CN108982326A - A kind of simplification prediction technique of the saturation soil body osmotic coefficient based on fractal theory - Google Patents
A kind of simplification prediction technique of the saturation soil body osmotic coefficient based on fractal theory Download PDFInfo
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- 239000002689 soil Substances 0.000 title claims abstract description 56
- 230000003204 osmotic effect Effects 0.000 title claims abstract description 18
- 238000000034 method Methods 0.000 title claims description 25
- 230000035699 permeability Effects 0.000 claims abstract description 59
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims abstract description 38
- 230000008595 infiltration Effects 0.000 claims abstract description 15
- 238000001764 infiltration Methods 0.000 claims abstract description 15
- 239000011800 void material Substances 0.000 claims description 16
- 229920006395 saturated elastomer Polymers 0.000 claims description 13
- 239000011148 porous material Substances 0.000 claims description 12
- 230000008569 process Effects 0.000 claims description 11
- HPNSNYBUADCFDR-UHFFFAOYSA-N chromafenozide Chemical compound CC1=CC(C)=CC(C(=O)N(NC(=O)C=2C(=C3CCCOC3=CC=2)C)C(C)(C)C)=C1 HPNSNYBUADCFDR-UHFFFAOYSA-N 0.000 claims description 10
- 239000012466 permeate Substances 0.000 claims description 5
- 238000009795 derivation Methods 0.000 claims description 3
- 238000009738 saturating Methods 0.000 claims description 3
- 230000035515 penetration Effects 0.000 claims description 2
- 238000004836 empirical method Methods 0.000 abstract description 3
- 238000011160 research Methods 0.000 abstract description 3
- 230000015572 biosynthetic process Effects 0.000 description 26
- 238000003786 synthesis reaction Methods 0.000 description 26
- 238000000465 moulding Methods 0.000 description 5
- 239000004576 sand Substances 0.000 description 5
- 239000011159 matrix material Substances 0.000 description 2
- 238000006467 substitution reaction Methods 0.000 description 2
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
- 230000007812 deficiency Effects 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 230000003993 interaction Effects 0.000 description 1
- 230000007246 mechanism Effects 0.000 description 1
- 238000012795 verification Methods 0.000 description 1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N15/00—Investigating characteristics of particles; Investigating permeability, pore-volume or surface-area of porous materials
- G01N15/08—Investigating permeability, pore-volume, or surface area of porous materials
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- Investigation Of Foundation Soil And Reinforcement Of Foundation Soil By Compacting Or Drainage (AREA)
Abstract
The invention discloses a kind of present invention, and TK saturation permeability coefficient model and soil-water characteristic curve fractal model to be combined to propose a kind of simplified prediction saturation soil body osmotic coefficient model
Description
Technical field
The invention belongs to soil body saturation permeability coefficient studying technological domains in building, geotechnical engineering, and in particular to Yi Zhongji
In the simplification prediction technique of the saturation soil body osmotic coefficient of fractal theory.
Background technique
The affecting laws for deforming soil body saturation permeability coefficient and air-entry value are to establish to consider waterpower, the mutual shadow of mechanical characteristic
Loud soil constitutive model, carries out the basis of the researchs such as saturated soil wind-structure interaction, therefore proves the soil body under deformation condition
The relationship of saturation permeability coefficient and air-entry value has great importance.For the saturation permeability coefficient under deformation condition, current one
As by establishing and the empirical relation of void ratio is predicted that this method is not deep enough to Study on Correlative Mechanisms, precision of prediction
It is to be improved.
Summary of the invention
The purpose of the present invention is to the deficiencies of above-mentioned technology, provide a kind of saturation soil body penetration based on fractal theory
The simplification prediction technique of coefficient overcomes and based on empirical method and calculates cumbersome lack to predicting coefficient of permeability in the prior art
Point.
To achieve the above object, the simplifying for saturation soil body osmotic coefficient based on fractal theory designed by the present invention is predicted
Method, the simplified prediction technique are as follows:
A kind of simplified prediction saturation soil body is proposed in conjunction with TK saturation permeability coefficient model and soil-water characteristic curve fractal model
Infiltration coefficient model, be saturated soil body osmotic coefficient simplifies prediction are as follows:
In formula (1), ksFor saturation permeability coefficient；kcIt is infiltration proportionality constant；Porosity φ=e/1+e, e are hole
Than；D is fractal dimension；ψaFor air-entry value；Wherein,γ is severe, and μ is pore water pressure, piFor i-stage hole
Gap channel physical length and soil sample length L ratio are pi, TsFor surface tension, α is contact angle.
