CN113125262A - Method for quickly forecasting deformation of breakable calcareous sand in loading process - Google Patents

Method for quickly forecasting deformation of breakable calcareous sand in loading process Download PDF

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CN113125262A
CN113125262A CN202110413272.4A CN202110413272A CN113125262A CN 113125262 A CN113125262 A CN 113125262A CN 202110413272 A CN202110413272 A CN 202110413272A CN 113125262 A CN113125262 A CN 113125262A
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金炜枫
马永航
陶颖
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Zhejiang Lover Health Science and Technology Development Co Ltd
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Abstract

The invention relates to a method for quickly forecasting deformation of breakable calcareous sand in a loading process, which is used for decoupling the calculation of stress ratio and body strain, and can calculate the change of the stress ratio along with shear strain independently and then calculate the change of the body strain along with the shear strain without interactively calculating the stress ratio and the body strain increment in each increment step, thereby simplifying the calculation process and improving the calculation efficiency.

Description

Method for quickly forecasting deformation of breakable calcareous sand in loading process
Technical Field
The invention belongs to the field of geotechnical engineering research, and particularly relates to a rapid prediction method for deformation of breakable calcareous sand in a loading process.
Background
The calcareous sand used for the marine artificial hydraulic reclamation island has obvious particle crushing property after being loaded. For the breakable calcareous sand, a large number of triaxial test researches are carried out to analyze the stress-strain characteristics of the breakable calcareous sand, but a method is not available at present, namely, the deformation of the breakable calcareous sand in the loaded breaking process can be quickly forecasted, for example, when the vertical direction has continuous compressive strain, the changes of the forecasting stress and the volume deformation are decoupled. In the existing method, the stress and the volume deformation need to be interactively calculated at each time step, the calculation of the stress and the volume deformation is not decoupled, and the calculation program is more complex.
Disclosure of Invention
The invention provides a rapid forecasting method for deformation of breakable calcareous sand in a loading process, which aims to decouple and forecast the stress and the volume deformation of the breakable calcareous sand in the loading process and carry out rapid forecasting on the deformation of the breakable calcareous sand in the loading process without interactively calculating the stress and the volume deformation of a soil sample at each time step.
The invention relates to some abbreviations and symbols, the following are notes:
σ1and σ'1: vertical stress, σ ', to which the aggregate of particles is subjected'1For effective stress, where σ1And σ'1Taking the same value;
σ2and σ3，σ′2And σ'3: horizontal stress, σ, to which the assembly of particles is subjected2And σ3Is perpendicular to the direction of'2And σ'3For effective stress, where σ2And σ'2Taking the same value, σ3And σ'3Taking the same value;
ε1、ε2and ε3: strain and respectively stress sigma1、σ2And σ3The directions are the same;
p': the average effective stress of the steel is measured,
Figure BDA0003024795330000021
q: the shear stress q is set to a value of,
Figure BDA0003024795330000022
eta: the stress ratio eta is such that,
Figure BDA0003024795330000023
εv: bulk strain, epsilonv＝ε1+ε2+ε3；
εs: the shear strain is generated by the shear strain,
Figure BDA0003024795330000024
t0,t1,t2,…,ti,…,tn: the recorded starting time in the loading process is t0The time recorded later is t from small to large1,t2,…,ti,…,tnWhere i is more than or equal to 1 and less than or equal to n, and n +1 is the number of recorded time points;
(εv)i: t thiBody strain epsilon corresponding to timev；
(εs)i: t thiShear strain epsilon corresponding to times；
(△εv)i: increase in bulk strain, (. DELTA.. epsilon.)v)i＝(εv)i-(εv)i-1；
(△εs)i: increase in shear strain, (. DELTA.. epsilon.)s)i＝(εs)i-(εs)i-1；
