CN114329750A - Sand-gravel stratum earth pressure balance shield earth bin pressure design and control method - Google Patents

Sand-gravel stratum earth pressure balance shield earth bin pressure design and control method Download PDF

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CN114329750A
CN114329750A CN202210258034.5A CN202210258034A CN114329750A CN 114329750 A CN114329750 A CN 114329750A CN 202210258034 A CN202210258034 A CN 202210258034A CN 114329750 A CN114329750 A CN 114329750A
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pressure
soil
earth
excavation
strip
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CN114329750B (en
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张晋勋
孙正阳
江玉生
武福美
江华
周刘刚
殷明伦
张雷
李博
蒙世宇
龙长喜
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China University of Mining and Technology Beijing CUMTB
Beijing Urban Construction Group Co Ltd
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China University of Mining and Technology Beijing CUMTB
Beijing Urban Construction Group Co Ltd
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Abstract

The invention provides a sand-gravel stratum earth pressure balance shield earth bin pressure design and control method, which comprises the following steps: constructing a soil body loose soil pressure calculation model in an active limit balance state of a sandy gravel stratum above an interface, and calculating the interface loose soil pressure; constructing a soil body passive damaged soil pressure calculation model under a sand-gravel stratum passive limit balance state above the interface, and calculating the interface passive damaged soil pressure; constructing an excavation face limit support pressure calculation model, and calculating excavation face limit support pressure; calculating the optimal supporting pressure of the excavation surface; calculating to obtain the ultimate supporting pressure of the excavation surface considering the underground water; and determining the control principle of the supporting pressure of the excavation surface, and designing and controlling the pressure of the shield construction soil bin. The method can improve the safety of shield construction, provides a basis for the pressure control of the earth bin in the shield construction, reduces the influence of the earth pressure balance shield construction on the surrounding environment, and plays an important role in promoting the construction of urban subways.

Description

Sand-gravel stratum earth pressure balance shield earth bin pressure design and control method
Technical Field
The invention relates to the technical field of shield construction, in particular to a method for analyzing the stability of an earth pressure balance shield excavation surface in a sandy cobble stratum, and specifically relates to a pressure design and control method for an earth pressure balance shield earth bin in the sandy cobble stratum.
Background
The shield construction technology has the advantages of high mechanization degree, small safety risk, high construction speed, small influence on the surrounding environment and the like, and is widely applied to the construction of underground highways and railway tunnels. The method is characterized in that the supporting force of the excavation surface in the shield construction process is kept within a reasonable range to reduce the influence of the shield construction on the surrounding environment, and the control range of the supporting pressure of the excavation surface is determined to have important significance for the shield construction.
Supporting force (P) to the excavated surface during constructionBranch stand) The pressure of the soil body on the original side is the same as that of the soil body, and the soil body in front of the excavation surface can be regarded as the stress state is not changed; when P is presentBranch stand<P0When the stress state of the soil body on the excavation surface is changed, and when the supporting force is reduced to a certain value, the soil body on the excavation surface is in a limit balance state (the state of the soil body at the moment is defined as an active limit balance state, and the supporting force at the moment can be called as PLower bound of branch-lower bound) If the supporting force is less than PLower bound of branch-lower boundWhen the soil body on the excavation surface is damaged, the soil body above the excavation surface is collapsed; when P is presentBranch stand>P0When the stress state of the soil body on the excavation surface is changed, and when the supporting force is increased to a certain value, the soil body on the excavation surface is in a limit balance state (the state of the soil body at the moment is defined as a passive limit balance state, and the supporting force at the moment can be called as PUpper and lower bound of) When the supporting force is greater than PUpper and lower bound ofWhen the soil body on the excavation surface is damaged, the soil body above the excavation surface is shown to be raised. In actual shield construction, the supporting force of the shield on the excavation surface is difficult to fix at the original side pressure of the soil body, and in order to prevent the soil body of the excavation surface from being damaged, the supporting force should meet the requirement of PLower bound of branch-lower bound<PBranch stand<PUpper and lower bound of. Therefore, the determination of the excavation face supporting force corresponding to the two limit states is important for shield construction. The vertical soil pressure in the active limit equilibrium state is called as 'loose soil pressure'; the earth pressure at the passive limit equilibrium state is referred to as "passive earth-damaging pressure".
At present, passive destruction state research on soil above an excavation surface is less, and multiple researches on stratum loose soil pressure are developed based on soil mechanics related theories, wherein the stratum loose soil pressure theory with wide application comprises the following steps: the theory of full soil covering, the Terzaghi loose soil pressure theory, the Purchase arch theory and the like.
The full earthing theory does not consider the stress transfer between soil bodies under the loose load, so the method is suitable for the weak shallow buried stratum, and the calculation result is larger than the actual value; and the theory has poor applicability when the soil is hard or the buried depth is large.
The Terzaghi loose soil pressure theory considers the influence of the size of a tunnel, the burial depth, the cohesive force of soil and an internal friction angle on the stability of a soil body, is applicable to strata which possibly generate an arch effect, and has the problem of uncertainty in the determination of some key parameters in the theory. Secondly, the existing theory for calculating the pressure on the excavation face side is less, or the mode of directly multiplying the vertical pressure by the upper side pressure coefficient is inaccurate and needs to be optimized.