Further, the combination TK saturation permeability coefficient model and soil-water characteristic curve fractal model propose a kind of simplification
Detailed process is as follows for prediction saturation soil body osmotic coefficient model:
TK saturation permeability coefficient model is
In formula (2), ksFor saturation permeability coefficient；kcIt is infiltration proportionality constant；θsIndicate saturation moisture content；θrIt indicates most
Small size water content；Wherein,γ is severe, and μ is pore water pressure, piIt is practical for i-stage pore channel
Length and soil sample length L ratio are pi, TsFor surface tension, α is contact angle；
Soil-water characteristic curve fractal model is
In formula (3), θ is volumetric water content, e0For initial void ratio, ψaFor air-entry value, ψ is matric suction；
Using ψ >=ψ in the formula (3) of soil-water characteristic curve fractal modelaFormula formula (2) is derived, formula
(3) both sides derivation simultaneously can obtain
Formula (4) are substituted into formula (2) and are obtained
In formula (5), kcTo permeate proportionality constant, since volumetric water content θ corresponds to ψ, θrTo indicate minimum volume water content
Corresponding ψd, saturated volume moisture content θsCorresponding ψa, can directly replace, ψ is matric suction, ψaFor air-entry value, ψdFor the suction of maximum matrix
Power, D are fractal dimension；
It from which further follows that
Due to D-5 < -2 and ψa< < ψd, (ψ can be ignoredd/ψa)D-5, can be by formula (6) abbreviation
Compared with prior art, the invention has the following advantages that present invention combination TK saturation permeability coefficient model and Tu Shui
Indicatrix fractal model proposes a kind of simplified prediction saturation soil body osmotic coefficient model, obtains the infiltration of the corresponding saturation soil body
Coefficient (permeability) overcomes and based on empirical method and calculates cumbersome disadvantage to the prediction of infiltration coefficient in the prior art, right
It has great significance in practical engineering application and theoretical research.
Detailed description of the invention
Fig. 1 is the prognostic chart that Wuhan cohesive soil predicts saturation permeability coefficient according to air-entry value measured value in embodiment；
Fig. 2 is the prognostic chart that Touchet silt loam predicts saturation permeability coefficient according to air-entry value measured value in embodiment；
Fig. 3 is the prognostic chart that Columbia sandy loam predicts saturation permeability coefficient according to air-entry value measured value in embodiment；
Fig. 4 is the prognostic chart that the fluffing of moulding sand predicts saturation permeability coefficient according to air-entry value measured value in embodiment.
Specific embodiment
The following further describes the present invention in detail with reference to the accompanying drawings and specific embodiments.
A kind of simplification prediction technique of the saturation soil body osmotic coefficient (permeability) based on fractal theory, specific method is such as
Under:
It is mentioned in conjunction with TK saturation permeability coefficient model (pottery hole saturation permeability coefficient model) and soil-water characteristic curve fractal model
A kind of simplified prediction saturation soil body osmotic coefficient (permeability) model, saturation soil body osmotic coefficient (permeability) simplify prediction out
Are as follows:
In formula (1), ksFor saturation permeability coefficient；kcIt is infiltration proportionality constant；Porosity φ=e/1+e, e are hole
Than；D is fractal dimension；ψaFor air-entry value；Wherein,γ is severe, and μ is pore water pressure, piFor i-stage hole
Gap channel physical length and soil sample length L ratio are pi, TsFor surface tension, α is contact angle.
It is mentioned in conjunction with TK saturation permeability coefficient model (pottery hole saturation permeability coefficient model) and soil-water characteristic curve fractal model
Detailed process is as follows for a kind of simplified prediction saturation soil body osmotic coefficient (permeability) model out:
TK saturation permeability coefficient model is
In formula (2), ksFor saturation permeability coefficient；kcIt is infiltration proportionality constant；θsIndicate saturation moisture content；θrIt indicates most
Small size water content；Wherein,γ is severe, and μ is pore water pressure, piIt is practical for i-stage pore channel
Length and soil sample length L ratio are pi, TsFor surface tension, α is contact angle；
Soil-water characteristic curve fractal model is
In formula (3), θ is volumetric water content, e0For initial void ratio, ψaFor air-entry value, ψ is matric suction；
Using ψ >=ψ in the formula (3) of soil-water characteristic curve fractal modelaFormula formula (2) is derived, formula
(3) both sides derivation simultaneously can obtain
Formula (4) are substituted into formula (2) and are obtained
In formula (5), kcTo permeate proportionality constant, since volumetric water content θ corresponds to ψ, θrTo indicate minimum volume water content
Corresponding ψd, saturated volume moisture content θsCorresponding ψa, can directly replace, ψ is matric suction, ψaFor air-entry value, ψdFor the suction of maximum matrix
Power, D are fractal dimension；
It from which further follows that
Due to D-5 < -2 and ψa< < ψd, (ψ can be ignoredd/ψa)D-5, can be by formula (6) abbreviation
In conjunction with soil-water characteristic curve and TK saturation permeability coefficient model, using fractal theory, derives and simplify prediction saturation
Soil body osmotic coefficient (permeability) model divides shape form, predict soil body saturation permeability coefficient and air-entry value square at anti-
Than.
