CN114117581B - Slurry penetration range calculation method in tunnel shallow-buried-section high-pressure jet grouting pile method reinforcement - Google Patents

Slurry penetration range calculation method in tunnel shallow-buried-section high-pressure jet grouting pile method reinforcement Download PDF

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CN114117581B
CN114117581B CN202111236001.2A CN202111236001A CN114117581B CN 114117581 B CN114117581 B CN 114117581B CN 202111236001 A CN202111236001 A CN 202111236001A CN 114117581 B CN114117581 B CN 114117581B
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slurry
penetration
range
permeation
jet grouting
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CN114117581A (en
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徐华
韩富庆
张瑜
娄健
马增琦
冯波
郭国和
陈壮
赵乡委
王伟力
万永涛
孙文晋
王歆宇
孙润方
李奕信
闫文斌
董横飞
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Guangdong Provincial Highway Construction Co ltd
Guangdong Yunmao Expressway Co ltd
Xu Hua
Southwest Jiaotong University
Chengdu Univeristy of Technology
Fifth Engineering Co Ltd of China Railway 11th Bureau Group Co Ltd
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Guangdong Provincial Highway Construction Co ltd
Guangdong Yunmao Expressway Co ltd
Southwest Jiaotong University
Chengdu Univeristy of Technology
Fifth Engineering Co Ltd of China Railway 11th Bureau Group Co Ltd
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    • G06FELECTRIC DIGITAL DATA PROCESSING
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Abstract

The invention discloses a calculation method for a slurry permeation range in tunnel shallow-buried-section high-pressure jet grouting pile method ground surface reinforcement, which comprises the steps of establishing a calculation model for the slurry one-way permeation range in rock and soil mass around a pile and determining key parameters of the model; substituting the model established in the previous step into the columnar penetration to complete the construction of the high-pressure jet grouting pile slurry penetration filling range plane analysis model; and calculating the slurry penetration range of the high-pressure jet grouting pile according to the plane analysis model of the slurry penetration filling range of the high-pressure jet grouting pile in the step. The method can calculate the slurry permeation range, permeation coefficient reduction range and strength improvement range of the tunnel shallow-buried weak surrounding rock high-pressure jet grouting pile method surface reinforcement, has the advantages of simplicity, easiness in operation and the like in practical engineering application, provides important reference basis for design of pile spacing and pile size, permeation effect size and reinforcement effect evaluation in high-pressure jet grouting pile reinforcement engineering, effectively reduces material waste and greatly saves cost.

Description

Slurry penetration range calculation method in tunnel shallow-buried section high-pressure jet grouting pile method reinforcement
Technical Field
The invention relates to the technical field of tunnel engineering and high-pressure jet grouting pile method reinforcement engineering, in particular to a slurry penetration range calculation method in tunnel shallow-section high-pressure jet grouting pile method ground surface reinforcement.
Background
In the traditional method for reinforcing surrounding rocks at a shallow-buried section of a tunnel, in-tunnel reinforcement and earth surface reinforcement are usually adopted, wherein the in-tunnel reinforcement method is used for reinforcing the surrounding rocks in front within a certain range in front of a tunnel face, however, a pre-support means for in-tunnel reinforcement is limited by a site in the tunnel, so that the construction difficulty is increased, the construction progress is slowed down, and the reinforcement effect is difficult to ensure; compared with the in-tunnel reinforcing method, the earth surface reinforcing method is used for reinforcing the stratum at the lower part of the earth surface through earth surface construction, and has the advantages of wide reinforcing range, controllable reinforcing quality, construction period guarantee and the like. The ground surface high pressure jet grouting pile method is a ground surface reinforcing method for constructing a high pressure jet grouting pile on the ground surface to reinforce rock and soil mass within the construction range of the jet grouting pile on the lower part of the ground surface, and has been widely applied to ground surface reinforcing engineering in the industries of subways, railways, highways and the like in recent years. The high-pressure jet grouting pile method is mainly used for achieving the purpose of stratum reinforcement through interaction of high-pressure slurry and soft rock-soil bodies, is different from the action mechanism of a high-pressure jet grouting pile in the construction foundation reinforcement engineering and the highway subgrade reinforcement engineering, and in the construction foundation reinforcement engineering, the high-pressure jet grouting pile mainly plays a role of a pile body and forms a composite foundation together through the pile and soil between piles to bear vertical load; for the earth surface reinforcement project of the shallow buried section of the tunnel, the high-pressure jet grouting pile mainly achieves the reinforcement purposes of improving the integrity of surrounding rocks, improving the strength of the surrounding rocks, reducing the permeability of the surrounding rocks and the like by the replacement, extrusion, permeation and filling actions of high-pressure slurry and a weak surrounding rock soil body, so that the major disasters of collapse, roof collapse, water burst, mud burst and the like of the tunnel are prevented, and the guarantee is provided for the safe excavation of the tunnel.
The study of the pile-forming reinforcement technology by the high-pressure jet grouting pile method for the shallow-buried section of the tunnel at the present stage shows that during the construction of the high-pressure jet grouting pile, the slurry spraying pipe is inserted into the stratum, the high-pressure slurry forms huge pressure at the outlet of the nozzle instantly due to the blocking effect of the surrounding soil body, the surrounding stratum is cut and crushed, and the slurry and the crushed soil body are fully stirred by the high-pressure jet flow along with the rotation of the drill rod to be remolded to form a cement solidification body. Based on the method, a pile body formed after pile forming is divided into the following three parts: the homogeneous slurry part is used for forming a consolidated body almost completely by mixed slurry, the high-pressure slurry completely crushes the soil body in the area, the soil particles and the cement slurry are fully mixed to form homogeneous slurry, and finally the cement soil consolidated body is formed; stirring the mixed part, wherein a part of large-particle soil bodies are embedded in the consolidated body, the high-pressure slurry speed in the region is sharply reduced, the cutting effect on the soil bodies is reduced, a part of hard soil bodies cannot be fully cut, and hard particles which cannot be broken in the homogeneous slurry region are also moved to the region along with the bundle of the high-pressure slurry; the high-pressure slurry extrudes the permeation part, the high-pressure slurry can not be directly stirred and cut, the high-pressure slurry enables the pore water pressure of the soil body in the region to be increased steeply, the part is extruded and compacted under the action of pressure, meanwhile, the high-pressure slurry enters the pores of the soil body under the action of pressure, original pore water is discharged, and cement particles in the slurry complete hydration.