In 1907, russian scientists pronoto quaternary yakonof created the theory of pous. The theory is based on the loose theory, and the excavation is believed to cause a balance arch in a parabola shape to be formed above the tunnel when the tunnel is in a loose medium, and the surrounding rock pressure born by the deeply buried loose rock mass tunnel top is only the self weight of the rock mass in the pressure arch. At present, the formula theory for calculating the surrounding rock pressure of the deep-buried tunnel under broken and loose surrounding rocks is mainly obtained by further derivation and summarization based on the Purchase theory. The calculation formula adopted in the current specification of China is determined by summarizing and analyzing collapse data of hundreds of drilling and blasting tunnels in China, the calculation method given by the specification is an empirical formula essentially, the application range of the calculation formula is a tunnel constructed by drilling and blasting in rock mass, and the problem of application of the Purcher arch theory in soft tunnels is yet to be researched.
Therefore, it is necessary to provide a new and more scientific method for designing and controlling the earth pressure balance shield earth chamber pressure in the sandy gravel stratum.
Disclosure of Invention
In view of the defects of the prior art, the main object of the present invention is to provide a design and control method for earth pressure balance shield earth warehouse in sandy gravel stratum, so as to solve one or more problems in the prior art.
The technical scheme of the invention is as follows:
a sand and gravel stratum earth pressure balance shield earth bin pressure design and control method comprises the following steps:
the method comprises the following steps: constructing a soil body loose soil pressure calculation model in an active limit balance state of a sandy gravel stratum above an interface, and calculating the interface loose soil pressure;
step two: constructing a soil body passive damaged soil pressure calculation model under a sand-gravel stratum passive limit balance state above the interface, and calculating the interface passive damaged soil pressure;
step three: constructing an excavation face ultimate support pressure calculation model, and calculating excavation face ultimate support pressures in different ultimate balance states according to the interface soil pressure calculation result;
step four: calculating the optimal supporting pressure of the excavation surface;
step five: calculating the underground water level pressure to obtain the ultimate supporting pressure of the excavation surface considering the underground water;
step six: and determining the control principle of the supporting pressure of the excavation surface, and designing and controlling the pressure of the shield construction soil bin.
Preferably, the first step specifically includes:
(1) assumptions of the calculation model
Assuming that the slip surface is a vertical surface, the width of a slip body is the diameter of a tunnel and is defined as 2B, and meanwhile, defining the lateral pressure coefficient K of a soil body as the ratio of the normal stress of the soil body on the slip surface to the average vertical stress;
(2) sand cobble stratum soil loose soil pressure calculation
According to the assumption of the model, the corner distribution formula of the maximum principal stress on the differential soil strips around the horizontal direction is as follows:
Figure 633544DEST_PATH_IMAGE001
in the formula:
Figure 764311DEST_PATH_IMAGE002
is the principal stress rotation angle at the slip plane; b is half of the width of the sliding body; x is the horizontal distance from the differential soil strips to the center of the tunnel;
Figure 699906DEST_PATH_IMAGE003
is the principal stress rotation angle at x;
the included angle between the large main stress on the sliding surface and the normal direction of the sliding surface is
Figure 548914DEST_PATH_IMAGE004
Then, then
Figure 798629DEST_PATH_IMAGE002
Is composed of
Figure 783903DEST_PATH_IMAGE004
The following can be obtained:
Figure 890399DEST_PATH_IMAGE005
further we can differentiate the stress at different x on the soil strip as:
Figure 429965DEST_PATH_IMAGE006
Figure 483371DEST_PATH_IMAGE007
Figure 854310DEST_PATH_IMAGE008
in the formula: kaThe active soil pressure coefficient is the active soil pressure coefficient,
Figure 633172DEST_PATH_IMAGE009
；
Figure 191193DEST_PATH_IMAGE010
is the horizontal pressure at x;
Figure 517132DEST_PATH_IMAGE011
is the vertical pressure at x;
Figure 8156DEST_PATH_IMAGE012
is the maximum principal stress at x;
Figure 659717DEST_PATH_IMAGE013
is the minimum principal stress at x;
Figure 236192DEST_PATH_IMAGE014
is the shear stress at x;
the vertical stress of the horizontal micro-segment dx on the micro-divided soil strip is:
Figure 365822DEST_PATH_IMAGE015
after the horizontal integration of the vertical stress on the differential soil strips, dividing the horizontal integration by the width 2B to obtain the average vertical stress on the differential soil strips, namely:
Figure 180194DEST_PATH_IMAGE016
the soil body lateral pressure coefficient K is:
Figure 799394DEST_PATH_IMAGE017
the following formula can be obtained according to the stress balance of the micro soil strips in the vertical direction:
Figure 597586DEST_PATH_IMAGE018
solving the differential equation to obtain
Figure 530907DEST_PATH_IMAGE019
The expression of (a) is:
Figure 199786DEST_PATH_IMAGE020
considering the boundary conditions: z =0, σv=p0Can beObtaining:
Figure 989887DEST_PATH_IMAGE021
in the formula:
Figure 275375DEST_PATH_IMAGE019
i.e. loosening of soil pressure, P0Is the earth surface load; gamma is the volume weight of the soil body; b is half of the width of the sliding body; k is the lateral pressure coefficient at the slip plane; phi is the internal friction angle of the soil body.
