CN110705015B - Foam improved soil permeability prediction method based on interaction of foam and soil particles - Google Patents

Foam improved soil permeability prediction method based on interaction of foam and soil particles Download PDF

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CN110705015B
CN110705015B CN201910789077.4A CN201910789077A CN110705015B CN 110705015 B CN110705015 B CN 110705015B CN 201910789077 A CN201910789077 A CN 201910789077A CN 110705015 B CN110705015 B CN 110705015B
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foam
soil
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黄硕
王树英
钟嘉政
胡钦鑫
刘朋飞
蔡根森
瞿勇
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Central South University
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Abstract

The invention discloses a foam improved soil permeability prediction method based on interaction of foam and soil particles, which is based on the interaction of the foam and the soil particles in foam improved soil (namely the influence of the soil particles on the number of effective seepage channels of the foam), utilizes a pure foam seepage theory, considers the seepage of fluid in a pore channel of the foam improved soil as Poisea flow, and establishes a permeability coefficient prediction method under the condition of fully improving the foam improved soil. Since the soil and the foam are particle aggregates with highly non-uniform particle diameters, their respective effective particle diameters d are selected10As its effective particle size during the calculation of the permeability coefficient. The method can provide a scientific method for predicting the permeability of the foam improved sandy muck in the shield tunnel construction process, and provides guidance for selecting foam improvement parameters of different grades of sandy stratums, so that the risk of tunneling and gushing of the shield in a water-rich stratum is effectively avoided.

Description

Foam improved soil permeability prediction method based on interaction of foam and soil particles
Technical Field
The invention belongs to the technical field of shield tunnel engineering construction, and particularly relates to a foam-based improved soil permeability prediction method.
Background
The slag soil generated in the shield tunneling process is required to have good flow plasticity, good impermeability, appropriate compressibility, low adhesion and small internal friction angle. The guarantee of the impermeability of the dregs is a key factor of the safe tunneling of the shield, and if the impermeability of the dregs is not improved in place, the gushing of the screw conveyor is easily induced, so that a large seepage force is generated, the stability of the tunnel face is not facilitated, and the settlement and even instability of the ground surface are caused, so that a cake-shaped impermeable layer needs to be formed in front of the shield through the improvement of the dregs in the tunneling process of the shield. Common muck modifier comprises foam, bentonite slurry and high molecular polymer, and the foam is most widely applied to muck modification due to the advantages of low price, simple and convenient preparation and the like.
However, due to the instability of the foam itself, the permeability of the foam-modified soil actually shows a certain time-varying property in that the permeability coefficient of the foam-modified soil is stabilized at a lower level for a certain period of time at the initial stage of the permeation, and thereafter the permeability coefficient gradually increases with time and finally tends to be stabilized. Therefore, to prevent gushing during shield tunneling, the permeability coefficient of the foam-modified soil should be maintained at 10-6～10-5m/s or less. Numerous scholars have explored the permeability of foam-modified soils. The basic composition of the foam modified soil is soil and foam for modifying the soil, wherein the particle size of the soil has an important influence on the permeability of the modified soil. The foam has better effect of improving the permeability of sandy soil and has poorer effect of improving silt and pebble soil.
The research on the permeability of the foam-improved soil currently mostly stays at the qualitative analysis stage of the experimental results, Bezuijen et al (A Decode of progress. GeoDelft 1995-2005(pp.41-47)) introduces the Blake-Kozeny equation into the calculation of the permeability of the foam-improved soil, but the assumed conditions have limitations and the prediction error is larger when the porosity of the foam-improved soil is smaller, so that the research result about the effective calculation theory of the permeability coefficient of the foam-improved soil is up to now.
Disclosure of Invention
The present application is directed to solving at least one of the problems in the prior art. Therefore, one of the purposes of the invention is to provide a foam-improved soil permeability prediction method based on the interaction of foam and soil particles, which has the advantages of simple process, clear logic and high practicability.