M: material parameters and equal to critical stress ratio;
k2: a parameter;
beta: parameter and
Figure BDA0003024795330000025
pa: atmospheric pressure;
p′0: an initial average effective stress;
ξ1and xi2: calculating a beta parameter;
α: material parameter,. alpha. - (C)2+1)exp(-C1εs)+(C2-1)exp(-εs)+1；
C1And C2: calculating an alpha parameter;
the technical scheme of the invention is as follows: a method for quickly forecasting the deformation of breakable calcareous sand in a loading process comprises the following steps:
step 1: let the vertical stress of the aggregate of sand particles be sigma1Stress on the horizontal plane is respectively sigma2And σ3Where σ is2And σ3Is perpendicular to the direction of the particle assembly and the strain of the particle assembly is epsilon1、ε2And ε3In which strain epsilon1、ε2And ε3Respectively in the direction of the stress sigma1、σ2And σ3The directions are the same; defining average effective stress p', shear stress q, stress ratio eta, and bulk strain epsilonvAnd shear strain epsilons：
Figure BDA0003024795330000031
Figure BDA0003024795330000032
Figure BDA0003024795330000033
εv＝ε1+ε2+ε3 (4)
Figure BDA0003024795330000034
Step 2: calculating the stress ratio:
the stress ratio eta is calculated by the following formula:
Figure BDA0003024795330000035
where M is a material parameter and is equal to the critical stress ratio, k2Is a parameter, β is a parameter;
Figure BDA0003024795330000036
in the above formula paIs largeGas pressure, p'0Is the initial mean effective stress, ξ1And xi2Is a parameter;
thus resulting from shear strain epsilonsThe stress ratio eta can be directly calculated;
and step 3: calculating the volume deformation:
let the start time recorded during loading be t0The time recorded later is t from small to large1,t2,…,ti,…,tnWhere 1 ≦ i ≦ n, n +1 is the number of recorded time points, let tiBody strain epsilon corresponding to timevIs (epsilon)v)iLet a tiShear strain epsilon corresponding to timesIs (epsilon)s)iLet the shear strain increment (Delta epsilon) generated by two adjacent time differencess)iEqual, define the bulk strain increment ([ Delta ] [ epsilon ]v)iAnd increase in shear strain (DELTA ε)s)i：
(△εv)i＝(εv)i-(εv)i-1 (8)
(△εs)i＝(εs)i-(εs)i-1 (9)
Where the strain (epsilon) is cut at every moments)iAnd increase in shear strain (DELTA ε)s)iFor a known set value, the volume strain increment (Δ ε) is calculated as followsv)i：
Figure BDA0003024795330000041
In the above formula, α is a material parameter, and a relationship of α with a change in shear strain is defined as:
α＝-(C2+1)exp(-C1εs)+(C2-1)exp(-εs)+1 (11)
in the above formula C1And C2For the material parameter, each t can be calculated from the equation (10)i(i is more than or equal to 1 and less than or equal to n) corresponding to the momentv)iBy increasing these bulk strains by an amount (. DELTA.. di-elect cons.)v)iWhen added together, the body strain (epsilon) at each moment is obtainedv)iI.e., (. epsilon.)v)i＝(εv)i-1+(△εv)iAnd the initial t is known0Time body strain (Delta epsilon)v)iIs 0.
In step 2, calculating to obtain a stress ratio eta, and calculating to obtain an effective stress sigma 'in the horizontal direction'2And σ'3When the stress is constant and equal, the vertical effective stress sigma 'can be obtained'1And average effective and shear stresses:
Figure BDA0003024795330000051
Figure BDA0003024795330000052
in step 3, when the strain is horizontal2And ε3When the two strains are equal, the vertical strain epsilon can be obtained1And strain in horizontal direction epsilon3：
Figure BDA0003024795330000053
The invention has the beneficial effects that: stress ratio and body strain are calculated and decoupled, stress ratio changing along with shear strain can be calculated independently, then body strain changing along with shear strain is calculated, and stress ratio and body strain increment do not need to be calculated in each increment step in an interactive mode, so that the calculation process is simplified, and the calculation efficiency is improved. In addition, the calculation formula of the ratio of the volume strain increment and the shear strain increment given by the formula (10) along with the stress ratio is more in line with the test curve of the breakable calcareous sand compared with the existing formula.
