CN113155612A - Deformation prediction method for microfiber mixed silica sol solidified calcareous sand - Google Patents

Deformation prediction method for microfiber mixed silica sol solidified calcareous sand Download PDF

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CN113155612A
CN113155612A CN202110413264.XA CN202110413264A CN113155612A CN 113155612 A CN113155612 A CN 113155612A CN 202110413264 A CN202110413264 A CN 202110413264A CN 113155612 A CN113155612 A CN 113155612A
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CN113155612B (en
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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 deformation forecasting method for microfiber mixed silica sol solidified calcareous sand, which is used for more accurately forecasting volume deformation and volume deformation rate in a stress process of a silica gel-microfiber-sand complex formed after microfiber mixed silica sol seepage solidified calcareous sand.

Description

Deformation prediction method for microfiber mixed silica sol solidified calcareous sand
Technical Field
The invention belongs to the field of geotechnical engineering research, and particularly relates to a deformation forecasting method for microfiber mixed silica sol solidified calcareous sand.
Background
The silica sol is formed by suspending nano-scale silica particles in water, has viscosity similar to that of water, and is quickly infiltrated through sandy soil, and then the silica particles are gathered into silica gel with a three-dimensional network structure, so that a solidified soil body is cemented. However, a large number of micro-cracks exist in the silica gel, so that the micro-fibers are mixed in the silica sol, then the silica sol seeps through a soil body to form a silica gel-micro-fiber-sand complex, and the micro-fibers can inhibit the micro-cracks of the silica gel from expanding, so that the strength of the sand solidified by the seepage of the silica sol is improved.
However, after the microfibril mixed silica sol is used for curing the calcareous sand, when a cured soil body deforms under the stress, the deformation of the cured soil body is influenced by the crushing of the calcareous sand, the cementation failure of the silica gel and the reinforcing of the microfibril, and a large error exists in the prediction of the deformation of the silica gel-microfibril-sand complex by using a conventional method, so that a method is lacked, and the volume deformation rate of the silica gel-microfibril-sand complex formed after the microfibril mixed silica sol is percolated and cured the calcareous sand can be accurately predicted in the stress process.
Disclosure of Invention
The invention provides a deformation forecasting method for microfiber mixed silica sol solidified calcareous sand, which aims to accurately forecast volume deformation and volume deformation rate of a silica gel-microfiber-sand complex formed after microfiber mixed silica sol seepage solidified calcareous sand in a stress process.
The invention relates to some abbreviations and symbols, the following are notes:
σ1': vertical stress to which the aggregate of particles is subjected;
σ′2and σ3': horizontal stress, σ ', to which the aggregate of particles is subjected'2And σ3The direction of' is vertical;
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 BDA0003024795260000021
q: the shear stress q is set to a value of,
Figure BDA0003024795260000022
eta: the stress ratio eta is such that,
Figure BDA0003024795260000023
ηcritical: critical stress ratio η;
ηpeak: peak stress ratio η;
εv: bulk strain, epsilonv＝ε1+ε2+ε3；
εs: the shear strain is generated by the shear strain,
Figure BDA0003024795260000024
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；
ηi：tiStress ratio eta at time (i is more than or equal to 1 and less than or equal to n)i；
f(εs)：f(εs) Is shear strain epsilonsA function of (a);
B1、C1、C2and C3：B1、C1、C2And C3Is the parameter of the model and is,
Figure BDA0003024795260000031
α: a material coefficient;
k: a material coefficient;
e0: an initial void ratio;
ec: a critical void ratio;
e：tiat the moment (i is more than or equal to 1 and less than or equal to n), the porosity ratio is increased;
kappa: a coefficient of restitution;
m: material parameter equal to critical stress ratio etacritical；
m: and (4) material parameters.