In order to solve the technical problems, the invention adopts the following technical scheme:
a foam improved soil permeability prediction method based on interaction of foam and soil particles comprises the following steps:
step 1: calculating the equivalent diameter D of the berraph channel interface in the foam system
Step 2: calculating the flow q of a single pareto channel in a foam system according to the equivalent diameter D of the pareto channel interface obtained in the step 1
And step 3: calculating the number of effective seepage channels of the foam improved soil
Wherein, the total effective seepage channel quantity s in the foam improved soil is calculated by adopting the following formula:
Figure BDA0002178970930000021
wherein: d10,sIs the effective particle size of the soil particles, d10,fThe effective grain size of the foam is shown, p is the porosity of the foam improved soil, and S is the cross-sectional area of the foam improved soil sample;
and 4, step 4: obtaining an expression of the permeability coefficient of the foam improved soil according to the flow q and the number s of the effective seepage channels obtained in the step 2 and the step 3:
k＝AB
in the formula:
Figure BDA0002178970930000022
the ratio of the total area (sW) of effective seepage channels in soil to the sectional area (S) of the whole foam improved soil is shown;
Figure BDA0002178970930000023
the average permeability coefficient of a single platogram channel in the foam;
Figure BDA0002178970930000024
beta represents the fineness of the foam relative to the soil particles; gamma is the water gravity; mu is the dynamic viscosity of water; i is the hydraulic gradient of seepage and W is the cross-sectional area of the channel of the single platogram.
Further, it was analyzed that the permeability coefficient k of the foam-modified soil approaches to that of pure foam as the porosity p of the foam-modified soil approaches to 1fAnd meanwhile, the foaming rate of the foam is used for expressing the porosity of the pure foam, so that the expression form of the calculation formula of the permeability coefficient of the foam improved soil can be optimized by combining the foaming rate of the foam, and the optimized calculation formula of the permeability coefficient of the foam improved soil is obtained.
Further, the porosity is p for a pure foamfThe permeability coefficient of pure foam can be deduced by combining the formula parameter B to solve the formula:
Figure BDA0002178970930000031
is due to the fact that
Figure BDA0002178970930000032
Then
Figure BDA0002178970930000033
The foaming ratio FER of the foam is:
Figure BDA0002178970930000034
wherein: vfIs the volume of foam emitted; vlVolume of solution used for foaming;
since the pores between the foams are filled with water, the porosity available for flow-through in the foam is taken to be
Figure BDA0002178970930000035
By using
Figure BDA0002178970930000036
Replacement of
Figure BDA0002178970930000037
The solution for k can be further optimized as:
Figure BDA0002178970930000038
further, the concrete solving process of the number of the effective seepage channels of the foam improved soil is as follows:
calculating the number m of soil particles on the cross section area of the foam improved soil sample and the number of foams as n:
Figure BDA0002178970930000039
Figure BDA00021789709300000310
wherein: p is the porosity of the foam improved soil, S is the cross-sectional area of the foam improved soil sample, d10,fIs the effective particle size of the foam, d10,sIs the effective particle size of the soil particles;
the number of bubbles n in an isostatically stacked foam aggregate is related to the number of berrah channels s':
s′＝2n
because effective seepage channels in the foam cannot be formed due to the contact of the foam and the soil particles, once the effective seepage channels in the foam mixed with the soil particles in the foam are correspondingly reduced, the total number n' of the foam in contact with the soil particles is as follows:
Figure BDA0002178970930000041
in the formula: l is the sum of the peripheral lengths of all the particles on the section of the foam-modified soil, i.e. l ═ pi md10,s；
Further derivation yields:
Figure BDA0002178970930000042
since each foam, once in contact with the soil particle boundary, reduces one plat channel, the number of losses Δ s of foam in contact with soil particles in the plat channel is:
Figure BDA0002178970930000043
further, the total effective number s of the seepage channels in the foam-modified soil is:
Figure BDA0002178970930000044
further, the concrete solving process of the permeability coefficient of the foam improved soil is as follows:
according to the flow Q and the number s of the effective seepage channels, the total seepage flow Q on the cross section of the foam improved soil sample is as follows:
Q＝sq
calculating the seepage flow rate of the foam improved soil according to the relation between the fluid flow rate v and the flow rate Q:
Figure BDA0002178970930000045
from Darcy's law
v＝ki
The formula of the combined type can obtain a calculation formula of the permeability coefficient of the foam improved soil:
Figure BDA0002178970930000046
the final calculation formula of the permeability coefficient k of the foam improved soil can be further derived through the formula.