Below with reference to classics saturation permeability coefficient model known to two kinds, corresponding infiltration is derived respectively using fractal theory
Saturating Modulus Model divides shape form, passes through experimental verification simplified prediction saturation soil body osmotic coefficient (permeability) proposed by the present invention
The relationship that soil body saturation permeability coefficient and air-entry value square are inversely proportional is predicted in model, to reach prediction soil body saturation
The purpose of coefficient (permeability).
CCG model
Mualem model
In formula (7), formula (8): ksFor saturation permeability coefficient；kcIt is infiltration proportionality constant；ψ is matric suction；θsIt indicates
Saturation moisture content；θrIndicate minimum volume water content；Wherein,γ is severe, and μ is pore water pressure, piFor
I-stage pore channel physical length and soil sample length L ratio are pi, TsFor surface tension, α is contact angle.
CCG model is derived using existing soil-water characteristic curve fractal model formula (3)
Enable θ=x and in the saturated condition volumetric water contentIt can obtainSubstitute into ψ >=ψ in formula (3)aSaturation situation in
It from which further follows that
Formula (10) formula substitution formula (7) formula is obtained
Formula (11) obtains
Because of θr< < θs, therefore (θ can be ignoredr/θs)(5-D)/(3-D)And (θr/θs)(8-2D)/(3-D), then formula (12) obtains
In formula (13), kcIt is infiltration proportionality constant；Porosity φ=e/1+e；D is fractal dimension；ψaFor air-entry value.
Mualem model is derived using existing soil-water characteristic curve fractal model formula (3)
Formula (4) formula substitution formula (8) formula is obtained
In formula (14), kcTo permeate proportionality constant, since volumetric water content θ corresponds to ψ, θrTo indicate that minimum volume is aqueous
Measure corresponding ψd, saturated volume moisture content θsCorresponding ψa, can directly replace, porosity φ=e/1+e, ψ are matric suction, ψaFor into
Gas value, ψdFor maximum matric suction, D is fractal dimension；
It can further obtain:
Because of 4-D > 1, ψa< < ψd, therefore negligible (ψa/ψd)4-D, then formula (15) obtains
Wherein, in formula (16), kcIt is infiltration proportionality constant；Porosity φ=e/1+e；D is fractal dimension；ψaFor air-entry value.
The saturation permeability coefficient model of analysis and contrast equation (1), formula (13) and formula (16) divides shape form, discovery
Formula (1), formula (13) and formula (16) show square being inversely proportional for saturation permeability coefficient and air-entry value.And preliminary analysis
It is found that the variation range of air-entry value is bigger, then influence of the air-entry value to saturation permeability coefficient is bigger.
Below based on the experimental data of four kinds of soil bodys, to square pass being inversely proportional of saturation permeability coefficient and air-entry value
System is verified, and key data index is shown in Table 1.
Below with reference to specifically example is applied, the invention will be further described:
Soil sample used in the present embodiment is Wuhan cohesive soil, Touchet silt loam, Columbia sandy loam and the fluffing of moulding sand.By
In similar soil sample, Fractal dimensions are almost equal under the conditions of different initial void ratios.Permeate proportionality constant kcIt should for same soil sample
Value is constant, proportionality constant k in formula (1), formula (13) and formula (16)cBeing for the same class soil body is constant.
So according to saturation permeability coefficient (permeability), the air-entry value, hole of (maximum initial void ratio) soil sample before deformation
Than can calculating synthesis in formula (1), formula (13) and formula (16), (synthesis includes than column constant than column constant
kc, Fractal dimensions value all constant terms).
