CN113125263B - Forecasting method for stress deformation of silica sol cured non-breakable sandy soil - Google Patents
Forecasting method for stress deformation of silica sol cured non-breakable sandy soil Download PDFInfo
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- CN113125263B CN113125263B CN202110413274.3A CN202110413274A CN113125263B CN 113125263 B CN113125263 B CN 113125263B CN 202110413274 A CN202110413274 A CN 202110413274A CN 113125263 B CN113125263 B CN 113125263B
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Abstract
The invention relates to a forecasting method for stress deformation of silica sol solidified non-breakable sand, which is characterized in that a model is established for a silica gel-sand complex formed after silica sol seeps non-breakable sand from the angle of particle friction and cementation failure, the volume deformation and the volume deformation rate in the stress process are more accurately forecasted, and the typical characteristics of the volume deformation rate can be forecasted.
Description
Technical Field
The invention belongs to the field of geotechnical engineering research, and particularly relates to a prediction method for stress deformation of silica sol-cured non-breakable sandy soil.
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. The sand on land is generally non-breakable quartz sand, and after the quartz sand is solidified by silica sol, cementing damage and failure can occur in the stress process. The conventional method for forecasting the deformation of the silica sol solidified quartz sand has a large error, so that a method is lacked, and the volume deformation rate of a silica gel-quartz sand complex formed after the silica sol seeps into the quartz sand can be accurately forecasted in the stress process.
Disclosure of Invention
The invention provides a forecasting method for the stress deformation of silica sol cured non-breakable sandy soil, which aims to accurately forecast the volume deformation and the volume deformation rate of a silica gel-quartz sand complex formed after silica sol seeps quartz sand in the stress process.
The invention relates to some abbreviations and symbols, the following are notes:
σ 1 : vertical stress to which the aggregate of particles is subjected;
σ 2 and σ 3 : horizontal stress, σ, to which the assembly of particles is subjected 2 And σ 3 The direction of (A) is vertical;
ε 1 、ε 2 and ε 3 : strain and respectively stress sigma 1 、σ 2 And σ 3 The directions are the same;
p: the average effective stress of the steel is measured,
q: the shear stress q is a stress that is applied,
ε v : bulk strain, epsilon v ＝ε 1 +ε 2 +ε 3 ；
ε s : the shear strain is set to a value that is,
dε v : a bulk strain increment;
dε s : a shear strain increment;
d: for the solidified soil sample, the work generated by friction and silica gel cementation failure when the solidified soil sample is stressed;
E B : energy given off by failure of the silica gel bond;
m: material parameters and equal to critical stress ratio;
beta: is equal to the average effective stress p 0 Parameter of interest, β ═ k β1 p 0 +k β2 ；
k β1 ，k β2 : is a material parameter;
ρ 2 ：ρ 2 (ε s ) Is a variable related to shear strain;
α: parameter, and
τ 1 ,τ 2 : d epsilon in Legendre transform v And d ε s The corresponding conjugate variable is τ 1 ,τ 2 And p ═ τ 1 ，q-ρ 2 (ε s )＝τ 2 ；
B y1 ,B y2 And B y3 ：
A parameter related to shear strain, and
B 1 ,B 2 ,B 3 ,B 4 and B 5 ：ρ 2 A parameter related to shear strain, and
k B1 and k B2 : parameter, and B 4 ＝-k B1 p 0 +k B2 。
The technical scheme of the invention is as follows: a forecasting method for stress deformation of silica sol cured non-breakable sandy soil comprises the following steps:
step 1: setting the vertical stress of the silica sol cured non-breakable sandy soil to be sigma 1 Stress on the horizontal plane is respectively sigma 2 And σ 3 Where σ is 2 And σ 3 Is perpendicular to the direction of the particle assembly, the strain of the particle assembly is epsilon 1 、ε 2 And ε 3 Wherein strain ε 1 、ε 2 And ε 3 Respectively in the direction of the stress sigma 1 、σ 2 And σ 3 The directions are the same; defining average effective stress p, shear stress q, stress ratio eta, and bulk strain epsilon v And shear strain epsilon s ：
ε v ＝ε 1 +ε 2 +ε 3
And 2, step: let the work D generated by friction and silica gel bond failure be:
m is a material parameter and is equal to a critical stress ratio, beta is the initial average effective stress p 0 Parameter of interest, p 2 (ε s ) D ε is a variable related to shear strain v D ε being the increase in bulk strain s For shear strain increments, E B The energy given off for the failure of the silicone gel bond,
is E B For epsilon s Partial derivatives of (d);
taking a parameter alpha:
let d ε in Legendre transform v And d ε s The corresponding conjugate variable is τ 1 ,τ 2 ，τ 1 ,τ 2 And p, q are related as follows:
legendre transformation is carried out on the formula (1), and the formulas (2) and (3) are substituted to obtain the following equation:
and step 3: taking each shear strain increment, the ratio of the bulk strain to the shear strain increment is:
and 4, step 4: calculating the current shear strain ε s To the next shear strain epsilon s +dε s Delta d epsilon of body strain v ：
From equation (5), the volume strain increment is calculated
And 5: calculating shear strain ε s +dε s Body strain at time: d epsilon obtained by calculation in the step 4 v With current shear strain epsilon s Adding the corresponding bulk strains to obtain epsilon s +dε s Time bulk strain epsilon v Namely: epsilon v ←ε v +dε v ；
Step 6: calculating the shear strain ε by equation (4) s +dε s Corresponding to
Will epsilon s +dε s Calculated by substituting formula (4)
And 7: repeating the step 4 to the step 6 to obtain the body strain sum corresponding to each shear strain in the loading process
Preferably, in the formula (4)
The relationship to shear strain is:
in the above formula B y1 ，B y2 And B y3 Are parameters. Get B y1 When the number is equal to 1, the alloy is put into a container,
in relation to shear strain
The actual independent parameter is B y2 ,B y3 。
Preferably, in the formula (5) (. rho) 2 The relationship to shear strain is:
in the above formula B 1 ,B 2 ,B 3 ,B 4 And B 5 Are parameters.
Get B 2 ＝2，
(8) The formula is simplified as follows:
in the above formula, the independent parameter is B 1 ，B 4 ，B 5 。
Preferably, β is the sum of the mean effective stress p 0 Parameter of interest, β ═ k β1 p 0 +k β2
k β1 And k β2 Is a material parameter.
Preferably, B 4 Is and initial mean stress p 0 A parameter of interest, and B 4 ＝-k B1 p 0 +k B2 And k is B1 And k B2 Is a material parameter.
When the horizontal effective stress sigma 2 And σ 3 When the stress is constant and equal, the vertical effective stress sigma can be obtained 1 And average effective stress and shearStress:
preferably, in step 7, if the stress-strain relationship is obtained for the triaxial test, the stress-strain relationship is obtained by
Calculating the shear stress q as:
the invention has the beneficial effects that: the volume deformation and the volume deformation rate of a silica gel-quartz sand complex formed after silica sol seeps quartz sand are more accurately forecasted in the stress process.
Drawings
FIG. 1 is a schematic diagram of a silica gel-silica sand composite formed after silica sol has percolated through the silica sand, and subjected to vertical and horizontal stresses;
FIG. 2 is a graph showing the variation of shear stress with shear strain and the variation of bulk strain with shear strain;
FIG. 3 is a graph of the ratio of bulk strain increase to shear strain increase versus stress.
1 is a silica gel-quartz sand composite.
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:
σ 1 : vertical stress to which the assembly of particles is subjected
σ 2 And σ 3 : particle assembly receiverTo horizontal stress, σ 2 And σ 3 Is directed perpendicularly to
ε 1 、ε 2 And epsilon 3 : strain and respectively stress sigma 1 、σ 2 And σ 3 Same direction
p: the average effective stress of the steel is measured,
p 0 : initial mean effective stress
q: the shear stress q is set to a value of,
ε v : bulk strain, epsilon v ＝ε 1 +ε 2 +ε 3
ε s : the shear strain is generated by the shear strain,
dε v : increase in bulk strain
dε s : increment of shear strain
D: work produced by friction and silica gel cementation failure when stressed on a solidified soil sample
E B : energy released by failure of silica gel cementation
M: material parameter equal to critical stress ratio
Beta: is equal to the initial mean effective stress p 0 Parameter of interest, β ═ k β1 p 0 +k β2
k β1 ，k β2 : as a parameter of the material
ρ 2 ：ρ 2 (ε s ) As a variable related to shear strain
α: parameter(s)And is made of
τ 1 ,τ 2 : d epsilon in Legendre transform v And d ε s The corresponding conjugate variable is τ 1 ,τ 2 ，
And p ═ τ 1 ，q-ρ 2 (ε s )＝τ 2
B y1 ,B y2 And B y3 ：
A parameter that is related to the shear strain,
and is provided with
B 1 ,B 2 ,B 3 ,B 4 And B 5 ：ρ 2 A parameter related to the shear strain of the steel,
and is
k B1 And k B2 : parameter, and B 4 ＝-k B1 p 0 +k B2
Example 1
Performing seepage curing on Fujian quantan standard sand by using 30% silica sol, wherein the sand is quartz sand, and performing drainage triaxial tests with confining pressure of 200kPa and 300kPa, wherein the stress on a horizontal plane is sigma respectively 2 And σ 3 And σ is 2 And σ 3 Equal to the confining pressure, volume deformation and volume deformation rate are predicted based on the method proposed herein.