The slurry extrusion and penetration part can not directly impact and damage the soil body in the area, but can still extrude and compact the surrounding soil body in the jet edge area, and simultaneously the slurry can also penetrate into the soil body pores to reinforce the surrounding soil body.
At present, research on the penetration filling effect of slurry of a high-pressure jet grouting pile is still lacked, and for the research on the penetration filling effect of the slurry, due to the influence of factors such as slurry pressure, porosity of rock and soil mass, a calculation method for a specific slurry penetration filling range and a rock and soil mass property lifting range in the range is not available at present, so that an important reference basis is difficult to provide for the design of pile spacing and pile size, the penetration size and the reinforcement effect in the high-pressure jet grouting pile reinforcement engineering, and certain waste is not avoided, so that a method capable of effectively calculating the slurry penetration range in the high-pressure jet grouting pile method reinforcement of a tunnel shallow-buried section is urgently needed.
Disclosure of Invention
The invention provides a slurry penetration range calculation method in the tunnel shallow-buried section high-pressure rotary jet grouting pile method, which aims to solve the problems that in the prior art, the research on slurry penetration filling effect is less, the specific penetration filling range of slurry is difficult to determine, the reinforcing effect of a slurry penetration filling area cannot be quantitatively analyzed and the like in the tunnel shallow-buried weak surrounding rock ground surface high-pressure rotary jet grouting pile reinforcing method.
In order to achieve the purpose, the invention provides the following technical scheme: the method for calculating the slurry penetration range in the high-pressure jet grouting pile method reinforcement of the shallow buried section of the tunnel comprises the following steps of:
s1, establishing a calculation model of the unidirectional slurry penetration range in the rock-soil mass around the pile and determining key parameters of the model;
s2, substituting the model in the step S1 into cylindrical penetration to complete construction of a high-pressure jet grouting pile slurry penetration filling range plane analysis model;
and S3, calculating the slurry penetration range of the high-pressure jet grouting pile according to the high-pressure jet grouting pile slurry penetration filling range plane analysis model in the step S2.
Preferably, the establishing of the calculation model of the unidirectional slurry permeability range in the rock-soil mass and the determination of the key parameters of the model in the step S1 specifically include:
s11, determining factors of a slurry permeation path;
s12, simplifying the flowing direction of the slurry in the tortuous pipeline to obtain a simplified rock-soil body plane seepage pipeline model, solving the parameters of the simplified model, and setting conditions according to the model;
s13, according to the model and the parameters in the step S12, the seriousness is gamma, and the initial osmotic resistance stress in the rock-soil body is p 0 Osmotic pressure of p 0 + Δ p; let the y-flowing slurry with the width Deltax and the length b' and the x-flowing slurry with the length Deltax and the width Deltay lose the pressure of the slurry to p 0 The dissipated energy is the same, the solution of delta y at the infiltration end point and the infiltration starting point is solved, a calculation model of the unidirectional infiltration range of the slurry in the rock-soil mass around the pile is established, and the residual area which can infiltrate along the x direction in the x direction pipeline is equivalent to a new area with the width of b 0 Penetrating the pipe of (a) to finally obtain b 0 The solution of (1).
Preferably, the factors for determining the slurry permeation path in step S11 are specifically: the tortuosity xi is adopted to reflect the flowing tortuosity and tortuosity of slurry in the porous medium, the pores in the rock and soil mass are equivalent to permeation pipelines with tortuosity xi along the permeation direction one by one,
Figure GDA0003891275850000041
wherein L is e Indicates the actual flow path length of the slurry, L s The actual flow path of the slurry is shown to be corresponding to the straight line length, and xi represents the tortuosity of the porous medium and is distributed between 2.00 and 2.50.
Preferably, in step S12, the flowing direction of the slurry in the meandering pipe is simplified into a forward osmosis x direction and a vertical osmosis y direction, the pipes in the forward osmosis direction are combined into one osmotic pipe having a width B, the porosity of a rock-soil mass is made to be α, the width is made to be B,
Figure GDA0003891275850000042
the pipelines in the vertical permeation direction are a large number of equal-length permeation pipelines with the length of b' and the extremely small width,
Figure GDA0003891275850000043
obtaining a simplified rock-soil body plane seepage pipeline model; the setting conditions are as follows:
a. the slurry is Newtonian, the hydraulic gradient at any position in the X-direction permeation pipeline is the same, and j is the same 0
The process of transferring energy to the flowing slurry in the y direction by the flowing slurry in the x direction has no energy loss.