Drawings
FIG. 1 is a schematic view of an assembly of sand particles stressed vertically and horizontally;
FIG. 2 is a graph showing the variation of stress ratio and bulk strain with shear strain;
FIG. 3 is a graph of the ratio of bulk strain increase to shear strain increase versus stress ratio.
Fig. 1. assembly of sand particles.
Detailed Description
In order to make the technical means, innovative features, objectives and effects of the present invention apparent, the present invention will be further described with reference to the following detailed drawings.
With the aggregate 1 of sand particles shown in FIG. 1, stress σ is applied in the vertical direction1Is stressed horizontally by a stress2And σ3，σ2And σ3Is vertical. Carrying out a triaxial test with a confining pressure sigma2＝σ3And a change curve of the stress ratio with the shear strain and a change curve of the body strain with the shear strain can be drawn. The confining pressures in the three-axis test of the breakable calcareous sand are 100kPa, 200kPa, 300kPa, 500kPa, 700kPa and 900kPa, and the corresponding stress ratio curve and the corresponding body strain curve are shown in FIG. 2. FIG. 3 shows σ2＝σ3The ratio of the increase in bulk strain to the increase in shear strain at 900kPa is plotted against the stress ratio.
The invention relates to some abbreviations and symbols, the following are notes:
σ1and σ'1: vertical stress, σ ', to which the aggregate of particles is subjected'1For effective stress, where σ1And σ'1Take the same value
σ2And σ3，σ′2And σ'3: horizontal stress, σ, to which the assembly of particles is subjected2And σ3Is perpendicular to the direction of'2And σ'3For effective stress, where σ2And σ'2Taking the same value, σ3And σ'3Take the same value
ε1、ε2And ε3: strain and respectively stress sigma1、σ2And σ3Same direction
p': the average effective stress of the steel is measured,
Figure BDA0003024795330000061
q: the shear stress q is set to a value of,
Figure BDA0003024795330000062
eta: the stress ratio eta is such that,
Figure BDA0003024795330000063
εv: bulk strain, epsilonv＝ε1+ε2+ε3
εs: the shear strain is generated by the shear strain,
Figure BDA0003024795330000064
t0,t1,t2,…,ti,…,tn: the recorded starting time in the loading process is t0The time recorded later is t from small to large1,t2,…,ti,…,tnWhere 1 ≦ i ≦ n, n +1 is the number of recorded time points
(εv)i: t thiBody strain epsilon corresponding to timev
(εs)i: t thiShear strain epsilon corresponding to times
(△εv)i: increase in bulk strain, (. DELTA.. epsilon.)v)i＝(εv)i-(εv)i-1
(△εs)i: increase in shear strain, (. DELTA.. epsilon.)s)i＝(εs)i-(εs)i-1
M: material parameter equal to critical stress ratio
k2: parameter(s)
Beta: parameter and
Figure BDA0003024795330000071
pa: atmospheric pressure
p′0: initial mean effective stress
ξ1And xi2: calculating beta parameter
α: material parameter,. alpha. - (C)2+1)exp(-C1εs)+(C2-1)exp(-εs)+1
C1And C2: calculating alpha parameter
The technical scheme of the invention is as follows: a method for quickly forecasting the deformation of breakable calcareous sand in a loading process comprises the following steps:
step 1: let the vertical stress of the aggregate of sand particles be sigma1Stress on the horizontal plane is respectively sigma2And σ3Where σ is2And σ3Is perpendicular to the direction of the particle assembly and the strain of the particle assembly is epsilon1、ε2And ε3In which strain epsilon1、ε2And ε3Respectively in the direction of the stress sigma1、σ2And σ3The directions are the same; defining average effective stress p', shear stress q, stress ratio eta, and bulk strain epsilonvAnd shear strain epsilons：