Preferably, the second step specifically comprises:
(1) assumptions of the calculation model
Assuming that a slip surface is a vertical surface, and the width of a slip body is the diameter of the tunnel and is defined as 2B;
(2) pebble stratum soil passive damage soil pressure calculation
Taking K as the lateral pressure coefficient of the slip surface when the soil body is passively damagedp=Ka，KaThe active soil pressure coefficient is the active soil pressure coefficient,
Figure 277966DEST_PATH_IMAGE022
；
when the slider is in ultimate balance state, carry out the atress analysis to the inside differential soil strip of slider, the vertical direction atress of soil body is balanced, then has:
Figure 535772DEST_PATH_IMAGE023
the above formula is modified to obtain:
Figure 496775DEST_PATH_IMAGE024
the solution of this first order non-homogeneous linear differential equation is:
Figure 472821DEST_PATH_IMAGE025
carry-in boundaryThe condition is that, when z =0,
Figure 13524DEST_PATH_IMAGE026
=P0c is obtained, and when z = H, the pressure on the slider is:
Figure 421109DEST_PATH_IMAGE027
in the formula (I), the compound is shown in the specification,
Figure 818593DEST_PATH_IMAGE028
i.e. passively breaking the earth pressure, P0Is the earth surface load;K a the active soil pressure coefficient is the active soil pressure coefficient,
Figure 281935DEST_PATH_IMAGE029
(ii) a B is half of the width of the sliding body; gamma is the volume weight of the soil body; phi is the internal friction angle of the soil body.
Preferably, in the third step, when the excavation face limit support pressure calculation model is constructed, the excavation face limit support pressure includes excavation face lower limit support pressure and excavation face upper limit support pressure, and when the excavation face limit support pressure is calculated, the wedge is divided into n differential soil strips in an inclined manner in a direction consistent with the inclined plane of the wedge.
Preferably, (1) the calculation model of the lower limit support pressure of the excavation surface is as follows:
determining the horizontal plane as the maximum main stress plane and the angle between the slip plane and the horizontal planeαIs composed of
Figure 360749DEST_PATH_IMAGE030
(ii) a The wedge-shaped body is degenerated into a triangular differential soil strip 1 at the right-angle vertex of the right-angle triangular slider, and the rest positions are trapezoidal differential soil strips i;
(2) the upper limit support pressure calculation model of the excavation surface is as follows:
determining the shield excavation surface as the maximum main stress surface, wherein the angle between the slip surface and the excavation surface is
Figure 389885DEST_PATH_IMAGE030
And further the angle between the slip plane and the horizontal planeαIs composed of
Figure 692691DEST_PATH_IMAGE031
(ii) a The wedge-shaped body is degenerated into a triangular differential soil strip 1 at the right-angle peak of the right-angle triangular slider, and the rest positions are trapezoidal differential soil strips i.
Preferably, the lower limit supporting pressure of the excavation face is calculated as follows:
the force balance equation in the normal direction of the excavation surface of the soil strip i is as follows:
Figure 643329DEST_PATH_IMAGE032
vertical force balance equation of soil i:
Figure 260255DEST_PATH_IMAGE033
in the formula:
Figure 612739DEST_PATH_IMAGE034
supporting pressure (N) of the excavation surface to which the soil strips are subjected;
Figure 352025DEST_PATH_IMAGE035
the friction force (N) borne by each side surface of the soil strip is related to the soil loosening pressure of the upper soil body borne by the wedge-shaped body and the side surface area of the soil strip when the lower limit supporting force is calculated;
Figure 321118DEST_PATH_IMAGE036
the soil strips are subjected to the normal supporting force (N) of the next soil strip;
Figure 741735DEST_PATH_IMAGE037
subjecting the soil strip to the normal pressure (N) of the previous soil strip;
Figure 948726DEST_PATH_IMAGE038
the coefficient of friction between the soil strips;
Figure 858913DEST_PATH_IMAGE039
the upper load (N) to the soil strip, and
Figure 534876DEST_PATH_IMAGE019
related, equal to the loose soil pressure
Figure 493605DEST_PATH_IMAGE019
The product of the area of the horizontal plane on the soil strip;
Figure 178271DEST_PATH_IMAGE040
is the gravity (N) of the soil strip;
according to the above formula, F when i =1gp0=0, the above equation can be changed to force balance equation for soil bar 1;
combining the force balance equation of the excavation surface normal direction of the soil strip i and the force balance equation of the soil body i in the vertical direction, and calculating the lower limit supporting pressure of the excavation surface
Figure 931463DEST_PATH_IMAGE034
：
Figure 140727DEST_PATH_IMAGE041
In summary, the following function is used to represent
Figure 699885DEST_PATH_IMAGE042
：
Figure 881467DEST_PATH_IMAGE043
In the formula (I), the compound is shown in the specification,
Figure 71140DEST_PATH_IMAGE019
in order to loosen the pressure of the soil,
Figure 502122DEST_PATH_IMAGE038
is the friction coefficient between the soil strips, K is the lateral pressure coefficient at the slip surface,iis a differential soil strip, and gamma is a soil volumeAnd D is the diameter of the tunnel,αis the angle between the slip plane and the horizontal plane.