Preferably, in step S13, the specific process of solving Δ y at the infiltration end point is:
pressure p at the beginning of x-direction channel micro-segment at the end point of permeation x1 =p 0 +γj 0 Δ x, and since the micro-segment Δ x is extremely small, p x1 Can be approximately equal to p 0 The width of the y-direction channel is delta x, and the length of the y-direction channel is b'; pressure p at the beginning of the micro-segment y1 Can be approximately equal to p 0 According to the set conditions in step S12, the pressure of the slurry on the micro-segment is linearly changed along the flowing direction of the slurry, and the energy of the micro-segment of the x-direction channel is completely converted into the energy of the micro-segment of the y-direction channel, so that the slurry can be obtained
Figure GDA0003891275850000051
Solving to obtain delta y which is approximately equal to b';
the specific process for solving the Δ y at the infiltration starting point is as follows:
the pressure at the tail end of the y-direction channel micro-segment at the infiltration starting point is p 0 (ii) a And because the width and the length of the y-direction channel are smaller, the pressure at the beginning of the micro-segment is approximately equal to p 0 The pressure at the beginning of the x-direction channel micro-segment is p 0 + Δ p, since the micro-segment Δ x is extremely small, there is also an x-channel micro-segment terminationPressure of approximately p 0 +Δp,Δx·b′p 0 =Δx·Δy·(p o + Δ p), when Δ p > p 0 When, Δ y ≈ 0;
b is described 0 The solution of (A) is as follows:
Figure GDA0003891275850000052
preferably, in step S2, the model in step S1 is substituted into cylindrical penetration, the forward penetration direction is converted into radial penetration, the vertical penetration direction is converted into circumferential penetration, the cylindrical penetration range is calculated through a penetration pipeline with a width increasing along with the increase of the radius R, the construction of a plane analysis model of the slurry penetration filling range of the high-pressure jet grouting pile is completed, the actual penetration filling range of the slurry is converted into the solution of the penetration distance of the slurry in the radial pipeline, that is, R is solved e -R p The solution of (1).
Preferably, the calculation of the slurry penetration range of the high-pressure jet grouting pile in the step S3 specifically includes:
according to the plane analysis model of the slurry penetration filling range of the high-pressure jet grouting pile, R is known e The maximum radius of the permeation filling ring, R is the radius of any part in the permeation filling ring, R p Half the penetration width of the radial penetration channel at the penetration start point, r e Half the width of the radial permeate channel at the permeate end point, R is half the width of the radial permeate channel at R; the penetration flow of the slurry in the penetration process is Q, the length of the pile body is L, and the formula (1-4) can be solved
Figure GDA0003891275850000053
And radial penetration rate
Figure GDA0003891275850000061
Meanwhile, let the penetration time of the slurry be t, then the average penetration speed
Figure GDA0003891275850000062
And osmotic flow
Figure GDA0003891275850000063
In the two-dimensional model, the seepage of slurry in the pores of the formation is equivalent to the laminar flow of fluid in a slit, the average flow velocity u of the slit section,
Figure GDA0003891275850000064
let the hydraulic gradient at R be j R Substituting R into formula (1-5) results in the penetration velocity v of the slurry in the radial channel at radius R R
Figure GDA0003891275850000065
Substituting v and Q into formula (1-6) can solve hydraulic gradient j R
Figure GDA0003891275850000066
Slurry from R p To penetrate into R e In the process, because the slurry seepage velocity is small, the reduction of the slurry pressure is as follows:
Figure GDA0003891275850000067
from R e >R p The following can be solved:
Figure GDA0003891275850000068
Figure GDA0003891275850000069
wherein C is a defined parameter, representing the division R p All but one influence R e The parameter of the factor (b) of (c),
according to formulae (1-9) andthe solution of the formula (1-10) can be used to obtain R e -R p And (4) completing the calculation of the slurry penetration range of the high-pressure jet grouting pile.
The invention has the beneficial effects that: the method can calculate the slurry permeation range of the surface reinforcement of the tunnel shallow-buried weak surrounding rock surface by the high-pressure jet grouting pile method, and calculate parameters such as the rock-soil body strength improvement amplitude of a permeation filling area, the permeation coefficient reduction amplitude of the permeation filling area and the like.
Drawings
FIG. 1 is a schematic flow chart of the process of the present invention;
FIG. 2 is a schematic view of a meandering tube in an embodiment;
FIG. 3 is a simplified rock-soil mass plane seepage pipeline model in the embodiment;
FIG. 4 is a Δ y analysis micro-segment model in the example, in which (a) of FIG. 4 is a Δ y analysis micro-segment model at the permeation end point, and (b) of FIG. 4 is a Δ y analysis micro-segment model at the permeation start point;
FIG. 5 is a model for calculating the unidirectional seepage range of rock-soil mass slurry in the embodiment;
FIG. 6 is a simplified computational model of the unidirectional seepage range of rock-soil mass slurry in the embodiment;
FIG. 7 is a plan analysis model of the slurry penetration filling range of the high-pressure jet grouting pile in the embodiment;
FIG. 8 is a model of water permeability analysis of the permeable filling area after the high-pressure jet grouting pile is constructed in the embodiment;
FIG. 9 is a graph showing the results of a direct shear test before reinforcing a gravel soil layer in the example;
FIG. 10 is a graph showing the results of the direct shear test after the gravel soil layer is consolidated in the examples;
fig. 11 is a graph of actual excavation measurements in the examples.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1 to 11, the present invention provides a technical solution: the method for calculating the slurry penetration range in the high-pressure jet grouting pile method reinforcement of the shallow buried section of the tunnel as shown in figure 1 comprises the following steps:
s1, establishing a calculation model of the unidirectional slurry penetration range in the rock-soil mass around the pile and determining key parameters of the model, and specifically comprising the following steps:
s11, determining factors of a slurry permeation path: in order to reflect the influence of the tortuosity of slurry flowing in porous media such as sandy soil, gravel soil, pebble soil, broken sandstone and the like on the permeability characteristics, tortuosity xi is adopted to reflect the tortuosity of slurry flowing in the porous media, and pores in rock and soil bodies are equivalent to permeation pipelines with tortuosity xi along the permeation direction one by one, as shown in fig. 2.
Figure GDA0003891275850000081
Wherein L is e Indicates the actual flow path length of the slurry, L s The actual flow path of the slurry is shown to be corresponding to the straight line length, and xi represents the tortuosity of the porous medium and is distributed between 2.00 and 2.50.