Figure BDA0003024795330000072
Figure BDA0003024795330000073
Figure BDA0003024795330000074
εv＝ε1+ε2+ε3 (4)
Figure BDA0003024795330000081
Step 2: calculating the stress ratio:
the stress ratio eta is calculated by the following formula:
Figure BDA0003024795330000082
where M is a material parameter and is equal to the critical stress ratio, k2As parameters, β is:
Figure BDA0003024795330000083
in the above formula paIs atmospheric pressure, p'0Is the initial mean effective stress, ξ1And xi2Is a parameter such that the shear strain εsThe stress ratio eta can be directly calculated;
in this example, the horizontal effective stress σ'2And σ'3Constant and equal, so that the vertical effective stress sigma 'can be obtained'1And average effective and shear stresses:
Figure BDA0003024795330000084
Figure BDA0003024795330000085
and step 3: calculating the volume deformation:
let the start time recorded during loading be t0The time recorded later is t from small to large1,t2,…,ti,…,tnWhere 1 ≦ i ≦ n, n +1 is the number of recorded time points, let tiBody strain epsilon corresponding to timevIs (epsilon)v)iLet a tiShear strain epsilon corresponding to timesIs (epsilon)s)iLet the shear strain increment (Delta epsilon) generated by two adjacent time differencess)iEquality, defining a volume strain increaseAmount (. DELTA.. di-elect cons.)v)iAnd increase in shear strain (DELTA ε)s)i：
(△εv)i＝(εv)i-(εv)i-1 (8)
(△εs)i＝(εs)i-(εs)i-1 (9)
Where the strain (epsilon) is cut at every moments)iAnd increase in shear strain (DELTA ε)s)iFor a known set value, the volume strain increment (Δ ε) is calculated as followsv)i：
Figure BDA0003024795330000091
In the above formula, α is a material parameter, and a relationship of α with a change in shear strain is defined as:
α＝-(C2+1)exp(-C1εs)+(C2-1)exp(-εs)+1 (11)
in the above formula C1And C2For the material parameter, each t can be calculated from the equation (10)i(i is more than or equal to 1 and less than or equal to n) corresponding to the momentv)iBy increasing these bulk strains by an amount (. DELTA.. di-elect cons.)v)iWhen added together, the body strain (epsilon) at each moment is obtainedv)iI.e., (. epsilon.)v)i＝(εv)i-1+(△εv)iAnd the initial t is known0Time body strain (Delta epsilon)v)iIs 0;
k2is a parameter, C1And C2It is calculated in the following manner,
Figure BDA0003024795330000092
C2＝-b1(p′0/pa)+b2，a1、a2、b1、b2are all parameters.
In this example, when the strain is horizontal ε2And ε3When the two strains are equal, the vertical strain epsilon can be obtained1And strain in horizontal direction epsilon3：
Figure BDA0003024795330000093
The values of the parameters are as follows:
TABLE 1 parameter values
Figure BDA0003024795330000101
The predicted shear stress curve and body strain curve are shown in fig. 2, and the predicted change curve of the ratio of the increment of body strain to the increment of shear strain along with the stress ratio is shown in fig. 3. In fig. 3, the prediction curves given by the conventional Cam-clay model are also given, and it can be seen that the conventional Cam-clay model does not describe the initial bending segment and the right-side hooking segment, and the prediction method given herein is more consistent with the actual experiment.