Preferably, the upper limit supporting pressure of the excavation face is calculated as follows:
the force balance equation in the normal direction of the excavation surface of the soil strip i is as follows:
Figure 599391DEST_PATH_IMAGE044
vertical force balance equation of soil i:
Figure 635480DEST_PATH_IMAGE045
in the formula:
Figure 58371DEST_PATH_IMAGE046
supporting pressure (N) of the excavation surface to which the soil strips are subjected;
Figure 445490DEST_PATH_IMAGE037
subjecting the soil strip to the normal pressure (N) of the previous soil strip;
Figure 238127DEST_PATH_IMAGE036
the soil strips are subjected to the normal supporting force (N) of the next soil strip;
Figure 128723DEST_PATH_IMAGE035
the friction force (N) borne by each side surface of the soil strip is related to the soil pressure of the passive damage of the upper soil body to the wedge-shaped body and the side surface area of the soil strip when the lower limit supporting force is calculated;
Figure 722515DEST_PATH_IMAGE039
the upper load (N) to the soil strip, and
Figure 331351DEST_PATH_IMAGE028
related, equal to passively damaging earth pressure
Figure 770423DEST_PATH_IMAGE028
With soilThe product of the area of the horizontal plane above the strip;
Figure 466590DEST_PATH_IMAGE040
is the gravity (N) of the soil strip;
Figure 965705DEST_PATH_IMAGE038
the coefficient of friction between the soil strips;
according to the above formula, F when i =1gp0=0, the above equation can be changed to force balance equation for soil bar 1;
combining the force balance equation of the excavation surface normal direction of the soil strip i and the force balance equation of the soil body i in the vertical direction, and calculating the upper limit supporting pressure of the excavation surface
Figure 858574DEST_PATH_IMAGE046
：
Figure 665118DEST_PATH_IMAGE047
In summary, the following function is used to represent
Figure 530306DEST_PATH_IMAGE046
：
Figure 465901DEST_PATH_IMAGE048
In the formula (I), the compound is shown in the specification,
Figure 580488DEST_PATH_IMAGE028
in order to passively destroy the soil pressure,
Figure 830204DEST_PATH_IMAGE038
is the friction coefficient between the soil strips, K is the lateral pressure coefficient at the slip surface,iis a differential soil strip, gamma is the volume weight of the soil body, D is the diameter of the tunnel,αis the angle between the slip plane and the horizontal plane.
Preferably, the fourth step specifically includes:
the original vertical pressure of different depths of stratum is produced by earth surface load and the earth pillar gravity of top, and is the same with the loose soil pressure of adopting full earthing theory to calculate, promptly:
Figure 346636DEST_PATH_IMAGE049
in the formula (I), the compound is shown in the specification,
Figure 187553DEST_PATH_IMAGE011
in order to be the vertical pressure of the formation,
Figure 258277DEST_PATH_IMAGE050
is used as the ground surface load,
Figure 46104DEST_PATH_IMAGE051
is the volume weight of the soil body,
Figure 682622DEST_PATH_IMAGE052
burying soil body deeply;
the original lateral pressure of the formation is related to the formation vertical pressure and the lateral pressure coefficient, namely:
Figure 897703DEST_PATH_IMAGE053
in the formula (I), the compound is shown in the specification,
Figure 455723DEST_PATH_IMAGE010
is the original lateral pressure;
Figure 88654DEST_PATH_IMAGE011
is the formation vertical pressure;
Figure 579678DEST_PATH_IMAGE054
is a lateral pressure coefficient;
and when the support pressure of the excavation surface is the same as the original side pressure of the stratum, the support pressure of the excavation surface is the optimal support pressure, and the stratum is minimally disturbed under the current support pressure.
Preferably, in step five, the groundwater level pressure calculation formula is as follows:
Figure 231239DEST_PATH_IMAGE055
in the formula:
Figure 10976DEST_PATH_IMAGE056
is the density of water; g is the acceleration of gravity;
Figure 202923DEST_PATH_IMAGE057
the height difference between the underground water level and the excavation surface position is obtained;
the ultimate supporting pressure of the excavation surface considering the underground water is the sum of the ultimate supporting pressure of the excavation surface and the underground water level pressure.
Preferably, in the sixth step, the control principle of the support pressure of the excavation face is as follows:
(1) the excavation face supporting pressure is set in the range of the lower limit supporting pressure and the original side pressure, for the lower limit of the supporting pressure control, a certain safety coefficient is considered on the basis of the lower limit supporting pressure, and 20kPa is added on the basis of the calculation result to serve as the lower limit of the control;
(2) during shallow earthing construction, under the condition that the power of shield equipment allows, the support pressure is greater than the lower limit support pressure plus 20kPa and less than the upper limit support pressure minus 20kPa, and is close to the original lateral pressure as much as possible;
(3) when the shield tunnel passes through the existing structure in a close-up mode, the support pressure is controlled within the original side pressure range and is close to the original side pressure, and the displacement in the stratum is guaranteed within a controllable range through follow-up auxiliary measures.
Compared with the prior art, the invention has the beneficial effects that: the method establishes a shield excavation face ultimate support pressure calculation model, deduces a calculation formula of excavation face ultimate support pressure, and obtains the soil pressure control ranges of different heights of the excavation face. The research result can provide guidance and reference for the shield construction soil pressure control. The method can improve the safety of shield construction, provides a basis for the pressure control of the earth bin in the shield construction, reduces the influence of the earth pressure balance shield construction on the surrounding environment, and plays an important role in promoting the construction of urban subways. Specifically, at least the following practical effects are obtained:
(1) a stratum passive damage soil pressure calculation method is deduced according to a stratum loose soil pressure calculation formula, the supporting force of an excavation surface is accurately controlled between the upper limit supporting pressure and the lower limit supporting pressure, the soil body of the excavation surface is prevented from being damaged during engineering construction, and the risk in the engineering construction is greatly reduced;
(2) the method adopts the inclined strip division method to calculate the support pressure of the excavation surface, can obtain the soil pressure control ranges of different heights of the excavation surface, and has more accurate calculation result.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below. It should be apparent that the drawings in the following description are merely exemplary, and that other embodiments can be derived from the drawings provided by those of ordinary skill in the art without inventive effort.
The structures, ratios, sizes, and the like shown in the present specification are only used for matching with the contents disclosed in the specification, so that those skilled in the art can understand and read the present invention, and do not limit the conditions for implementing the present invention, so that the present invention has no technical significance, and any structural modifications, changes in the ratio relationship, or adjustments of the sizes, without affecting the functions and purposes of the present invention, shall fall within the scope covered by the technical contents disclosed in the present invention.