S12, simplifying the flowing direction of the slurry in the tortuous pipeline to obtain a simplified rock-soil body plane seepage pipeline model, solving the parameters of the simplified model, and setting conditions according to the model.
For the convenience of quantitative calculation, the flowing direction of the slurry in the tortuous pipeline is simplified into a forward osmosis x direction and a vertical osmosis y direction, the pipelines in the forward osmosis direction are combined into an osmosis pipeline with the width B, the porosity of a rock-soil body is enabled to be alpha, the width of the rock-soil body is enabled to be B, fluid permeates along the length direction of the rock-soil body, the plane osmosis range of the rock-soil body is analyzed, and the width B of the tortuous pipeline after the rock-soil body is combined is obtained to be
Figure GDA0003891275850000082
In a circuitous pipeline with the original width b, the influence of the pipeline bending on the hydraulic gradient of the slurry is converted into the influence of the pipeline in the vertical permeation direction on the hydraulic gradient or the seepage velocity of the slurry in a straight pipeline with the same width b. According to the formula (1-2), the specific gravities of the forward osmosis direction pipeline and the vertical osmosis direction pipeline are respectively
Figure GDA0003891275850000083
Figure GDA0003891275850000091
The pipelines in the vertical penetration direction are a large number of equal-length seepage pipelines with the length of b' and the minimum width,
Figure GDA0003891275850000092
and obtaining a simplified rock-soil body plane seepage pipeline model, wherein the set conditions are as follows as shown in figure 3:
a. the slurry is Newtonian, and the hydraulic gradient at any position in the x-direction permeation pipeline is the same, and is j 0
The process of transferring energy to the flowing slurry in the y direction by the flowing slurry in the x direction has no energy loss.
S13, according to the model and the parameters in the step S12, the seriousness is gamma, and the initial osmotic resistance stress in the rock-soil body is p 0 Osmotic pressure of p 0 + Δ p; let the y-flowing slurry with the width Deltax and the length b' and the x-flowing slurry with the length Deltax and the width Deltay lose the pressure of the slurry to p 0 The same energy dissipated, Δ y analysisThe model is shown in fig. 4, wherein (a) in fig. 4 is a Δ y analysis micro-segment model at the permeation end point, and (b) in fig. 4 is a Δ y analysis micro-segment model at the permeation starting point, the solution of the permeation end point and the Δ y at the permeation starting point is solved, because the slurry pressure on the micro-segment is linearly changed along the slurry flow direction, and the pressure at the beginning and the end of the y-direction channel micro-segment at any position of the permeation range can be approximate to p 0 It can be known that the change of delta y along the penetration direction is also linear, so that a calculation model of the unidirectional penetration range of slurry in rock-soil mass is established, as shown in figure 5, the residual area of the x-direction pipeline, which can penetrate along the x direction, is equivalent to a new width b 0 The simplified model of the permeation pipeline (2) is shown in FIG. 6, in which the slurry only flows in the x direction, and finally the width b of the simplified x direction permeation channel is obtained 0 The solution of (1).
The specific process for solving Δ y at the infiltration end point is:
pressure p at the beginning of x-direction channel micro-segment at the end point of permeation x1 =p 0 +γj 0 Δ x, and since the fraction Δ x is extremely small, p x1 Can be approximately equal to p 0 The width of the y-direction channel is Deltax, the length is b', the pressure p at the beginning of the micro-segment is small y1 Can be approximately equal to p 0 According to the setting condition a in step S12, the pressure of the slurry on the micro-segment is linearly changed along the flowing direction of the slurry, and according to the setting condition b, the energy of the x-direction channel micro-segment is completely converted into the energy of the y-direction channel micro-segment, so that the slurry can be obtained
Figure GDA0003891275850000101
Solving to obtain delta y which is approximately equal to b'.
The specific process for solving the Δ y at the infiltration starting point is as follows:
the pressure at the tail end of the y-direction channel micro-segment at the infiltration starting point is p 0 (ii) a Since the width and the length of the y-direction channel are small, the pressure at the beginning of the micro-segment is approximately equal to p 0 The pressure at the beginning of the x-direction channel micro-segment is p 0 + Δ p, since the microsegment Δ x is extremely small, there is also an x-channel microsegment termination pressure of approximately p 0 +Δp,Δx·b′p 0 =Δx·Δy·(p o + Δ p), when Δ p > p 0 When Δ y ≈ 0.
Because the pressure of the slurry on the micro-segment is linearly changed along the flowing direction of the slurry, the pressure at the beginning and the end of the y-direction channel micro-segment at any position of the penetration range can be approximate to p 0 That is, a micro-segment is taken at any position in the penetration range, the energy for y-direction slurry penetration is constant, and the change of Δ y along the penetration direction is also linear. Therefore, the change curve of delta y along the x axis in grouting engineering can be obtained, and the residual area which can permeate along the x direction in the x direction pipeline is equivalent to a new width b 0 The equivalent area width of the permeation pipeline is b'/2, and the final simplified x-direction permeation channel width b is 0 Comprises the following steps:
Figure GDA0003891275850000102
and S2, substituting the model in the step S1 into column-shaped penetration to finish construction of a high-pressure jet grouting pile slurry penetration filling range plane analysis model.
The penetration of the slurry of the high-pressure jet grouting pile is cylindrical penetration, the model in the step S1 is substituted into the cylindrical penetration, the forward penetration direction is converted into radial penetration, the vertical penetration direction is converted into annular penetration, the cylindrical penetration range is calculated through a penetration pipeline with the width increasing along with the increase of the radius R, the penetration of the slurry in a radial channel is used for replacing the penetration after balancing the pressure loss of the slurry annular penetration to the radial penetration, as shown in figure 7, the construction of a plane analysis model of the slurry penetration filling range of the high-pressure jet grouting pile is completed, the actual penetration filling range of the slurry can be determined by calculating the penetration distance of the slurry in the radial pipeline, the actual penetration filling range of the slurry is converted into the solution of the penetration distance of the slurry in the radial pipeline, namely the R is solved e -R p The solution of (1).