The technical scheme of the invention is as follows: a deformation forecasting method for microfiber mixed silica sol solidified calcareous sand specifically comprises the following steps:
step 1: setting the vertical stress of a silica gel-microfiber-sand complex formed after the microfiber and silica sol are mixed to infiltrate and solidify calcareous sand1'the stress on the horizontal plane is respectively sigma'2And σ3', wherein σ'2And σ3The direction of ` is perpendicular, the strain of the particle assembly is ε1、ε2And ε3In which strain epsilon1、ε2And ε3Respectively in the direction of the stress sigma1′、σ′2And σ3The directions are the same; defining average effective stress p', shear stress q, stress ratio eta, and bulk strain epsilonvAnd shear strain epsilons：
Figure BDA0003024795260000032
Figure BDA0003024795260000033
Figure BDA0003024795260000034
εv＝ε1+ε2+ε3 (4)
Figure BDA0003024795260000041
Step 2: 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 (6)
(△εs)i＝(εs)i-(εs)i-1 (7)
Where the strain (epsilon) is cut at every moments)iAnd increase in shear strain (DELTA ε)s)iIs a known set value;
and step 3: calculating tiThe volume strain increment (delta epsilon) at the moment (i is more than or equal to 1 and less than or equal to n)v)i：
(△εv)i＝f(εs)·(△εs)i (8)
In formula (8), f (. epsilon.)s) Is shear strain epsilonsIs taken as a function of
Figure BDA0003024795260000042
Wherein, B1、C1、C2、C3Is a model parameter, B1Control curve f (. epsilon.)s) Width in horizontal direction, C1Control curve
Figure BDA0003024795260000043
Peak value, C2Correspond to
Figure BDA0003024795260000044
Shear strain at peak, C3Is approximately equal to
Figure BDA0003024795260000045
A minimum value;
and 4, step 4: calculating tiTime of day(1. ltoreq. i. ltoreq. n) bulk strain (. epsilon.)v)iAnd the void ratio e:
(εv)i＝(εv)i-1+(△εv)i (9)
e＝e0-(1+e0)(εv)i (10)
and 5: calculating tiStress ratio eta at time (i is more than or equal to 1 and less than or equal to n)i：
The stress ratio eta is calculated by the following formula:
Figure BDA0003024795260000051
in the above formula, α and K are material coefficients, ηpeakPeak stress ratio η; in the formula (11), eta is tiStress ratio eta at time (i is more than or equal to 1 and less than or equal to n)i，εsGet tiMoment shear strain (epsilon)s)i；
In step 5, formula (11), take
Figure BDA0003024795260000052
Wherein e0For initial void ratio, κ is the coefficient of restitution, and equation (11) is written as:
Figure BDA0003024795260000053
in formula (12), is
Figure BDA0003024795260000054
Wherein ecIs the critical void ratio, e is tiAt the moment (i is more than or equal to 1 and less than or equal to n), the porosity ratio, M is a material parameter and is equal to the critical stress ratio etacriticalM is a material parameter, wherein the critical state refers to a stable state after the stress ratio eta passes a peak value in a change curve along with the shear strain and a stable state after the body strain passes the peak value in the change curve along with the shear strain, and if the body strain is not stable after passing the peak value in the change curve along with the shear strain, the critical stress ratio eta is recorded at the last moment of loadingcriticalAnd critical void ratio ec(ii) a Get
Figure BDA0003024795260000055
Then, equation (12) is written as:
Figure BDA0003024795260000056
step 6: repeating the steps 3 to 5 until each t is calculatediVolume strain (epsilon) corresponding to time (i is more than or equal to 1 and less than or equal to n)v)iStress ratio etai。
In the calculation steps 1-6, the stress ratio eta is calculated and obtained when the stress is horizontal to the effective stress sigma'2And σ3Constant and equal, the effective vertical stress σ is obtained1', and mean effective and shear stresses:
Figure BDA0003024795260000061
Figure BDA0003024795260000062
in the above calculation steps 1 to 6, when the strain ε is measured in the horizontal direction2And ε3When the two strains are equal, the vertical strain epsilon can be obtained1And strain in horizontal direction epsilon3：
Figure BDA0003024795260000063
The invention has the beneficial effects that: the volume deformation and the volume deformation rate in the stress process of the silica gel-microfiber-sand complex formed by seepage and solidification of the calcareous sand by the microfiber-mixed silica sol are more accurately forecasted, namely the body strain epsilon is more accurately forecastedvVariation with load, and volume deformation ratio
Figure BDA0003024795260000064
As a function of loading.