Using the synthesis proportionality constant, deformed air-entry value and void ratio measured value can predict corresponding saturation and seep
Saturating coefficient (permeability).And since the synthesis scalefactor value of formula (13) and formula (16) is identical, therefore formula (13) predicted value
It is identical as formula (16) prediction result, therefore enumerate formula (13) in formula (13) and formula (16).K in specific formula (1)s
K in predicted value and formula (13)sThe calculating process of predicted value is by taking Wuhan cohesive soil and Touchet silt loam as an example.
Embodiment 1
According to the maximum initial void ratio e measured before the deformation of Wuhan listed in table 1 cohesive soil0=1.115, it is full
And osmotic coefficient ks=2.806E-04cm/s, air-entry value ψa=1.660kPa, porosity θ=0.527, respectively substitute into formula (1),
It can calculate separately out that formula (1), (synthesis includes k than column constant to the synthesis in formula (13) than column constant in formula (13)c、
All constant terms of Fractal dimensions value).The synthesis of formula (1) can be calculated than column constantAnd (6) formula
Synthesis is than column constantIn the situation known to the comprehensive proportionality constant of every kind of soil body, become
During shape, void ratio e and air-entry value ψ need to be only measureda(or obtaining through data fitting) can be to corresponding saturation permeability coefficient
Value is predicted.Such as work as e1=1.037, ψ1When=2.150kPa, corresponding formula (1)
1.62E-04cm/s, k in formula (13)s1Predicted value is 1.56E-04cm/s.For another example work as e2=0.964, ψ2=8.010KPa
When, comprehensive, in the formula (1) that at this time calculates k more constant than column constants2Predicted value is 1.12E-05cm/s, k in formula (13)s2
Predicted value is 1.05E-05cm/s.Remainder data calculating process is similar in the cohesive soil of Wuhan, does not make excessive tedious statement.
Embodiment 2
According to the maximum initial void ratio e measured before Touchet silt loam listed in table 1 deformation0=1.012,
Its saturated permeability is 0.695 μm2, air-entry value ψa=4.130kPa, porosity θ=0.503 substitute into formula (1), formula respectively
(13) it can calculate separately out that formula (1), (synthesis includes k than column constant to the synthesis in formula (13) than column constant inc, point dimension
All constant terms of number D value).The synthesis that formula (1) can be calculated is 23.567 than column constant and the synthesis of formula (13) is more normal than arranging
Number is 46.854.In the situation known to the comprehensive proportionality constant of every kind of soil body, in deformation process, need to only measure void ratio e and into
Gas value ψa(or obtaining through data fitting) can predict corresponding saturated permeability.Such as work as e1=0.916, ψ1=
When 5.070kPa, the synthesis of corresponding formula (1) than column constant, calculates at this time than the synthesis of column constant and formula (13)
Formula (1) ks1Predicted value is 0.438 μm2, formula (13) ks1Predicted value is 0.416 μm2.For another example work as e2=0.815, ψ2=
When 6.350KPa, comprehensive, formula (1) formula k at this time calculating more constant than column constants2Predicted value is 0.262 μm2, formula (13) ks2
Predicted value is 0.234 μm2.Remainder data calculating process is similar in Touchet silt loam, does not make excessive tedious statement.
Embodiment 3
According to the maximum initial void ratio e measured before Columbia sandy loam listed in table 1 deformation0=1.268, its
Saturated permeability is 2.470 μm2, air-entry value ψa=2.650kPa, porosity θ=0.559 substitute into formula (1), formula respectively
(13) it can calculate separately out that formula (1), (synthesis includes k than column constant to the synthesis in formula (13) than column constant inc, point dimension
All constant terms of number D value).The synthesis that formula (1) can be calculated is 31.029 than column constant and the synthesis of formula (13) is more normal than arranging
Number is 55.509.In the situation known to the comprehensive proportionality constant of every kind of soil body, in deformation process, need to only measure void ratio e and into
Gas value ψa(or obtaining through data fitting) can predict corresponding saturated permeability.Such as work as e1=1.114, ψ1=
When 3.340kPa, the synthesis of corresponding formula (1), than column constant, is calculated at this time than the synthesis of column constant and formula (13) formula
Formula (1) k outs1Predicted value is 1.465 μm2, formula (13) ks1Predicted value is 1.382 μm2.For another example work as e2=0.942, ψ2=
When 4.520KPa, comprehensive, formula (1) k at this time calculating more constant than column constants2Predicted value is 0.736 μm2, formula (13) ks2In advance
Measured value is 0.639 μm2.Remainder data calculating process is similar in Columbia sandy loam, does not make excessive tedious statement.