FIG. 1 is a schematic diagram of a calculation model of supporting pressure of an excavation face according to an embodiment of the invention;
FIG. 2 is a schematic representation of a sand and gravel formation surface collapse in accordance with an embodiment of the present invention;
FIG. 3 is a schematic view of a loose soil pressure calculation model according to an embodiment of the present invention;
FIG. 4 is a schematic view of a differential soil strip force analysis in accordance with one embodiment of the present invention;
FIG. 5 is a schematic diagram of a soil passive failure soil pressure calculation model according to an embodiment of the present invention;
FIG. 6 is a schematic view of a horizontal soil strip force analysis according to one embodiment of the present invention;
FIG. 7 is a schematic view of a front slide of an excavation face according to one embodiment of the present invention;
FIG. 8 is a schematic view of a horizontal differential soil bar according to one embodiment of the present invention;
FIG. 9 is a schematic view of a calculation model of a triangular soil strip 1 of the lower limit support pressure of the excavation face;
FIG. 10 is a stress analysis schematic diagram of a triangular soil strip 1 of the lower limit support pressure of the excavation face;
FIG. 11 is a schematic diagram of a calculation model of a trapezoidal differential soil strip i of the lower limit supporting pressure of an excavation face;
FIG. 12 is a schematic view of a force analysis of a trapezoidal differential soil strip i of a lower limit support pressure of an excavation face;
FIG. 13 is a schematic view of a calculation model of a triangular soil strip 1 of the upper limit supporting pressure of the excavation face;
FIG. 14 is a stress analysis schematic diagram of a triangular soil strip 1 of the upper limit support pressure of the excavation surface;
FIG. 15 is a schematic diagram of a calculation model of trapezoidal differential soil strips i of upper limit supporting pressure of an excavation face;
FIG. 16 is a schematic view of force analysis of a trapezoidal differential soil strip i of upper limit supporting pressure of an excavation face;
fig. 17 is a schematic diagram of the deformation range of the stratum under different support pressure conditions.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the embodiments of the present invention are described in further detail below with reference to the embodiments and the accompanying drawings. The exemplary embodiments and descriptions of the present invention are provided to explain the present invention, but not to limit the present invention.
In the present invention, unless otherwise expressly stated or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integrally formed; can be mechanically or electrically connected; either directly or indirectly through intervening media, either internally or in any other relationship. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
It is to be understood that the terms "comprises/comprising," "consisting of … …," or any other variation, are intended to cover a non-exclusive inclusion, such that a product, device, process, or method that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such product, device, process, or method if desired. Without further limitation, an element defined by the phrases "comprising/including … …," "consisting of … …," or "comprising" does not exclude the presence of other like elements in a product, device, process, or method that comprises the element.
It will be further understood that the terms "upper," "lower," "front," "rear," "left," "right," "top," "bottom," "inner," "outer," and the like, refer to an orientation or positional relationship as shown in the drawings, which is meant only to facilitate describing the invention and to simplify the description, and do not indicate or imply that the referenced device, component, or structure must have a particular orientation, be constructed or operated in a particular orientation, and is not to be construed as limiting the invention.
The following describes the implementation of the present invention in detail with reference to preferred embodiments.
In actual shield construction, the supporting force of the shield on the excavation surface is difficult to fix at the original side pressure of the soil body, and in order to prevent the soil body of the excavation surface from being damaged, the supporting force should meet the requirement of PLower bound of branch-lower bound<PBranch stand<PUpper and lower bound of. Therefore, the supporting force of the excavation surface corresponding to the two limit states is determined, and the control principle of the soil pressure in the construction process is provided, so that the method is of great importance to shield construction.
Therefore, the invention provides a sand-gravel stratum earth pressure balance shield earth bin pressure design and control method, which comprises the following steps:
the method comprises the following steps: constructing a soil body loose soil pressure calculation model in an active limit balance state of a sandy gravel stratum above an interface, and calculating the interface loose soil pressure;
step two: constructing a soil body passive damaged soil pressure calculation model under a sand-gravel stratum passive limit balance state above the interface, and calculating the interface passive damaged soil pressure;
step three: constructing an excavation face ultimate support pressure calculation model, and calculating excavation face ultimate support pressures in different ultimate balance states according to the interface soil pressure calculation result;
step four: calculating the optimal supporting pressure of the excavation surface;
step five: calculating the underground water level pressure to obtain the ultimate supporting pressure of the excavation surface considering the underground water;
step six: and determining the control principle of the supporting pressure of the excavation surface, and designing and controlling the pressure of the shield construction soil bin.
In the present invention, as shown in fig. 1, when analyzing the ultimate supporting pressure of the excavation face, the analysis is performed in two steps: firstly, taking an upper prism as an analysis object, and solving the vertical soil pressure at an interface; and then, taking the wedge body in front of the excavation surface as an analysis object, and combining the vertical soil pressure at the interface to obtain the ultimate supporting pressure of the excavation surface.
In the invention, the stratum vertical soil pressure under two limit states is calculated: the vertical soil pressure in the active limit equilibrium state is called as 'loose soil pressure'; the earth pressure at the passive limit equilibrium state is referred to as "passive earth-damaging pressure".