Drawings
FIG. 1 is a schematic diagram of a silica gel-microfiber-sand composite formed after infiltration of a microfiber mixed silica sol to solidify calcareous sand, and subjected to vertical and horizontal stresses;
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 delta to shear strain delta as a function of stress ratio;
1. and (3) carrying out seepage curing on the calcium sand by mixing the microfibers with the silica sol to form a silica gel-microfiber-sand complex.
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.
The invention relates to some abbreviations and symbols, the following are notes:
σ1': vertical stress to which the aggregate of particles is subjected
σ′2And σ3': horizontal stress, σ ', to which the aggregate of particles is subjected'2And σ3Direction of ` perpendicular ∈1、ε2And ε3: strain and respectively stress sigma1、σ2And σ3Same direction
p': the average effective stress of the steel is measured,
Figure BDA0003024795260000071
q: the shear stress q is set to a value of,
Figure BDA0003024795260000072
eta: the stress ratio eta is such that,
Figure BDA0003024795260000073
ηcritical: critical stress ratio eta
ηpeak: is the peak stress ratio eta
εv: bulk strain, epsilonv＝ε1+ε2+ε3
εs: the shear strain is generated by the shear strain,
Figure BDA0003024795260000074
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
ηi：tiStress ratio eta at time (i is more than or equal to 1 and less than or equal to n)i
f(εs)：f(εs) Is shear strain epsilonsFunction of (2)
B1、C1、C2And C3：B1、C1、C2And C3Is the parameter of the model and is,
Figure BDA0003024795260000081
α: coefficient of material
K: coefficient of material
e0: initial void ratio
ec: critical void ratio
e：tiThe porosity ratio at the time (i is more than or equal to 1 and less than or equal to n)
Kappa: coefficient of restitution
M: material parameter equal to critical stress ratio etacritical
m: parameters of the material
The technical scheme of the invention is as follows: a deformation forecasting method for microfiber mixed silica sol solidified calcareous sand specifically comprises the following steps:
step 1: as shown in figure 1, after mixing, the silica sol and the silicon carbide nanowires seep through calcareous sand to form a silica gel-microfiber-sand complex 1, and the vertical stress is set to be sigma1'the stress on the horizontal plane is respectively sigma'2And σ3', wherein σ'2And σ3The direction of ` is perpendicular, the strain of the particle assembly is ε1、ε2And ε3In which strain epsilon1、ε2And ε3Respectively in the direction of the stress sigma1′、σ′2And σ3The directions are the same; defining average effective stress p', shear stress q, stress ratio eta, and bulk strain epsilonvAnd shear strain epsilons：
Figure BDA0003024795260000082
Figure BDA0003024795260000083
Figure BDA0003024795260000084
εv＝ε1+ε2+ε3 (4)
Figure BDA0003024795260000091
In this series of testsIn the method, the vertical loading mode is strain loading, namely the horizontal displacement is a constant, the test is a drainage consolidation triaxial test, and the horizontal effective stress sigma 'is'2And σ3' constant and equal, and σ3' As confining pressure, confining pressure is set to 100kPa,200kPa and 600kPa, respectively, and horizontal strain epsilon is2And ε3Equal, there are the following 3 relations:
Figure BDA0003024795260000092
Figure BDA0003024795260000093
Figure BDA0003024795260000094
step 2: 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 (6)
(△εs)i＝(εs)i-(εs)i-1 (7)
Where the strain (epsilon) is cut at every moments)iAnd increase in shear strain (DELTA ε)s)iIs a known set value;
and step 3: calculating tiThe volume strain increment (delta epsilon) at the moment (i is more than or equal to 1 and less than or equal to n)v)i：
(△εv)i＝f(εs)·(△εs)i (8)
In formula (8), f (. epsilon.)s) Is shear strain epsilonsIs taken as a function of
Figure BDA0003024795260000101
Wherein B is1、C1、C2、C3Is a model parameter, B1Control curve f (. epsilon.)s) Width in horizontal direction, C1Control curve
Figure BDA0003024795260000102
Peak value, C2Correspond to
Figure BDA0003024795260000103
Shear strain at peak, C3Is approximately equal to
Figure BDA0003024795260000104
A minimum value;