And S3, calculating the slurry penetration range of the high-pressure jet grouting pile according to the high-pressure jet grouting pile slurry penetration filling range plane analysis model in the step S2.
The specific process comprises the following steps: according to the plane analysis model of the slurry penetration filling range of the high-pressure jet grouting pile, R is obtained e The maximum radius of the penetrating packing ring, R is penetrating packingRadius of any part in the circle, r p Half the penetration width of the radial penetration channel at the penetration start point, r e Half the width of the radial permeate channel at the permeate end point, R is half the width of the radial permeate channel at R; the penetration flow of the slurry in the penetration process is Q, the length of the pile body is L, and the formula (1-4) can be solved
Figure GDA0003891275850000111
And radial penetration rate
Figure GDA0003891275850000112
Meanwhile, let the penetration time of the slurry be t, then the average penetration speed
Figure GDA0003891275850000113
And osmotic flow
Figure GDA0003891275850000114
In the two-dimensional model, the seepage of slurry in the pores of the formation is equivalent to the laminar flow of fluid in a slit, the average flow velocity u of the slit section,
Figure GDA0003891275850000115
wherein, the average flow velocity of the u-slit section, the gravity of the gamma-fluid, the j-hydraulic gradient, the dynamic viscosity of the mu-fluid, and r 0 Half the section width.
Let the hydraulic gradient at R be j R Substituting R into formula (1-5) can obtain the penetration velocity v of the slurry in the radial channel at the radius R R
Figure GDA0003891275850000116
Substituting v and Q into formula (1-6) can obtain hydraulic gradient j R
Figure GDA0003891275850000117
Slurry from R p To penetrate into R e In the process, because the slurry seepage velocity is small, the reduction of the slurry pressure is as follows:
Figure GDA0003891275850000121
from R e >R p The following can be solved:
Figure GDA0003891275850000122
Figure GDA0003891275850000123
wherein C is a defined parameter which indicates the division of R p All but one influence R e The parameters of the factors of (a) and (b),
from the solutions of the formulae (1-9) and (1-10), R can be obtained e -R p And (4) completing the calculation of the slurry penetration range of the high-pressure jet grouting pile.
Permeability coefficient reduction amplitude calculation
In the penetration range calculation model, the slurry pressure in the middle area of the radial pipeline is lost due to the requirement of circumferential penetration, so that no slurry seepage exists in the area, and the slurry cannot fill all penetration pipelines in the penetration range tightly. Assuming the slurry can fill all pores except for the loss of osmotic power, at an osmotic pressure of p 0 The ratio of the area which cannot be filled with the slurry in the permeation pipeline to the total permeation pipeline area is as follows:
Figure GDA0003891275850000124
taking a piece of inter-pile soil with the width of D after the construction of the high-pressure jet grouting pile for water infiltration analysis, and simplifying the pores of the rock-soil massIs formed to a width of
Figure GDA0003891275850000125
The meandering conduit of (a); the calculus rate of the serous fluid is beta 2 Considering the non-dense portion of the slurry and the volume shrinkage portion of the slurry stone in the meandering pipe as the meandering pipe is uniformly distributed, a permeability analysis model of water in the permeation filling area after the high-pressure jet grouting pile is applied can be established, as shown in fig. 8, where D represents the width of the analysis model, and D represents the width of the analysis model 1 Denotes the width of the slurry consolidation in the tortuous penetration conduit, d 2 Indicates the width of a blank region formed by the slurry filling incompact and the slurry volume shrinkage.
Figure GDA0003891275850000126
Figure GDA0003891275850000131
Let the permeability coefficient of water in the slurry consolidation body be k 1 The permeability coefficient in the empty region of the permeation channel is k 2 The overall permeability coefficient k of water in the whole analysis model is
Figure GDA0003891275850000132
For sandy soil with the same grain size, the permeability coefficient and the porosity are approximately in a linear relationship, so when permeability analysis is carried out on a rock-soil body before reinforcement, after fine permeable pores in the rock-soil body are combined into a permeable channel, the permeability coefficient of the fine permeable pores is the same as that of the permeable pores before combination (the porosity of the pores and the channels per se is 100%), and the width of the permeable channel only represents the number of the permeable pores. The unidirectional permeability coefficient of the rock-soil mass before the construction of the high-pressure jet grouting pile is k 0 The permeation coefficient in the empty area of the permeation channel is k 2 Comprises the following steps:
k 2 =k 0 (3-5)
the united type (3-2), the formula (3-3), the formula (3-4) and the formula (3-5) can be solved:
Figure GDA0003891275850000133
calculation of stratum strength improvement range of permeable filling area
According to the grouting theory in rock-soil mass, the shear strength of the rock-soil mass after grouting can be enhanced, and the increment of cohesive force and internal friction angle respectively satisfy the following formulas:
Figure GDA0003891275850000134
Figure GDA0003891275850000135
in the formula:
Figure GDA0003891275850000136
the internal friction angle increment after grouting of the rock-soil body is compared with that before grouting;
delta c is the cohesive force increment after grouting of rock and soil mass compared with that before grouting;
Figure GDA0003891275850000137
respectively representing the internal friction angles of the slurry concretion body and the in-situ stratum rock and soil body;
c g 、c s respectively representing the cohesive force of the slurry concretion body and the in-situ stratum rock and soil body;
eta-grout injection rate, which can be expressed by the ratio of the volume of the grout stone to the volume of the original soil body.