The technical scheme of the invention is as follows: a forecasting method for stress deformation of silica sol cured non-breakable sandy soil comprises the following steps:
step 1: setting the vertical stress of the silica sol cured non-breakable sandy soil as sigma shown in figure 1 1 Stress on the horizontal plane is respectively σ 2 And σ 3 Where σ is 2 And σ 3 Is perpendicular to the direction of the particle assembly and the strain of the particle assembly is epsilon 1 、ε 2 And ε 3 Wherein strain ε 1 、ε 2 And ε 3 Respectively in the direction of the stress sigma 1 、σ 2 And σ 3 The directions are the same; defining average effective stress p, shear stress q, stress ratio eta, and bulk strain epsilon v And shear strain epsilon s ：
ε v ＝ε 1 +ε 2 +ε 3
And 2, step: let the work D generated by friction and silica gel bond failure be:
m is a material parameter and is equal to a critical stress ratio, beta is the initial average effective stress p 0 Parameter of interest, p 2 (ε s ) D ε is a variable related to shear strain v D ε being the increase in bulk strain s For shear strain increments, E B The energy given off for the failure of the silicone gel bond,
is E B For epsilon s Partial derivatives of (d);
taking a parameter alpha:
let d ε in Legendre transform v And d ε s The corresponding conjugate variable is τ 1 ,τ 2 ，τ 1 ,τ 2 And p, q are related as follows:
legendre transformation is carried out on the formula (1), and the formulas (2) and (3) are substituted to obtain the following equation:
and 3, step 3: taking the ratio of the body strain to the shear strain increment (i.e. the body strain rate or volume deformation rate) in each shear strain increment as:
and 4, step 4: calculating the current shear strain ∈ s To the next shear strain epsilon s +dε s Delta d epsilon of body strain v ：
From equation (5), the volume strain increment is calculated
Here, the
In relation to shear strain of
In the formula B y1 ，B y2 And B y3 Taking B as a parameter y1 When the number is equal to 1, the alloy is put into a container,
in relation to shear strain
Actual independent parameter is B y2 ,B y3 ；
Here ρ 2 Is composed of
In the formula B 1 ,B 2 ,B 3 ,B 4 And B 5 Is a parameter; get B 2 ＝2，
The actual independent parameter is B 1 ，B 4 ，B 5 (ii) a And B 4 Is the sum of the initial mean stress p 0 Parameter of interest, B 4 ＝-k B1 p 0 +k B2 And k is B1 And k B2 Is a material parameter;
and 5: calculating shear strain epsilon s +dε s Body strain at time:
d epsilon obtained by calculation in the step 4 v With current shear strain epsilon s Adding the corresponding bulk strains to obtain epsilon s +dε s Time bulk strain epsilon v Namely: epsilon v ←ε v +dε v ；
Step 6: calculating the shear strain ε from equation (4) s +dε s Corresponding to
Will epsilon s +dε s Corresponding to formula (4) calculation
In the formula (4), beta is the sum of the mean effective stress p 0 Parameter of interest, β ═ k β1 p 0 +k β2 ，k β1 And k β2 Is a material parameter; and calculating the shear stress from the triaxial test conditions
And 7: repeating the step 4 to the step 6 to obtain the body strain corresponding to each shear strain in the loading process,
And shear stress q.
The following table lists the values of the above calculated parameters.
Table 1 independent parameter values in the calculation process
| M | k β1 | k β2 | y B2 | y B3 | B 1 | k B1 | k B2 | B 5 |
| 1.4 | -0.251×10 -3 | 175.8 | 9 | 1.1 | 15 | -0.006×10 -3 | 3 | 0.023 |
FIG. 2 shows the curve of shear stress with shear strain and the curve of body strain with shear strain, which shows that the body strain forecast is more in line with the test condition; FIG. 3 shows the ratio of the increase in bulk strain to the increase in shear strain (i.e., the bulk strain rate or referred to as the bulk strain rate) versus stress curve where
The bending section obtained by the test is forecasted before the peak value
After the peak value, a downward hook returning curve obtained by the test is well forecasted.