Further, the solving process of the equivalent diameter of the berla channel interface is as follows: forming a plat diagram channel among every 3 bubbles in the foam system, calculating the equivalent diameter of the plat diagram channel by using a basic theory of hydraulics, regarding each foam enclosing the plat diagram channel as a circle, and obtaining the overflowing equivalent hydraulic radius and the equivalent diameter of the plat diagram channel by using the following formulas:
Figure BDA0002178970930000051
Figure BDA0002178970930000052
D＝4R
wherein: r is the hydraulic radius of the passage section of the plat drawing; w is the cross section of the passage of the platura; chi is the wet circumference of the passage of the platane; d is the equivalent diameter of the passage section of the platonic section.
Further, the specific solving process of the flow q of the single pareto channel is as follows:
the liquid in the foam flows in the passage of the berrah graph as the flow of the poiseuille, and the flow velocity equation of the flow of the poiseuille is as follows:
Figure BDA0002178970930000053
in the formula: u. ofpIs the flow velocity of each point in the channel section, d is the diameter of the flow passage, Δ p is the on-way pressure loss, r is the flow velocity and the distance between the calculation point and the central axis of the channel, μ is the dynamic viscosity of the fluid, and L is the channel length;
the average flow velocity of the fluid on the channel cross section can be obtained by the following formula:
Figure BDA0002178970930000054
in the formula: u is the permeation flow rate of the foam, i is the hydraulic gradient, and γ is the water gravity;
the formula above in conjunction yields the average flow velocity equation in the passage of the platane:
Figure BDA0002178970930000055
the flow q of the single pareto channel is:
Figure BDA0002178970930000056
compared with the prior art, the invention has the technical advantages that:
advantage (1): the model is a first calculation model of the permeability of the foam improved soil based on theoretical derivation, which is provided at the present stage, and the model derivation is carried out from basic science basic law, so that the model is supported by a relatively sufficient theory;
advantage (2): the model can calculate the permeability coefficient of the fully improved foam improved soil, and is particularly suitable for calculating the permeability coefficient of the foam improved soil with better original soil body grading. Normally, the calculated value of the model can be controlled to be in the same order of magnitude as the actual value;
advantage (3): the calculation formula of the model recommendation relates to the effective particle size d of the soil10,sEffective particle size d of the foam10,fThe model can be used for researching and analyzing the influence of each physical quantity on the permeability of the foam improved soil, and further guiding the scheme design when the foam is used for improving the permeability of the soil;
in conclusion, the shield foam improved soil permeability coefficient calculation model provided by the invention has novel entry point, can realize the prediction of the improved soil permeability coefficient under various different foam improvement working conditions, considers a plurality of key factors in the model establishing process to ensure that the model is real and effective, and finally provides the effective particle size d of the soil10,sEffective particle size d of the foam10,fAnd an improved soil permeability coefficient calculation formula of the foam improved soil porosity p.
Drawings
Figure 1 is pure foam percolation intent foam: (a) a foam seepage basic unit; (b) sectional view of foam basic unit seepage channel; (c) sectional view of seepage channel of foam basic unit;
FIG. 2 is a schematic diagram of the calculation of equivalent diameter of the passage of the platoon;
FIG. 3 is a schematic view of foam filling in soil: (a) a schematic diagram of a real filling mode of foam and soil; (b) the proportion of foam and soil in the foam improved soil is shown schematically;
FIG. 4 is a model of foam filling pattern between soil particles;
FIG. 5 is a schematic diagram showing the relationship between the number of passages in the platoon and the number of bubbles;
FIG. 6 is a schematic diagram of the calculation of the amount of foam contacting soil particles;
FIG. 7 shows the variation of the passage of the tara map with foam in contact with the soil: (a) the four foams are contacted with each other to form two schematic diagrams of the passage of the platane; (b) a schematic diagram of the passage of the tarmac maintained by the foam if the contact angle is not considered; (c) schematic representation of the attenuation of the passage of the platura due to the presence of contact angles when the foam contacts the surface of the soil particles.
Detailed Description
The present invention will be further described with reference to specific embodiments.