Claims (6)

1. A method for quickly forecasting the deformation of breakable calcareous sand in a loading process is characterized in that:
which comprises the following steps:
step 1: let the vertical stress of the aggregate of sand particles be sigma1Stress on the horizontal plane is respectively sigma2And σ3Where σ is2And σ3Is perpendicular to the direction of the particle assembly and the strain of the particle assembly is epsilon1、ε2And ε3In which strain epsilon1、ε2And ε3Respectively in the direction of the stress sigma1、σ2And σ3The directions are the same; defining average effective stress p', shear stress q, stress ratio eta, and bulk strain epsilonvAnd shear strain epsilons：
Figure FDA0003024795320000011
Figure FDA0003024795320000012
Figure FDA0003024795320000013
εv＝ε1+ε2+ε3 (4)
Figure FDA0003024795320000014
Step 2: calculating the stress ratio:
the stress ratio eta is calculated by the following formula:
Figure FDA0003024795320000015
where M is a material parameter and is equal to the critical stress ratio, k2Is a parameter, β is a parameter;
thus resulting from shear strain epsilonsThe stress ratio eta can be directly calculated;
and step 3: calculating the volume deformation:
let the start time recorded during loading be t0The time recorded later is t from small to large1,t2,…,ti,…,tnWhere 1 ≦ i ≦ n, n +1 is the number of recorded time points, let tiBody strain epsilon corresponding to timevIs (epsilon)v)iLet a tiShear strain epsilon corresponding to timesIs (epsilon)s)iLet the shear strain increment (Delta epsilon) generated by two adjacent time differencess)iEqual, define the bulk strain increment ([ Delta ] [ epsilon ]v)iAnd increase in shear strain (DELTA ε)s)i：
(△εv)i＝(εv)i-(εv)i-1 (8)
(△εs)i＝(εs)i-(εs)i-1 (9)
Where the strain (epsilon) is cut at every moments)iAnd increase in shear strain (DELTA ε)s)iFor a known set value, the volume strain increment (Δ ε) is calculated as followsv)i：
Figure FDA0003024795320000021
In the above formula, α is a material parameter, and each t can be calculated from the formula (10)iTime-dependent increase in body strain (Delta epsilon)v)iBy increasing these bulk strains by an amount (. DELTA.. di-elect cons.)v)iWhen added together, the body strain (epsilon) at each moment is obtainedv)iI.e., (. epsilon.)v)i＝(εv)i-1+(△εv)iAnd the initial t is known0Time body strain (Delta epsilon)v)iIs 0.
2. The method for rapidly forecasting the deformation of the breakable calcareous sand in the loading process according to claim 1, characterized in that: in the step 2, the step of the method is carried out,
Figure FDA0003024795320000022
in the above formula paIs atmospheric pressure, p'0Is the initial mean effective stress, ξ1And xi2Is a parameter.
3. The method for rapidly forecasting the deformation of the breakable calcareous sand in the loading process according to claim 1, characterized in that: in step 3, the relationship of α with the change in shear strain is defined as α ═ C2+1)exp(-C1εs)+(C2-1)exp(-εs)+1，C1And C2Is a material parameter.
4. The method for rapidly forecasting the deformation of the breakable calcareous sand in the loading process according to claim 1, characterized in that: in step 2, calculating to obtain a stress ratio eta, and calculating to obtain an effective stress sigma 'in the horizontal direction'2And σ3'constant and equal,' the vertical effective stress sigma 'can be obtained'1And average effective and shear stresses:
Figure FDA0003024795320000031
Figure FDA0003024795320000032
5. the method for rapidly forecasting the deformation of the breakable calcareous sand in the loading process according to claim 1, characterized in that: in step 3, when the strain is horizontal2And ε3When the two strains are equal, the vertical strain epsilon can be obtained1And strain in horizontal direction epsilon3：
Figure FDA0003024795320000033
6. The method for rapidly forecasting the deformation of the breakable calcareous sand in the loading process according to claim 3, characterized in that: c1And C2It is calculated in the following manner,
Figure FDA0003024795320000034
C2＝-b1(p′0/pa)+b2。
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CN110411804A (en) * 2019-09-02 2019-11-05 上海交通大学 A kind of contact face mechanical property test sample, preparation method and the test method of the soil body and structure
CN111024486A (en) * 2019-12-19 2020-04-17 南京航空航天大学 Creep behavior prediction method for unidirectional ceramic matrix composite
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