Claims (7)
1. A forecasting method for stress deformation of silica sol solidified non-breakable sandy soil is characterized in that: the method specifically comprises the following steps:
step 1: setting the vertical stress of the silica sol solidified non-breakable sandy soil to be sigma 1 Stress on the horizontal plane is respectively sigma 2 And σ 3 Where σ is 2 And σ 3 Is perpendicular to the direction of the particle assembly and the strain of the particle assembly is epsilon 1 、ε 2 And ε 3 In which strain epsilon 1 、ε 2 And ε 3 Respectively in the direction of the stress sigma 1 、σ 2 And σ 3 The directions are the same; defining average effective stress p, shear stress q, stress ratio eta, and bulk strain epsilon v And shear strain epsilon s ：
ε v ＝ε 1 +ε 2 +ε 3
Step 2: let the work D generated by friction and silica gel bond failure be:
m is a material parameter and is equal to a critical stress ratio, beta is the initial average effective stress p 0 Parameter of interest, p 2 (ε s ) D ε is a variable related to shear strain v D ε is the increase in bulk strain s For shear strain increments, E B The energy given off for the failure of the silicone gel bond,
is E B For epsilon s Partial derivatives of (d);
taking a parameter alpha:
let d ε in Legendre transform v And d ε s The corresponding conjugate variable is τ 1 ,τ 2 ，τ 1 ,τ 2 And p, q are related as follows:
legendre transformation is carried out on the formula (1), and the formulas (2) and (3) are substituted to obtain the following equation:
and step 3: taking each shear strain increment, the ratio of the bulk strain to the shear strain increment is:
and 4, step 4: calculating the current shear strain ∈ s To the next shear strain epsilon s +dε s Delta d epsilon of body strain v ：
From equation (5), the volume strain increment is calculated
And 5: calculating shear strain ε s +dε s Body strain at time: d epsilon obtained by calculation in the step 4 v With current shear strain epsilon s Adding the corresponding bulk strains to obtain epsilon s +dε s Time bulk strain epsilon v Namely: epsilon v ←ε v +dε v ；
Step 6: calculating the shear strain ε by equation (4) s +dε s Corresponding to
Will epsilon s +dε s Calculated by substituting formula (4)
And 7: repeating the step 4 to the step 6 to obtain the body strain sum corresponding to each shear strain in the loading process
2. The method for forecasting the stress deformation of the silica sol-cured non-breakable sandy soil according to claim 1, wherein the method comprises the following steps: in the formula (4)
The relationship to shear strain is:
in the above formula B y1 ，B y2 And B y3 Are parameters.
3. The method for forecasting the stress deformation of the silica sol-cured non-breakable sandy soil according to claim 2, wherein the method comprises the following steps: get B y1 ＝1，
In relation to shear strain
The actual independent parameter is B y2 ,B y3 。
4. The method for forecasting the stress deformation of the silica sol-cured non-breakable sandy soil according to claim 1, wherein the method comprises the following steps: in the formula (5) (. rho) 2 The relationship to shear strain is:
in the above formula B 1 ,B 2 ,B 3 ,B 4 And B 5 Are parameters.
5. The method for forecasting the stress deformation of the silica sol-cured non-breakable sandy soil according to claim 4, wherein the method comprises the following steps: get B 2 ＝2，
ρ 2 The relationship to shear strain is:
in the above formula, the independent parameter is B 1 ，B 4 ，B 5 。
6. The method for forecasting the stress deformation of the silica sol-cured non-breakable sandy soil according to claim 1, wherein the method comprises the following steps: beta is the sum of the initial mean effective stress p 0 Parameter of interest, β ═ k β1 p 0 +k β2 ，k β1 And k β2 Is a material parameter.
7. The method for forecasting the stress deformation of the silica sol-cured non-breakable sandy soil according to claim 1, wherein the method comprises the following steps: b is 4 Is the sum of the initial mean effective stress p 0 A parameter of interest, and B 4 ＝-k B1 p 0 +k B2 And k is B1 And k B2 Is a material parameter.
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| CN110411804B (en) * | 2019-09-02 | 2024-04-16 | 上海交通大学 | Test sample for mechanical properties of contact surface of soil body and structure, preparation method and test method |
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