A foam improved soil permeability prediction method based on interaction of foam and soil particles comprises the following steps:
step S1: it is believed that every 3 bubbles in the foam system enclosed a berrama channel in the shape of a concave triangle, as shown in figure 1. For the calculation of the channel flow velocity, the average flow velocity calculation formula of the flow of the Poiseuille in the circular tube is mostly used at present, and the seepage interface of the Bolavian channel in the foam seepage is a curved triangle as shown in the attached figure 2, so that the equivalent diameter of the curved triangle can be calculated by using the basic theory of hydraulics.
Step S2: according to the fact that the liquid in the foam flows in the berla graph channel as the flow of the poiseuille, the equivalent diameter of the curved triangle obtained in the step S1 is used to bring the equivalent diameter into a flow velocity equation of the flow of the poiseuille in the circular tube, and further the flow q of the single berla graph channel can be obtained.
Step S3: assuming that the soil is sufficiently improved by the foam, the foam fills the soil particle framework, the porosity of the foam-improved soil is p, the cross-sectional area of the foam-improved soil sample is S, the total area of the soil particles on the cross section is (1-p) S, and the total area of the pores is pS, and the area of the foam on the cross section is pS because the foam fills the soil particle framework, as shown in FIG. 3.
Since the soil particles and the foam are piled bodies having non-uniform particle diameters, in order to mathematically analyze the permeability of the soil particles and the foam, the effective particle diameters d of the soil particles and the foam are respectively taken10To analyze the permeability characteristics, let the effective particle size of the soil particles be d10,sEffective particle size of the foam is d10,fAnd the soil and the foam are respectively viewedAs diameter d10,sAnd d10,fA single diameter spherical particle packing body.
Note: the effective particle size is the particle size corresponding to the accumulated mass of the particles reaching 10% on the foam or soil grade matching characteristic curve.
Then the number of the soil particles on the section is m and the number of the foams is n can be obtained by using the geometric relation
Since the foam is filled in the pores between the soil particles, the filling manner can be generalized to the model shown in FIG. 4, i.e., the pores of the soil particles are uniformly and well filled with the foam with the diameter dfEvery three foams are contacted with each other to form a plat channel, and because of the hydrophilicity of the soil particle surface, the contact angle of the foams and the soil is generated, so that the plat channel can not be formed, and the plat channel is a seepage channel in the model. From FIG. 5, the number of each foam n in an isostatically stacked foam aggregate can be calculated as a function of the number of passages s' in the paregorian. Meanwhile, with reference to the attached figure 6, the total number n' of the foams contacting the soil particles can be obtained by utilizing the relevant geometric relationship.
From fig. 7, it can be seen that each foam, once contacting the boundary of the soil particle, will decrease one (two and a half) of the berlin channels, and the number Δ s of the loss of the foam contacting the berlin channels with the soil particle can be calculated, so that the total number s of effective seepage channels in the foam-improved soil can be known.
Step S4: and calculating the total permeation flow Q on the sectional area S, and substituting the total permeation flow Q into the related calculated amount obtained in the steps S1, S2 and S3 by combining Darcy' S law to obtain a calculation formula of the permeability coefficient of the foam improved soil.
Step S5: through analysis, when the porosity p of the foam improved soil is large, the permeability coefficient of the foam improved soil approaches to that of pure foam, and meanwhile, the foaming rate of the foam is used for representing the porosity of the pure foam, so that the expression form of the calculation formula of the permeability coefficient of the foam improved soil can be optimized by combining the foaming rate of the foam, and the final calculation formula of the permeability coefficient of the foam improved soil is obtained.
Example 1
A foam improved soil permeability prediction method based on interaction of foam and soil particles comprises the following steps:
step (1): calculating the equivalent diameter of the passage interface of the platoon
It is believed that every 3 bubbles in the foam system enclosed a concave-edged triangular berrah channel, as shown in figure 1.
At present, the average flow velocity calculation formula of the flow of the Poisea leaves in the circular tube is mostly used for calculating the flow velocity in the pipeline, and the seepage interface of a Bolata chart channel in foam seepage is a curved triangle as shown in figure 2, so that the equivalent diameter of the curved triangle can be calculated by using the basic theory of hydraulics. Each foam which encloses the passage of the plat is regarded as a circle, the equivalent hydraulic radius and the equivalent diameter of the passage of the plat can be obtained by using the formulas (1), (2) and (3), and an approximate model is shown as an attached figure 2.