and 4, step 4: calculating tiTime (i is more than or equal to 1 and less than or equal to n) volume strain (epsilon)v)iAnd the void ratio e:
(εv)i＝(εv)i-1+(△εv)i (9)
e＝e0-(1+e0)(εv)i (10)
and 5: calculating tiStress ratio eta at time (i is more than or equal to 1 and less than or equal to n)i：
The stress ratio eta is calculated by the following formula:
Figure BDA0003024795260000105
in the above formula, α and K are material coefficients, ηpeakPeak stress ratio η; in the formula (11), eta is tiStress ratio eta at time (i is more than or equal to 1 and less than or equal to n)i，εsGet tiMoment shear strain (epsilon)s)i；
In step 5, formula (11), take
Figure BDA0003024795260000106
Wherein e0For initial void ratio, κ is the coefficient of restitution, and equation (11) is written as:
Figure BDA0003024795260000107
in formula (12), is
Figure BDA0003024795260000108
Wherein ecIs the critical void ratio, e is tiAt the moment (i is more than or equal to 1 and less than or equal to n), the porosity ratio, M is a material parameter and is equal to the critical stress ratio etacriticalM is a material parameter, wherein the critical state refers to a stable state after the stress ratio eta passes a peak value in a change curve along with the shear strain and a stable state after the body strain passes the peak value in the change curve along with the shear strain, and if the body strain is not stable after passing the peak value in the change curve along with the shear strain, the critical stress ratio eta is recorded at the last moment of loadingcriticalAnd critical void ratio ec(ii) a Get
Figure BDA0003024795260000111
Then, equation (12) is written as:
Figure BDA0003024795260000112
step 6: repeating the steps 3 to 5 until each t is calculatediVolume strain (epsilon) corresponding to time (i is more than or equal to 1 and less than or equal to n)v)iStress ratio etai。
The control test sample is a series of silica gel-microfiber-sand composites 1 formed by mixing silica sol with a concentration of 20%, microfibril with a concentration of 0.01% and silicon carbide nanowires, and then infiltrating the mixture through calcareous sandIn the test, the vertical loading mode is strain loading, namely the horizontal displacement is a constant, the test is a drainage consolidation triaxial test, and the horizontal effective stress sigma 'is'2And σ3' constant and equal, and σ3' is a confining pressure set to 100kPa,200kPa and 600kPa, respectively.
As shown in FIG. 2, the upper part a shows that the curve of the stress ratio with shear strain and the curve of the body strain with shear strain at the ambient pressure of 100kPa,200kPa and 600kPa predicted by the method given herein can be seen to be well matched with the actual test curve; while the lower b part shows the conventional ratio of the increase in bulk strain to the increase in shear strain (Deltaε)v)i＝(M-η)·(△εs)iThe calculation of the obtained curve and other parts is the same as the method proposed here, and it can be seen that the error of the predicted body strain curve displayed in part b is larger, especially the error is very obvious when the shear strain is from 0-5%.
As shown in FIG. 3, the upper part a shows the curve of the ratio of the increment of body strain to the increment of shear strain at the ambient pressure of 100kPa,200kPa and 600kPa predicted by the method given herein as a function of the stress ratio, which shows the rate of volume deformation
Figure BDA0003024795260000121
Along with the change of loading, the forecast curve conforms to the same trend as the actual test curve, namely, the forecast curve rises to the peak value at the beginning, then falls and has a hook back to the left; while the lower b part shows the conventional ratio of the increase in bulk strain to the increase in shear strain (Deltaε)v)i＝(M-η)·(△εs)iThe resulting curves, and the other parts calculated as described herein, are the same, and it can be seen that the predicted volumetric deformation ratios shown in part b
Figure BDA0003024795260000122
The curve changing along with the loading does not accord with the actual test, the forecast is only a straight line, and the initial section in the actual test does not rise and the final hook returns leftwards.