At present, the hypothesis of research key parameters about Terzaghi loose soil pressure theory is that on the basis of the existing research, a full-section sandy gravel stratum shield construction loose soil pressure calculation model is established, and a reasonable loose soil pressure calculation formula is deduced. The method comprises the following steps:
(1) assumptions of the calculation model
1) Slip surface shape and slip width
As shown in fig. 2, it can be known from analysis of the existing research that the slip surface is mostly considered to be a combination of straight lines with different slopes by the existing research, and the slope change point of the straight line is the depth of the tunnel vault, and at the same time, a straight line is formed from the top of the tunnel vault to the ground surface. According to the research on the soil body arch effect development process, the sliding surface is expanded to a tower shape from a triangle, so that a vertical shape or even a basin shape is formed. The summary of the surface collapse forms of the sandy gravel stratum can show that the slip plane formed by the subsidence of the sandy gravel stratum is basically a vertical plane, so that the slip plane is assumed to be a vertical plane when the soil pressure calculation is carried out.
2) Coefficient of lateral pressure on slip plane
And (3) establishing a calculation method of the lateral pressure coefficient of the slip surface by considering the deflection of the main stress axis, the arc shape of the large main stress trajectory, and the shape and width of the slip surface. The definition of the lateral pressure coefficient in Terzaghi loose soil pressure theory is essentially the relationship between the vertical stress on the soil strips and the normal stress of the soil body on the slip surface. For the calculation of the lateral pressure coefficient in the soil, some scholars replace the lateral pressure coefficient on the slip surface, and also put forward a method for calculating the average lateral pressure coefficient by using the ratio of the average vertical stress to the horizontal stress. In the invention, the lateral pressure coefficient K is defined as the ratio of the soil body normal stress of the slip surface to the average vertical stress.
(2) Sand cobble stratum soil loose soil pressure calculation
As shown in fig. 3, according to the assumption of a calculation model, the width of the sliding body is defined to be 2B, the stress state of the differential soil strip is analyzed based on the principle of principal stress rotation theory and the arc-shaped large principal stress trajectory line, and the research of the existing literature proves that the principal stress rotation angles at different positions on the differential soil strip are linearly distributed, so that the formula of the distribution of the maximum principal stress on the differential soil strip around the rotation angle in the horizontal direction is as follows:
Figure 141929DEST_PATH_IMAGE001
in the formula:
Figure 698812DEST_PATH_IMAGE002
is the principal stress rotation angle at the slip plane; b is half of the width of the sliding body; x is the horizontal distance from the differential soil strips to the center of the tunnel;
Figure 497004DEST_PATH_IMAGE003
is the principal stress rotation angle at x;
the included angle between the large main stress on the sliding surface and the normal direction (horizontal direction) of the sliding surface is
Figure 994107DEST_PATH_IMAGE004
Then, then
Figure 662986DEST_PATH_IMAGE002
Is composed of
Figure 390770DEST_PATH_IMAGE004
The following can be obtained:
Figure 676258DEST_PATH_IMAGE005
according to the basic principle of assuming that the soil stress state on the same horizontal differential soil strip is in the same Moire stress circle and the Moire stress circle, the stress at different x positions on the horizontal differential soil strip can be expressed as follows:
Figure 210007DEST_PATH_IMAGE006
Figure 733393DEST_PATH_IMAGE007
Figure 897658DEST_PATH_IMAGE008
in the formula: kaThe active soil pressure coefficient is the active soil pressure coefficient,
Figure 936021DEST_PATH_IMAGE009
；
Figure 211144DEST_PATH_IMAGE010
is the horizontal pressure at x;
Figure 385774DEST_PATH_IMAGE011
is the vertical pressure at x;
Figure 455361DEST_PATH_IMAGE012
is the maximum principal stress at x;
Figure 184283DEST_PATH_IMAGE013
is the minimum principal stress at x;
Figure 59835DEST_PATH_IMAGE014
is the shear stress at x;
the vertical stress of the horizontal micro-segment dx on the micro-divided soil strip is:
Figure 88971DEST_PATH_IMAGE015
after the horizontal integration of the vertical stress on the differential soil strips, dividing the horizontal integration by the width 2B to obtain the average vertical stress on the differential soil strips, namely:
Figure 860618DEST_PATH_IMAGE016
the soil body lateral pressure coefficient K is:
Figure 545677DEST_PATH_IMAGE017
as shown in fig. 4, the force of the differential soil strip is analyzed, and the force of the differential soil strip includes: the self gravity of the soil body, the acting force of the overlying soil, the acting force of the lower soil body, the normal compressive stress of the slip plane and the friction force of the slip plane;
the following formula can be obtained according to the stress balance of the micro soil strips in the vertical direction:
Figure 224920DEST_PATH_IMAGE018
solving the differential equation to obtain
Figure 577404DEST_PATH_IMAGE019
The expression of (a) is:
Figure 254373DEST_PATH_IMAGE020
considering the boundary conditions: z =0, σv=p0The following can be obtained:
Figure 722001DEST_PATH_IMAGE021
in the formula:
Figure 142618DEST_PATH_IMAGE019
i.e. loosening of soil pressure, P0Is the earth surface load; gamma is the volume weight of the soil body; b is half of the width of the sliding body; k is the lateral pressure coefficient at the slip plane; phi is the internal friction angle of the soil body.
In the invention, the calculation of the loose soil pressure can be regarded as the active damage limit state of the prismatic soil body. In the shield construction process, the situation that the ground surface settlement is out of limit due to active damage of the soil body above the excavation surface is avoided, the construction parameters show that the support pressure of the excavation surface is not less than the limit value of the active damage, and besides, the situation that the ground surface is raised due to passive damage of the soil body above the excavation surface is also avoided in the shield construction process. At present, passive failure states of soil bodies above an excavation surface are rarely researched, and then the pressure on an interface when a prism soil body moves upwards to a soil body reaching a limit failure state is analyzed by considering the interaction between a sliding body and the surrounding soil bodies according to the principle that Terzaghi establishes a loose soil pressure calculation model.