Figure BDA0002178970930000081
Figure BDA0002178970930000082
D＝4R (3)
Wherein: r is the hydraulic radius of the passage section of the plat drawing; w is the cross section of the passage of the platura; chi is the wet circumference of the passage of the platane; d is the equivalent diameter of the passage section of the platura; d10,fIs the effective particle size of the foam.
Step (2): calculating the flow q of a single platogram channel
According to the fact that the liquid in the foam flows in the berrah channel as the flow of the poiseuille, the flow velocity equation of the flow of the poiseuille in the circular tube is shown as the formula (4).
Figure BDA0002178970930000083
In the formula: u. ofpIs the flow velocity of each point in the cross section of the channel, d is the diameter of the flow passage, Δ p is the on-way pressure loss, r is the flow velocity and the distance of the calculation point from the central axis of the channel, μ is the dynamic viscosity of the fluid, and L isThe length of the channel.
The average flow velocity of the fluid on the channel section can be obtained by the formula (4) as shown in the formula (5):
Figure BDA0002178970930000084
the equations of the average flow velocity in the passage of the platofram can be obtained by the joint methods (1), (2), (3) and (5), as shown in formula (6).
Figure BDA0002178970930000091
In the formula: dfIs the characteristic diameter of the foam; u is the permeation flow rate of the foam, i is the hydraulic gradient, γ is the water gravity, and μ is the dynamic viscosity of the water.
The flow q of the single pareto channel is:
Figure BDA0002178970930000092
and (3): calculating the number of effective seepage channels of the foam improved soil
Assuming that the soil is sufficiently improved by the foam, the foam fills the soil particle framework, the porosity of the foam-improved soil is p, the cross-sectional area of the foam-improved soil sample is S, the total area of the soil particles on the cross section is (1-p) S, and the total area of the pores is pS, and the area of the foam on the cross section is pS because the foam fills the soil particle framework, as shown in FIG. 3.
Since the soil particles and the foam are piled bodies with non-uniform particle sizes, in order to perform mathematical analysis on the permeability of the soil particles and the foam, the effective particle sizes of the soil particles and the foam are respectively taken to analyze the permeability characteristics. Assuming that the effective particle diameter of the soil particles is d10,sEffective particle size of the foam is d10,fAnd the soil and the foam are respectively regarded as the diameter d10,sAnd d10,fThe single-diameter spherical particle accumulation body of (1) has dfIs equal to d10,f。
Note: the effective particle size is the particle size corresponding to the accumulated mass of the particles reaching 10% on the foam or soil grade matching characteristic curve.
Assuming that the number of soil particles on the cross section is m and the number of foams is n, m and n can be calculated by the formulas (8) and (9).
Figure BDA0002178970930000093
Figure BDA0002178970930000094
As the foam is filled in the pores among the soil particles, the filling mode can be generalized to a model as shown in figure 4, and the pores of the soil particles are uniformly and well filled with the foam with the diameter dfEvery three foams are contacted with each other to form a plat channel, and because of the hydrophilicity of the soil particle surface, the contact angle of the foams and the soil is generated, so that the plat channel can not be formed, and the plat channel is a seepage channel in the model. As shown in fig. 4.
As can be seen from the model shown in FIG. 5, the number of each foam n in the isostatically stacked foam aggregate is related to the number of passages s' in the pareto as shown in equation (10).
s′＝2n (10)
However, as can be seen from the foregoing, the effective seepage channels in the foam cannot be formed when the foam contacts the soil particles, so that the effective seepage channels in the foam are correspondingly reduced once the soil particles are mixed in the foam, and the total number n' of the foam contacting the soil particles can be calculated by using the formulas (10) and (11), as shown in fig. 6.
Figure BDA0002178970930000101
In the formula: l is the sum of the peripheral lengths of all the particles on the section of the foam-modified soil, i.e. l ═ pi md10,s。
The relation of the equation (12) is derived by combining the equations (8) and (11).
Figure BDA0002178970930000102
n' is the total number of foams contacted with the soil particles.
Figure 7 shows the variation of the platoon channels when such foam interacts with soil particles.