The slurry injection quantity eta obtained by analyzing based on a seepage analysis model is as follows:
Figure GDA0003891275850000141
the joint type (4-1), the formula (4-2) and the formula (4-3) can be solved to obtain the improvement rates of the internal friction angle and the cohesive force of the stratum after the permeable filling respectively as follows:
Figure GDA0003891275850000142
Figure GDA0003891275850000143
the method calculates prediction and verifies actual test value
The new house tunnel of Guangdong Yumao highway is disconnect-type tunnel, and the tunnel within range distributes the shallow section of burying of many places, and shallow section stratum top-down mainly does: ploughing and planting soil, silty clay, silty clay, gravelly soil, fully weathered deteriorated sandstone and stroke weathered deteriorated sandstone. Most of the tunnel body of the shallow buried section of the tunnel is located in the fully-weathered deteriorated sandstone, the surrounding rock level is V, and due to the fact that the stratum of the shallow buried section is soft and the surface and underground water systems are developed, the shallow buried section is pre-reinforced by adopting a surface high-pressure jet grouting pile pre-reinforcement scheme after comprehensive consideration.
According to survey design data and field test data of the shallow buried section of the new-house tunnel, the cohesive force of the gravel soil before the wall rock reinforcement of the shallow buried section of the new-house tunnel is 21.4kPa, and the internal friction angle is 24.8 degrees; initial average normal stress sigma of gravel layer 0 About 140kPa, poisson's ratio 0.28, modulus of elasticity 14.01MPa; the tortuosity of the pores of the rock-soil body is usually between 2 and 2.5, and the middle value of the broken stone soil layer is 2.25; the porosity of the crushed stone layer is 20%. Due to the diffusion of the jet flow, when the jet flow reaches the edge of the pile body, the jet flow pressure is concentrated within about 20 cm of the moving direction of the jet flow; from the lifting speed of the jet pipe, it is known that the duration of the compressive stress of the jet flow on the periphery of the pile is about 60s. According to the dynamic viscosity of pure cement slurry with the water-cement ratio of 1: 1 at different time, the dynamic viscosity of the gravel soil layer is taken to be 8 MPa.s in combination with engineering experience.
The method calculates the prediction
The first step is as follows: the values of the permeate fill range calculation parameters were solved and collated as shown in table 1.
TABLE 1 calculation of parameter values for permeation fill ranges
Figure GDA0003891275850000151
The second step: the value of the parameter C is 2.85 according to the formula (1-10), and the distance R from the edge of the infiltration filling area to the center of the pile body can be obtained according to the formula (1-9) e Comprises the following steps:
Figure GDA0003891275850000152
then under the construction parameters of the shallow buried section of the new house tunnel, the radial range of the penetration filling in the gravel soil layer is as follows:
R e -R p =0.56R p (5-2)
the third step: the permeability reduction calculation parameter values of the permeability filling area are solved and arranged, as shown in table 2.
TABLE 2 calculation of permeability reduction in permeable packing area parameter values
Figure GDA0003891275850000153
The slurry adopted by the construction of the high-pressure jet grouting pile at the shallow-buried section of the tunnel is pure cement slurry with the water cement ratio of 1: 1, according to engineering experience, the calculus rate is usually between 75% and 95%, and the average value of the calculus rate of the slurry in a gravel soil layer penetration filling area is 85%; the permeability coefficient of the calculus body is usually less than 10 -6 cm/s, the specific value has little influence on the result, and the permeability coefficient of the slurry concretion body in the penetration filling area in the gravel soil layer is 1 multiplied by 10 -6 cm/s. In addition, according to the variable water head permeability test result, the permeability coefficient of the gravel soil layer before reinforcement is 1.5 multiplied by 10 -3 cm/s. All the calculated parameters of the degree of permeability reduction are thus available.
The fourth step: the permeability coefficient after the permeation filling area is reinforced can be solved to be k according to the formula (3-6),
k=4.38×10 -4 cm/s (5-3)
and then the formula calculation value of the permeability coefficient reduction range of the penetration filling area of the gravel soil layer after construction is as follows:
Figure GDA0003891275850000154
the fifth step: the values of the calculated parameters for the strength increase amplitude of the infiltration filling area were solved and collated, as shown in table 3.
The cohesive force c of the slurry stone body of the high-pressure rotary jet grouting pile at the shallow buried section of the tunnel g About 736.6kPa, internal friction angle
Figure GDA0003891275850000164
About 33.9. All calculation parameters of the strength improvement range of the permeable filling area can be obtained by combining the related test data of the known gravel layer and the stratum parameter values, and the calculation parameters are shown in a table 3.
TABLE 3 penetration filling zone Strength improvement amplitude calculation parameter values
Figure GDA0003891275850000161
And a sixth step: according to the formula (4-4) and the formula (4-5), the formula estimation value of the improvement degree of the stratum shear strength can be obtained:
Figure GDA0003891275850000162
Figure GDA0003891275850000163
the actual increase of cohesive force and internal friction angle of the penetration filling area after reinforcement is 288.40% and 3.17% respectively, and the actual decrease of the permeability coefficient of the penetration filling area after reinforcement in the gravel soil layer is 70.80%.
Actual test value
The pile body cross section is observed through excavation in the tunnel, actual excavation measurement is shown in figure 11, and the result shows: the pile forming radius in the gravel soil is 0.34m, and the radial thickness of a filling area is 0.21m. The ratio of the actual filling range to the pile radius is found to be 0.618.
The penetration filling area after the high-pressure jet grouting pile is constructed is sampled on site by adopting a penetration cutting ring, an indoor variable water head penetration test is carried out on a sample body, the experimental data are shown in table 4, the penetration coefficient after reinforcement is also obtained by the average value of three groups of tests, and the average value of the test results of three groups of actual penetration coefficients of the rock and soil body in the penetration filling area after reinforcement is 3.97 multiplied by 10 - 4 m/s; the permeability coefficient before reinforcing is 1.5 multiplied by 10 -3 cm/s shows that the actual permeability coefficient reduction rate after the penetration filling area in the gravel soil layer is reinforced is 73.53%.