Claims (5)

1. A deformation forecasting method for microfiber mixed silica sol solidified calcareous sand is characterized by comprising the following steps:
which comprises the following steps:
step 1: let us assume that the vertical stress is σ 'for a silica gel-microfiber-sand composite body formed by seepage-curing calcareous sand with microfiber-mixed silica sol'1In the horizontal plane, the stress is σ'2And σ'3Wherein σ'2And σ'3Is perpendicular to the direction of the particle assembly and the strain of the particle assembly is epsilon1、ε2And ε3In which strain epsilon1、ε2And ε3Is respectively equal to the stress sigma'1、σ′2And σ'3The directions are the same; defining average effective stress p', shear stress q, stress ratio eta, and bulk strain epsilonvAnd shear strain epsilons：
Figure FDA0003024795250000011
Figure FDA0003024795250000012
Figure FDA0003024795250000013
εv＝ε1+ε2+ε3 (4)
Figure FDA0003024795250000014
Step 2: 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 tiTime of dayCorresponding body strain epsilonvIs (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 (6)
(△εs)i＝(εs)i-(εs)i-1 (7)
Where the strain (epsilon) is cut at every moments)iAnd increase in shear strain (DELTA ε)s)iIs a known set value;
and step 3: calculating tiTime-volume strain increase (Delta epsilon)v)i：
(△εv)i＝f(εs)·(△εs)i (8)
And 4, step 4: calculating tiTime volume strain (epsilon)v)iAnd the void ratio e:
(εv)i＝(εv)i-1+(△εv)i (9)
e＝e0-(1+e0)(εv)i (10)
and 5: calculating tiMoment to moment stress ratio etai：
The stress ratio eta is calculated by the following formula:
Figure FDA0003024795250000021
in the above formula, α and K are material coefficients, ηpeakPeak stress ratio η; in the formula (11), eta is tiMoment to moment stress ratio etai，εsGet tiMoment shear strain (epsilon)s)i；
Step 6: repetition ofStep 3-step 5, until each t is calculatediTime-corresponding body strain (epsilon)v)iStress ratio etai。
2. The method for forecasting the deformation of the microfiber mixed silica sol solidified calcareous sand according to claim 1, wherein the method comprises the following steps: in step 3, in formula (8), f (. epsilon.)s) Is shear strain epsilonsIs taken as a function of
Figure FDA0003024795250000022
Wherein B is1、C1、C2、C3Are the model parameters.
3. The method for forecasting the deformation of the microfiber mixed silica sol solidified calcareous sand according to claim 2, wherein the method comprises the following steps: b is1Control curve f (. epsilon.)s) Width in horizontal direction, C1Control curve
Figure FDA0003024795250000023
Peak value, C2Correspond to
Figure FDA0003024795250000024
Shear strain at peak, C3Is approximately equal to
Figure FDA0003024795250000025
A minimum value.
4. The method for forecasting the deformation of the microfiber mixed silica sol solidified calcareous sand according to claim 1, wherein the method comprises the following steps: in step 5, formula (11), take
Figure FDA0003024795250000031
Wherein e0For initial void ratio, κ is the coefficient of restitution, and equation (11) is written as:
Figure FDA0003024795250000032
5. the method for forecasting the deformation of the microfiber mixed silica sol solidified calcareous sand according to claim 4, wherein the method comprises the following steps: in formula (12), is
Figure FDA0003024795250000033
Wherein ecIs the critical void ratio, e is tiThe time-to-time porosity ratio, M is a material parameter and is equal to the critical stress ratio etacriticalM is a material parameter, taking
Figure FDA0003024795250000034
Then, equation (12) is written as:
Figure FDA0003024795250000035
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