Referring to the form of the slip plane in the loose soil pressure calculation, as shown in fig. 5 and 6, the following assumptions are made in the establishment of the soil passive failure model: the slip face was vertical and the slip width was the tunnel diameter, defined as 2B.
When the sliding body moves upwards, the stress of the soil body in the sliding body in the vertical direction is continuously increased, and the vertical direction is always the main stress direction until the soil body is passively damaged;
taking K as the lateral pressure coefficient of the slip surface when the soil body is passively damagedp=Ka，KaThe active soil pressure coefficient is the active soil pressure coefficient,
Figure 411925DEST_PATH_IMAGE022
；
when the slider is in ultimate balance state, carry out the atress analysis to the inside differential soil strip of slider, the vertical direction atress of soil body is balanced, then has:
Figure 259796DEST_PATH_IMAGE023
the above formula is modified to obtain:
Figure 185026DEST_PATH_IMAGE024
the solution of this first order non-homogeneous linear differential equation is:
Figure 940493DEST_PATH_IMAGE025
bringing in a boundary condition, when z =0,
Figure 798727DEST_PATH_IMAGE026
=P0c is obtained, and when z = H, the pressure on the slider is:
Figure 83078DEST_PATH_IMAGE027
in the formula (I), the compound is shown in the specification,
Figure 230026DEST_PATH_IMAGE028
i.e. passively breaking the earth pressure, P0Is the earth surface load;K a the active soil pressure coefficient is the active soil pressure coefficient,
Figure 54762DEST_PATH_IMAGE029
(ii) a B isHalf the width of the slider; gamma is the volume weight of the soil body; phi is the internal friction angle of the soil body.
In the invention, a calculation method of loose soil pressure and passive damaged soil pressure at an arch top above an excavation surface is researched, and ultimate supporting pressure of the excavation surface is analyzed on the basis. And analyzing the support pressure of the excavation surface under different limit states by taking the soil body in front of the excavation surface as a research object.
As shown in fig. 7 and 8, when the excavation face support pressure is calculated, the stability of the excavation face is analyzed by assuming that the sliding body of the soil body in front of the excavation face is a wedge-shaped body and dividing the soil body into n pieces by a striping method, and a stable limit balance state equation of the excavation face is derived to further calculate the limit support pressure of the excavation face. When the soil body damage is calculated, the soil body is divided in an inclined mode, which is different from the common horizontal dividing and vertical dividing modes. The following assumptions were made in building the calculation model:
(1) the sliding surface of the soil body instability in front of the shield excavation surface is an inclined surface, the angle between the inclined surface and the horizontal plane is alpha, and the right-angled triangular sliding body is a wedge-shaped body;
(2) the pressure of two vertical side surfaces of the wedge-shaped body has a linear relation with the larger value of the horizontal or vertical pressure, and the linear coefficient is k;
(3) the uniform force on each face reduces to a concentrated force on the centroid.
The invention discloses an excavation face ultimate support pressure calculation model which comprises an excavation face lower limit support pressure calculation model and an excavation face upper limit support pressure calculation model.
As shown in fig. 9 to 12, in the excavation face lower limit support pressure calculation model:
(1) macroscopically, the horizontal plane is the maximum principal stress plane, so the angle between the slip plane and the horizontal plane is consideredαIs composed of
Figure 236345DEST_PATH_IMAGE030
Taking differential soil strips at different positions to analyze the stress of the trapezoidal differential soil strip i (a conventional soil strip) and the triangular soil strip (the trapezoidal differential soil strip degenerates into a triangle at the right-angle vertex of a right-angle triangle slip body);
(2) based on the established model, combining with the stress analysis of the soil strips in the extreme balance state, a force balance equation of each soil strip i can be established, and then the lower limit support pressure of the excavation surface can be solved;
the force balance equation in the normal direction of the excavation surface of the soil strip i is as follows:
Figure 957176DEST_PATH_IMAGE032
vertical force balance equation of soil i:
Figure 591420DEST_PATH_IMAGE033
in the formula:
Figure 157530DEST_PATH_IMAGE034
supporting pressure (N) of the excavation surface to which the soil strips are subjected;
Figure 521516DEST_PATH_IMAGE035
the friction force (N) borne by each side surface of the soil strip is related to the soil loosening pressure of the upper soil body borne by the wedge-shaped body and the side surface area of the soil strip when the lower limit supporting force is calculated;
Figure 180292DEST_PATH_IMAGE036
the soil strips are subjected to the normal supporting force (N) of the next soil strip;
Figure 567411DEST_PATH_IMAGE037
subjecting the soil strip to the normal pressure (N) of the previous soil strip;
Figure 671633DEST_PATH_IMAGE038
the coefficient of friction between the soil strips;
Figure 93388DEST_PATH_IMAGE039
the upper load (N) to the soil strip, and
Figure 890442DEST_PATH_IMAGE019
related, equal to the loose soil pressure
Figure 296016DEST_PATH_IMAGE019
The product of the area of the horizontal plane on the soil strip;
Figure 203929DEST_PATH_IMAGE040
is the gravity (N) of the soil strip;
according to the above formula, F when i =1gp0=0, the above equation can be changed to force balance equation for soil bar 1;
lower limit support pressure of excavation face
Figure 745769DEST_PATH_IMAGE034
Combining the normal force balance equation of the excavation surface of the soil strip i with the vertical force balance equation of the soil body i to calculate the lower limit supporting pressure of the excavation surface
Figure 713725DEST_PATH_IMAGE034
：
Figure 606594DEST_PATH_IMAGE041
In summary, the following function is used to represent
Figure 52619DEST_PATH_IMAGE042
：
Figure 917807DEST_PATH_IMAGE043
In the formula (I), the compound is shown in the specification,
Figure 853402DEST_PATH_IMAGE019
in order to loosen the pressure of the soil,
Figure 967989DEST_PATH_IMAGE038
is the friction coefficient between the soil strips, K is the lateral pressure coefficient at the slip surface,iis a differential soil strip, gamma is the volume weight of the soil body, D is the diameter of the tunnel,αis the angle between the slip plane and the horizontal plane.