Table 4 variable head permeability test data after gravel soil layer consolidation
Figure GDA0003891275850000171
Indoor direct Shear tests are carried out on soil samples in a penetration filling area after the crushed stone soil layer is reinforced and taken out on site, a Shear TracII full-automatic direct Shear apparatus is adopted, the vertical pressure is respectively set to be 100kPa, 200kPa and 300kPa, and the Shear strength curves of the soil before and after reinforcement are obtained according to a molar-coulomb Shear strength formula, as shown in figures 9 and 10. The average measured value of three groups of tests is taken as the final data result, and the result shows that the cohesive force of the penetration area of the reinforced gravel soil layer is 88.4kPa, and the internal friction angle is 26.2 degrees; the cohesive force and the internal friction angle of the gravel soil layer before reinforcement are respectively 21.4kPa and 24.8 degrees, and the actual increase of the cohesive force and the internal friction angle of the penetration filling area after reinforcement is respectively 311.21 percent and 5.64 percent
Penetration Range analysis
And calculating the penetration filling range of the slurry and measuring the parameters of the crushed stone soil layer of the shallow buried section of the new house tunnel to obtain the penetration filling radial range of the slurry in the crushed stone soil layer which is 0.56 time of the pile-forming radius. In actual measurement after reinforcement, the pile forming radius of the gravel soil layer is 0.34m, and the radial range of slurry permeation filling is 0.21m, namely the radial range of slurry permeation filling is 0.618 times of the pile forming radius of the pile body.
In general, the predicted value of the slurry permeation filling range is slightly smaller than the measured value, and is slightly conservative, but the difference value of the two values is small; therefore, the prediction and calculation reliability of the penetration filling range in the gravel soil layer is high.
Permeability coefficient reduction amplitude analysis
After the data such as the porosity of the stratum, the permeability coefficient before reinforcement and the like are obtained, the predicted value of the permeability coefficient reduction range formula of the new house tunnel crushed stone soil layer permeable filling area rock soil mass is calculated to be 70.80%. After field sampling and indoor permeability test are carried out on the reinforced gravel soil layer permeable filling area, the actual reduction range of the permeability coefficient is measured to be 73.53%.
Therefore, the actual reduction amplitude of the permeability coefficient of the reinforced gravel soil layer is larger than the predicted value, the difference value of the actual reduction amplitude of the permeability coefficient of the reinforced gravel soil layer and the predicted value is smaller, and the prediction calculation of the reduction amplitude of the permeability coefficient has higher reliability.
Intensity improvement magnitude analysis
The method comprises the steps of carrying out on-site sampling and direct shear test on a broken stone soil layer rock-soil mass before reinforcing construction, and obtaining the cohesive force and the internal friction angle of the broken stone soil layer before reinforcing. The shear strength parameter of the slurry stone body, the shear strength parameter of the gravel soil before reinforcement and the like are calculated by adopting a prediction formula, and the improvement ranges of the cohesive force and the internal friction angle of the gravel soil layer after reinforcement are 288.40% and 3.17% respectively. The shear strength parameter of the reinforced gravel soil layer penetration filling area is measured through an indoor direct shear test, and according to the test result, the actual measurement values of the cohesive force and the internal friction angle increase of the rock and soil mass of the reinforced gravel soil layer penetration filling area are 311.21% and 5.64% respectively.
It can be seen that the actual increase amplitude of cohesive force is slightly higher than the predicted value, and the actual increase amplitude of the internal friction angle is close to twice of the formula estimated value, which shows that the prediction calculation of the increase amplitude of the shear strength is relatively conservative; in general, the calculation of the prediction of the magnitude of the increase in the intensity of the infiltration filling zone also has higher reliability.
In conclusion, in a gravel soil layer with strong permeability, the comparison results of the predicted values and the actual measured values of parameters such as the radial range of the slurry permeation filling, the reduction range of the permeation coefficient of the permeation filling area, the strength improvement range of the permeation filling area and the like show that: the predicted value is basically matched with the field measured value, and the difference value is small. In conclusion, in the stratum with stronger permeability, the calculation result of the related prediction of the slurry permeation filling effect of the high-pressure jet grouting pile is more consistent with the actual engineering situation on the whole, and the reliability is higher.
Although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that modifications may be made to the embodiments described in the foregoing embodiments, or equivalents may be substituted for elements thereof.