As can be seen from fig. 7, once each foam contacts the boundary of the soil particle, one (two and a half) of the berline channels are reduced, and the number Δ s of the loss of the foam contacting the soil particle in the berline channels can be calculated by using equation (12).
Figure BDA0002178970930000103
Then, the total effective number s of seepage channels in the foam-modified soil is shown in the combined formulas (9), (10) and (13):
Figure BDA0002178970930000104
and (4): calculating permeability coefficient of foam improved soil
After the calculation formula of the single platogram channel flow Q and the effective seepage channel number S is derived, the total seepage flow Q on the cross section area S is as follows:
Q＝sq (15)
calculating the seepage flow rate of the foam improved soil according to the relation between the fluid flow rate v and the flow rate Q:
Figure BDA0002178970930000111
from Darcy's law
v＝ki (17)
Formula (18) for calculating permeability coefficient of foam-modified soil obtained in united states (16) and (17)
Figure BDA0002178970930000112
In the formula: s is the number of effective seepage channels, q is the flow rate of a single effective seepage channel, S is the sectional area of the foam improved soil, and i is the hydraulic gradient of seepage.
The final calculation equation (19) from the introduction (18) of equations (7) and (14) yields the permeability coefficient k (m/s) of the foam-modified soil.
Figure BDA0002178970930000113
In the formula:
Figure BDA0002178970930000114
d10,f，d10,sthe effective particle sizes (mm) of the foam and the soil are respectively, and beta represents the fineness of the foam relative to the soil particles; p is the porosity of the foam-modified soil; gamma is the water gravity (kN/m)3) (ii) a μ is the dynamic viscosity (Pa · s) of water.
Expression (20) is simplified in expression (19)
k＝AB (20)
In the formula:
Figure BDA0002178970930000115
the ratio of the total area (sW) of effective seepage channels in soil to the sectional area (S) of the whole foam improved soil is shown;
Figure BDA0002178970930000116
is the average permeability coefficient of a single berramat channel in the foam.
And (5): calculation formula for optimizing permeability coefficient of foam improved soil
When the porosity p of the foam-modified soil is large, the formula (21)
Figure BDA0002178970930000117
It can be seen that when p is large, the foam can still be completely filledThe filling pores approach a constant to improve the permeability of the soil. At the moment, the influence of the soil on the permeability of the foam improved soil is small, the influence of the foam on the permeability of the foam improved soil is absolutely dominant, and the permeability coefficient of the foam improved soil is close to the permeability coefficient k of pure foamf。
The average permeability coefficient of a single berla channel in the foam can be known from the parameter B of the formula (20). The porosity is p for pure foamfThe permeability coefficient of the pure foam can be deduced by combining the parameter B of formula (20) as shown in formula (22)
Figure BDA0002178970930000121
From the foregoing analysis, it can be seen that
Figure BDA0002178970930000122
Combine (21) and (22) to obtain
Figure BDA0002178970930000123
However, in practice the porosity p of the pure foam isfCannot be a constant, where pfThe constant is calculated because the filling state of the foam in the soil and the particle size distribution of the foam are both limited in the analysis process, and the state of the foam is fixed in the model establishment process, so that p is derivedfIs a constant, varies from the real case, and p is considered belowfCorrected for the true porosity of the foam.
The foaming ratio FER of the foam is defined by the formula (23):
Figure BDA0002178970930000124
wherein: vfIs the volume of foam emitted; vlVolume of solution used for foaming.
Since the pores between the foams are filled with water, the porosity available for flow-through in the foam is taken to be
Figure BDA0002178970930000125
By using
Figure BDA0002178970930000126
Replacement of
Figure BDA0002178970930000127
Then equation (19) can be further optimized as equation (24)
Figure BDA0002178970930000128
Then
Figure BDA0002178970930000129
The calculation steps of the foam improved soil permeability calculation model based on the interaction of the foam and the soil particles need to be described as follows:
description (1): the invention adopts the particle diameter d corresponding to the accumulated mass of 10 percent of particles on the grading curve of the foam and soil particles when deducing the permeability coefficient of the foam improved soil10As the respective effective particle diameters d of the foam and the soil at the time of calculation10,f、d10,sIn fact, the analysis of the permeability of the porous medium often considers that the fine particles are more critical to the influence of the permeability, and a particle grading curve d is taken in the calculation model10The corresponding particle size has some rationality as its calculated effective particle size.