Embodiment 4
According to the maximum initial void ratio e measured before the fluffing of moulding sand listed in table 1 deformation0=0.852, its saturation
Rate is 139.200 μm2, air-entry value ψa=0.490kPa, porosity θ=0.460, substitute into formula (1), can in formula (13) respectively
Calculate separately out that formula (1), (synthesis includes k than column constant to the synthesis in formula (13) than column constantc, Fractal dimensions values
All constant terms).The synthesis that formula (1) can be calculated is 72.656 than column constant and the synthesis of formula (13) is than column constant
157.949.In the situation known to the comprehensive proportionality constant of every kind of soil body, in deformation process, void ratio e and air-entry value need to be only measured
ψa(or obtaining through data fitting) can predict corresponding saturated permeability.Such as work as e1=0.825, ψ1=0.520kPa
When, the synthesis of corresponding formula (1) than the synthesis of column constant and formula (13) than column constant, the formula (1) that calculates at this time
ks1Predicted value is 121.451 μm2, formula (13) ks1Predicted value is 119.340 μm2.For another example work as e2=0.799, ψ2=0.540KPa
When, comprehensive, formula (1) k at this time calculating more constant than column constants2Predicted value is 112.621 μm2, formula (13) ks2Predicted value is
106.781μm2.Remainder data calculating process is similar in the fluffing of moulding sand, does not make excessive tedious statement.
In conclusion table 1 and Fig. 1, Fig. 2, Fig. 3, Fig. 4 show for cohesive soil, silt loam, sandy loam and fluffing of moulding sand number
According to being analyzed, theoretical and saturation permeability coefficient (permeability) and measured value as obtained by formula (1) proposed by the present invention are obtained
More closely, confirming that the present invention is a kind of method of easy and practical prediction soil body saturation permeability coefficient (permeability).
Air-entry value, saturation permeability coefficient measured value and the predicted value of 1 four kinds of soil bodys of table
Claims (2)
1. a kind of simplification prediction technique of the saturation soil body osmotic coefficient based on fractal theory, it is characterised in that: the simplification is pre-
Survey method is as follows:
A kind of simplified prediction saturation soil body penetration is proposed in conjunction with TK saturation permeability coefficient model and soil-water characteristic curve fractal model
Modulus Model, be saturated soil body osmotic coefficient simplifies prediction are as follows:
In formula (1), ksFor saturation permeability coefficient；kcIt is infiltration proportionality constant；Porosity φ=e/1+e, e are void ratio；D is
Fractal dimension；ψaFor air-entry value；Wherein,γ is severe, and μ is pore water pressure, piFor i-stage pore channel
Physical length and soil sample length L ratio are pi, TsFor surface tension, α is contact angle.
2. the simplification prediction technique of the saturation soil body osmotic coefficient based on fractal theory, feature exist according to claim 1
In: the combination TK saturation permeability coefficient model and soil-water characteristic curve fractal model propose that a kind of simplified prediction saturation soil body seeps
Detailed process is as follows for saturating Modulus Model:
TK saturation permeability coefficient model is
In formula (2), ksFor saturation permeability coefficient；kcIt is infiltration proportionality constant；θsIndicate saturation moisture content；θrIndicate minimum volume
Water content；Wherein,γ is severe, and μ is pore water pressure, piFor i-stage pore channel physical length with
Soil sample length L ratio is pi, TsFor surface tension, α is contact angle；
Soil-water characteristic curve fractal model is
In formula (3), θ is volumetric water content, e0For initial void ratio, ψaFor air-entry value, ψ is matric suction；
Using ψ >=ψ in the formula (3) of soil-water characteristic curve fractal modelaFormula formula (2) is derived, formula (3) two
Side derivation simultaneously can obtain
Formula (4) are substituted into formula (2) and are obtained
In formula (5), kcTo permeate proportionality constant, since volumetric water content θ corresponds to ψ, θrTo indicate that minimum volume water content is corresponding
ψd, saturated volume moisture content θsCorresponding ψa, can directly replace, ψ is matric suction, ψaFor air-entry value, ψdFor maximum matric suction, D
For fractal dimension；
It from which further follows that
Due to D-5 < -2 and ψa< < ψd, (ψ can be ignoredd/ψa)D-5, can be by formula (6) abbreviation
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| CN110018102A (en) * | 2019-04-19 | 2019-07-16 | 湖北工业大学 | A kind of bimodal SWCC fractal fitting model |
| CN113310871A (en) * | 2021-05-21 | 2021-08-27 | 湖北工业大学 | Simplified and unified method for predicting air intake value based on saturated permeability coefficient |
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