Claims (3)

1. The method for calculating the slurry penetration range in the tunnel shallow-buried-section high-pressure jet grouting pile method ground surface reinforcement is characterized by comprising the following steps of:
s1, establishing a calculation model of the unidirectional slurry penetration range in the rock-soil mass around the pile and determining key parameters of the model;
s2, substituting the model in the step S1 into cylindrical penetration to complete construction of a high-pressure jet grouting pile slurry penetration filling range plane analysis model;
s3, calculating the slurry penetration range of the high-pressure jet grouting pile according to the high-pressure jet grouting pile slurry penetration filling range plane analysis model in the step S2;
the step S1 of establishing a calculation model of the unidirectional slurry penetration range in the rock-soil mass around the pile and determining key parameters of the model specifically comprises the following steps:
s11, determining a slurry permeation path factor;
s12, simplifying the flowing direction of the slurry in the tortuous pipeline to obtain a simplified rock-soil body plane seepage pipeline model, solving the parameters of the simplified model, and setting conditions according to the model;
s13, according to the model and the parameters in the step S12, the seriousness is gamma, and the initial osmotic resistance stress in the rock-soil body is p 0 Osmotic pressure of p 0 + Δ p; let the y-flowing slurry with the width Deltax and the length b' and the x-flowing slurry with the length Deltax and the width Deltay lose the pressure of the slurry to p 0 The dissipated energy is the same, the solution of delta y at the infiltration end point and the infiltration starting point is solved, a calculation model of the unidirectional infiltration range of the slurry in the rock-soil mass around the pile is established, and the residual region infiltrated along the x direction in the x direction pipeline is equivalent to a new region with the width of b 0 Penetrating the pipe of (a) to finally obtain b 0 The solution of (2);
in step S13, the specific process of solving Δ y at the infiltration end point is:
initial pressure p of x-direction channel micro-segment at permeation endpoint x1 =p 0 +γj 0 Δ x, and since the micro-segment Δ x is extremely small, p x1 Is approximately equal to p 0 The width of the y-direction channel is delta x, and the length is b'; pressure p at the beginning of the micro-segment y1 Is approximately equal to p 0 According to the set conditions in the step S12, the pressure of the slurry on the micro-segment is changed linearly along the flowing direction of the slurry, and the energy of the x-direction channel micro-segment is completely converted into the energy of the y-direction channel micro-segment to obtain
Figure FDA0003930479670000021
Solving to obtain delta y which is approximately equal to b';
the specific process for solving the Δ y at the infiltration starting point is as follows:
the pressure at the end of the y-direction channel micro-section at the infiltration starting point is p 0 (ii) a Since the width and the length of the y-direction channel are small, the pressure at the beginning of the micro-segment is approximately equal to p 0 The pressure at the beginning of the x-direction channel micro-segment is p 0 + Δ p, since the micro-segment Δ x is extremely small, there is also an x-channel micro-segment ending pressure of approximately p 0 +Δp,Δx·b′p 0 =Δx·Δy·(p 0 + Δ p), when Δ p > p 0 When, Δ y ≈ 0;
b is 0 The solution of (a) is:
Figure FDA0003930479670000022
in step S2, substituting the model in the step S1 into cylindrical penetration, converting the forward penetration direction into radial penetration, converting the vertical penetration direction into annular penetration, calculating the cylindrical penetration range through a penetration pipeline with the width increasing along with the increase of the radius R, completing the construction of a plane analysis model of the high-pressure jet grouting pile slurry penetration filling range, converting the actual penetration filling range of the slurry into the solution of the penetration distance of the slurry in the radial pipeline, namely solving the R e -R p The solution of (2);
the concrete process of calculating the slurry penetration range of the high-pressure jet grouting pile in the step S3 is as follows:
according to a plane analysis model of a high-pressure jet grouting pile slurry penetration filling range, R e The maximum radius of the permeation filling ring, R is the radius of any part in the permeation filling ring, R p Half the penetration width of the radial penetration channel at the penetration start point, r e Half of the width of the radial permeation channel at the permeation endpoint, R is half of the width of the radial permeation channel at R, alpha is porosity, and xi represents the tortuosity of the porous medium; the penetration flow of the slurry in the penetration process is Q, the length of the pile body is L, and the formula (1-4) is solved to obtain
Figure FDA0003930479670000023
And radial penetration rate
Figure FDA0003930479670000024
Meanwhile, let the penetration time of the slurry be t, then the average penetration speed
Figure FDA0003930479670000025
And osmotic flow
Figure FDA0003930479670000026
In the two-dimensional model, the seepage of slurry in the pores of the formation is equivalent to the laminar flow of fluid in a slit, the average flow velocity u of the slit section,
Figure FDA0003930479670000031
let the hydraulic gradient at R be j R Substituting R into the formula (1-5) to obtain the penetration velocity v of the slurry in the radial channel at the radius R R
Figure FDA0003930479670000032
Substituting v and Q into formula (1-6) to obtain hydraulic gradient j R
Figure FDA0003930479670000033
Slurry from R p To penetrate into R e In the process, because the slurry seepage velocity is small, the reduction of the slurry pressure is as follows:
Figure FDA0003930479670000034
from R e >R p And resolving to obtain:
Figure FDA0003930479670000035
Figure FDA0003930479670000036
wherein C is a defined parameter which indicates the division of R p All but one influence R e The parameters of the factors of (a) and (b),
obtaining R from the solutions of the formulae (1-9) and (1-10) e -R p Finish the solution ofAnd (4) calculating the slurry penetration range of the paired high-pressure jet grouting piles.
2. The method for calculating the slurry penetration range in the ground surface reinforcement by the high-pressure jet grouting pile method for the shallow tunnel segment according to claim 1, wherein the method comprises the following steps: the factors for determining the slurry permeation path in the step S11 are specifically: the tortuosity xi is adopted to reflect the flowing tortuosity of the slurry in the porous medium, the pores in the rock-soil body are equivalent to permeation pipelines with the tortuosity xi along the permeation direction,
Figure FDA0003930479670000041
wherein L is e Indicates the actual flow path length of the slurry, L s The actual flowing path of the slurry is correspondingly straight and long, and xi represents the tortuosity of the porous medium and is distributed between 2.00 and 2.50.
3. The method for calculating the slurry penetration range in the ground surface reinforcement by the high-pressure jet grouting pile method for the shallow tunnel segment according to claim 1, wherein the method comprises the following steps: in step S12, the flowing direction of the slurry in the circuitous pipeline is simplified into a forward osmosis x direction and a vertical osmosis y direction, the pipelines in the forward osmosis direction are combined into a osmosis pipeline with the width of B, the porosity of a rock-soil body is made to be alpha, the width is made to be B,
Figure FDA0003930479670000042
the pipelines in the vertical permeation direction are a large number of equal-length permeation pipelines with the length of b' and the extremely small width,
Figure FDA0003930479670000043
obtaining a simplified rock-soil body plane seepage pipeline model; the setting conditions are as follows:
a. the slurry is Newtonian, the hydraulic gradient at any position in the X-direction permeation pipeline is the same, and j is the same 0
The process of transferring energy to the flowing slurry in the y direction by the flowing slurry in the x direction has no energy loss.
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