Description (2): the calculation method adopted in the step 3 for the foam number n' contacting with the soil particle surface is to use the sum of the external perimeter of all the soil particles on the cross section, i ═ pi md10,sDivided by the equivalent particle size d of the foam10,fAnd (6) performing calculation. Since the foam adheres to the outer surface of the soil particles, the total length of the outer surface is the total space available for adhesion of the foam, and the equivalent particle size of the foam is considered to be a dimension of the entire foam, the sum of the outer perimeters of all the soil particles on the cross section is divided by the equivalent particle size of the foam, and the value obtained by dividing the sum by the contact number n 'of the foam and the surface of the soil particles is considered to be the contact number n'.
Compared with the prior art, the foam improved soil permeability calculation model adopting the scheme has the technical advantages that:
advantage (1): the model is a first calculation model of the permeability of the foam improved soil based on theoretical derivation, which is provided at the present stage, and the model derivation is carried out from basic science basic law, so that the model is supported by a relatively sufficient theory;
advantage (2): the model can calculate the permeability coefficient of the fully improved foam improved soil, and is particularly suitable for calculating the permeability coefficient of the foam improved soil with better original soil body grading. Normally, the calculated value of the model can be controlled to be in the same order of magnitude as the actual value;
advantage (3): the calculation formula of the model recommendation relates to the effective particle size d of the soil10,sEffective particle size d of the foam10,fThe model can be used for researching and analyzing the influence of each physical quantity on the permeability of the foam improved soil, and further guiding the scheme design when the foam is used for improving the permeability of the soil;
in conclusion, the shield foam improved soil permeability coefficient calculation model provided by the invention has novel entry point, can realize the prediction of the improved soil permeability coefficient under various different foam improvement working conditions, considers a plurality of key factors in the model establishing process to ensure that the model is real and effective, and finally provides the effective particle size d of the soil10,sEffective particle size d of the foam10,fAnd an improved soil permeability coefficient calculation formula of the foam improved soil porosity p.
The above examples are merely illustrative for clearly illustrating the present invention and are not intended to limit the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. Nor is it intended to be exhaustive of all embodiments. And obvious variations or modifications of the invention may be made without departing from the scope of the invention.

Claims (7)

1. A foam improved soil permeability prediction method based on interaction of foam and soil particles is characterized by comprising the following steps:
step 1: calculating the equivalent diameter D of the berraph channel interface in the foam system
Step 2: calculating the flow q of a single pareto channel in a foam system according to the equivalent diameter D of the pareto channel interface obtained in the step 1
And step 3: calculating the number of effective seepage channels of the foam improved soil
Wherein, the total effective seepage channel quantity s in the foam improved soil is calculated by adopting the following formula:
Figure FDA0002178970920000011
wherein: d10,sIs the effective particle size of the soil particles, d10,fThe effective grain size of the foam is shown, p is the porosity of the foam improved soil, and S is the cross-sectional area of the foam improved soil sample;
and 4, step 4: obtaining an expression of the permeability coefficient of the foam improved soil according to the flow q and the number s of the effective seepage channels obtained in the step 2 and the step 3:
k＝AB
in the formula:
Figure FDA0002178970920000012
the total area of effective seepage channels in the soil accounts for the proportion of the sectional area of the whole foam improved soil;
Figure FDA0002178970920000013
the average permeability coefficient of a single platogram channel in the foam;
Figure FDA0002178970920000014
beta represents the fineness of the foam relative to the soil particles; gamma is the water gravity; mu is the dynamic viscosity of water; i is the hydraulic gradient of seepage and W is the cross-sectional area of the channel of the single platogram.
2. The prediction method according to claim 1, characterized in thatCharacterized in that: the permeability coefficient k of the foam-improved soil is close to that of pure foam when the porosity p of the foam-improved soil is close to 1fAnd meanwhile, the foaming rate of the foam is used for expressing the porosity of the pure foam, so that the expression form of the calculation formula of the permeability coefficient of the foam improved soil can be optimized by combining the foaming rate of the foam, and the optimized calculation formula of the permeability coefficient of the foam improved soil is obtained.
