoretical interval [x of strain stress1, x2] and the reason of stress q
Opinion interval [y1, y2], two grades of mathematical features include initial value, incremental, concavity and convexity and answer
Power maximum;
(3) Selection Model core function: according to one-level mathematical feature, chooses suitable model core letter
Number f (ε), and determine that the interval of its independent variable is [X1, X2], the interval of dependent variable
For [Y1, Y2];
(4) dependent variable mapping function is built: described dependent variable mapping function F (ε) can keep from becoming
The interval of amount is constant, and is mapped as one by one by the interval of strain stress: [Y1, Y2] → [y1,
y2];
(5) independent variable mapping function is built: described independent variable mapping function g (ε) contains Rate mapping
Parameter and shape map parameter;The interval that simultaneously can keep dependent variable is constant, and will be from
The interval of variable is mapped as one by one: [X1, X2] it is mapped as [x one by one1, x2];Guarantee to map
Two grades of mathematical features of rear model mate with measured stress strain data;
(6) ess-strain fundamental formular is set up: dependent variable mapping function F (ε), independent variable are mapped
Function g (ε) brings model core function f (ε) into, sets up the fundamental formular containing undetermined parameter
Q=F (f (g (ε)));
(7) mathematical feature of fundamental formular is verified: the one-level mathematics of inspection ess-strain fundamental formular is special
Seek peace two grades of mathematical features, check its whether mathematical feature with measured data coincide;
(8) stress-strain diagram matching: use ess-strain fundamental formular bent to single confined pressure ess-strain
Line matching, determines the parameter in the fundamental formular that each confined pressure is corresponding;
(9) littoral soft soil strees strain model is determined: analyze each parameter and the number of confined pressure in fundamental formular
Relation, obtains the model parameter expressed with confined pressure, sets up the strees strain model of the strand soil body.
2. littoral soft soil strees strain model based on high-order Hyperbolic Mapping modeling as claimed in claim 1
Method, it is characterised in that: described step (1) carries out the strand under 3 to 5 confined pressures soft
The three-axis force test of soil, it is thus achieved that the stress-strain data that each confined pressure is corresponding;Described confined pressure
For the horizontal pressure force around the sample of applying in triaxial test, use σ3Represent.
3. littoral soft soil strees strain model based on high-order Hyperbolic Mapping modeling as claimed in claim 1
Method, it is characterised in that: described stress is the deviatoric stress in triaxial test, described strain
For the axial strain in triaxial test.
4. littoral soft soil strees strain model based on high-order Hyperbolic Mapping modeling as claimed in claim 1
Method, it is characterised in that: described model core function is trigonometric tangential function, described because of
Variable mappings function is linear function, and described independent variable mapping function is high-order hyperbolic functions.
5. littoral soft soil strees strain model based on high-order Hyperbolic Mapping modeling as claimed in claim 1
Method, it is characterised in that: the mathematical property of described model core function is not by measured data
The constraint of two grades of mathematical features.
6. littoral soft soil strees strain model based on high-order Hyperbolic Mapping modeling as claimed in claim 1
Method, it is characterised in that: the mapping rates that described Rate mapping state modulator independent variable is interval,
The mapping rates i.e. strained.
7. littoral soft soil strees strain model based on high-order Hyperbolic Mapping modeling as claimed in claim 1
Method, it is characterised in that: core function in described shape map state modulator mapping process
Shape, makes core function more mate the secondary characteristics of measured data, or makes the most unmatched
Core function and two grades of mathematics characteristic matching of measured data.
8. littoral soft soil strees strain model based on high-order Hyperbolic Mapping modeling as claimed in claim 1
Method, it is characterised in that: described ess-strain fundamental formular meets one-level mathematical feature and two
Level mathematical feature and the mathematic(al) representation containing undetermined parameter, its undetermined parameter can be enclosed by single
The measured stress strain data of pressure determines.
9. littoral soft soil strees strain model based on high-order Hyperbolic Mapping modeling as claimed in claim 1
Method, it is characterised in that: described strees strain model is based on ess-strain fundamental formular
Set up, containing model parameter;Its model parameter is by the fundamental formular parameter obtained under each confined pressure
Matching obtains, and is all the function of confined pressure, and is only the function of confined pressure.
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