3. The prediction method according to claim 2, characterized in that: the porosity is p for pure foamfAnd the permeability coefficient of the pure foam can be deduced by combining the parameter B to solve the formula:
Figure FDA0002178970920000021
is due to the fact that
Figure FDA0002178970920000022
Then
Figure FDA0002178970920000023
The foaming ratio FER of the foam is:
Figure FDA0002178970920000024
wherein: vfIs the volume of foam emitted; vlVolume of solution used for foaming;
because the pores between the foams are filled with water, the porosity of the foam which can be used for overflowing is taken
Figure FDA0002178970920000025
By using
Figure FDA0002178970920000026
Replacement of
Figure FDA0002178970920000027
The solution for k can be further optimized as:
Figure FDA0002178970920000028
4. a prediction method according to any one of claims 1 to 3, characterized in that: the concrete solving process of the number of the effective seepage channels of the foam improved soil is as follows:
calculating the number m of soil particles on the cross section area of the foam improved soil sample and the number of foams as n:
Figure FDA0002178970920000029
Figure FDA00021789709200000210
the number of bubbles n in an isostatically stacked foam aggregate is related to the number of berrah channels s':
s′＝2n
because effective seepage channels in the foam cannot be formed due to the contact of the foam and the soil particles, once the effective seepage channels in the foam mixed with the soil particles in the foam are correspondingly reduced, the total number n' of the foam in contact with the soil particles is as follows:
Figure FDA00021789709200000211
in the formula: l is the sum of the peripheral lengths of all the particles on the section of the foam-modified soil, i.e. l ═ pi md10,s；
Further derivation yields:
Figure FDA0002178970920000031
since each foam, once in contact with the soil particle boundary, reduces one plat channel, the number of losses Δ s of foam in contact with soil particles in the plat channel is:
Figure FDA0002178970920000032
further, the total effective number s of the seepage channels in the foam-modified soil is:
Figure FDA0002178970920000033
5. the prediction method according to claim 4, wherein the concrete solving process of the permeability coefficient of the foam improved soil is as follows:
according to the flow Q and the number s of the effective seepage channels, the total seepage flow Q on the cross section of the foam improved soil sample is as follows:
Q＝sq
calculating the seepage flow rate of the foam improved soil according to the relation between the fluid flow rate v and the flow rate Q:
Figure FDA0002178970920000034
from Darcy's law
v＝ki
The formula of the combined type can obtain a calculation formula of the permeability coefficient of the foam improved soil:
Figure FDA0002178970920000035
the final calculation formula of the permeability coefficient k of the foam improved soil can be further derived through the formula.
6. The prediction method according to claim 5, wherein: the solving process of the equivalent diameter of the berragraph channel interface is as follows: forming a plat diagram channel among every 3 bubbles in the foam system, calculating the equivalent diameter of the plat diagram channel by using a basic theory of hydraulics, regarding each foam enclosing the plat diagram channel as a circle, and obtaining the overflowing equivalent hydraulic radius and the equivalent diameter of the plat diagram channel by using the following formulas:
Figure FDA0002178970920000036
Figure FDA0002178970920000041
D＝4R
wherein: r is the hydraulic radius of the passage section of the plat drawing; χ is the wet circumference of the passage of berraph.
7. The prediction method according to claim 6, wherein: the specific solving process of the flow q of the single pareto channel is as follows:
the liquid in the foam flows in the passage of the berrah graph as the flow of the poiseuille, and the flow velocity equation of the flow of the poiseuille is as follows:
Figure FDA0002178970920000042
in the formula: u. ofpThe flow velocity of each point in the cross section of the channel, D is the diameter of the overflowing pipeline, Δ p is the on-way pressure loss, r is the flow velocity and the distance between a calculation point and the central axis of the channel, and L is the length of the channel;
the average flow velocity of the fluid on the channel cross section can be obtained by the following formula:
Figure FDA0002178970920000043
the formula above in conjunction yields the average flow velocity equation in the passage of the platane:
Figure FDA0002178970920000044
wherein: dfIs the characteristic diameter of the foam, df＝d10,f；
The flow q of the single pareto channel is:
Figure FDA0002178970920000045
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