As shown in fig. 13-16, in the calculation model of the upper limit supporting pressure of the excavation surface:
(1) when the upper limit support pressure of the excavation surface is calculated, the macroscopically shield excavation surface is the maximum main stress surface, so that the angle between the slip surface and the excavation surface is considered to be
Figure 217704DEST_PATH_IMAGE030
I.e. at an angle alpha to the horizontal plane
Figure 937399DEST_PATH_IMAGE031
；
(2) Taking differential soil strips at different positions to respectively analyze the stress of a trapezoidal differential soil strip i (a conventional soil strip) and a triangular soil strip (the trapezoidal differential soil strip degenerates into a triangle at the right-angle vertex of a right-angle triangle slip), respectively establishing a force balance equation in the normal direction of the excavation surface and a force balance equation in the vertical direction, and determining the upper limit supporting pressure of the excavation surface;
the force balance equation in the normal direction of the excavation surface of the soil strip i is as follows:
Figure 43895DEST_PATH_IMAGE044
vertical force balance equation of soil i:
Figure 114619DEST_PATH_IMAGE045
in the formula:
Figure 902447DEST_PATH_IMAGE046
supporting pressure (N) of the excavation surface to which the soil strips are subjected;
Figure 771920DEST_PATH_IMAGE037
subjecting the soil strip to the normal pressure (N) of the previous soil strip;
Figure 49318DEST_PATH_IMAGE036
for receiving soil stripsNormal support force (N) of the next soil strip;
Figure 341759DEST_PATH_IMAGE035
the friction force (N) borne by each side surface of the soil strip is related to the soil pressure of the passive damage of the upper soil body to the wedge-shaped body and the side surface area of the soil strip when the lower limit supporting force is calculated;
Figure 933277DEST_PATH_IMAGE039
the upper load (N) to the soil strip, and
Figure 158722DEST_PATH_IMAGE028
related, equal to passively damaging earth pressure
Figure 810283DEST_PATH_IMAGE028
The product of the area of the horizontal plane on the soil strip;
Figure 652337DEST_PATH_IMAGE040
is the gravity (N) of the soil strip;
Figure 781967DEST_PATH_IMAGE038
the coefficient of friction between the soil strips;
according to the above formula, F when i =1gp0=0, the above equation can be changed to force balance equation for soil bar 1;
upper limit support pressure of excavated surface
Figure 330760DEST_PATH_IMAGE046
Combining the normal force balance equation of the excavation surface of the soil strip i with the vertical force balance equation of the soil body i to calculate the upper limit supporting pressure of the excavation surface
Figure 215540DEST_PATH_IMAGE046
：
Figure 13732DEST_PATH_IMAGE047
In summary, the following function is used to represent
Figure 212632DEST_PATH_IMAGE046
：
Figure 350352DEST_PATH_IMAGE048
In the formula (I), the compound is shown in the specification,
Figure 406033DEST_PATH_IMAGE028
in order to passively destroy the soil pressure,
Figure 160362DEST_PATH_IMAGE038
is the friction coefficient between the soil strips, K is the lateral pressure coefficient at the slip surface,iis a differential soil strip, gamma is the volume weight of the soil body, D is the diameter of the tunnel,αis the angle between the slip plane and the horizontal plane.
According to the method, when the optimal supporting pressure of the excavation face is determined, the supporting pressure of the tunnel face in the shield construction process is determined to be controlled between the upper limit supporting pressure and the lower limit supporting pressure according to the calculated supporting pressure, and when the supporting pressure exceeds the range, the soil body of the excavation face is damaged, so that the engineering risk is caused; in the process of shield construction, on the basis of avoiding the risk of the construction and avoiding the construction, the influence of shield construction on the surrounding environment is further reduced, and when the support pressure of the excavation face is the original lateral pressure of the stratum, the disturbance of the shield construction on the stratum is minimum.
In engineering, the original vertical pressure at different depths of the stratum is generally thought to be generated by earth surface load and the gravity of an upper earth pillar, which is the same as the loose soil pressure calculated by adopting a full earthing theory, namely:
Figure 428532DEST_PATH_IMAGE049
in the formula (I), the compound is shown in the specification,
Figure 686338DEST_PATH_IMAGE011
in order to be the vertical pressure of the formation,
Figure 116183DEST_PATH_IMAGE050
is used as the ground surface load,
Figure 390431DEST_PATH_IMAGE051
is the volume weight of the soil body,
Figure 665555DEST_PATH_IMAGE052
burying soil body deeply;
the original lateral pressure of the formation is related to the formation vertical pressure and the lateral pressure coefficient, namely:
Figure 309026DEST_PATH_IMAGE053
in the formula (I), the compound is shown in the specification,
Figure 175351DEST_PATH_IMAGE010
is the original lateral pressure;
Figure 701010DEST_PATH_IMAGE011
is the formation vertical pressure;
Figure 779824DEST_PATH_IMAGE054
is a lateral pressure coefficient;
in summary, when the excavation face supporting pressure is the same as the original side pressure of the stratum, the excavation face supporting pressure is the optimal supporting pressure, and the disturbance of the stratum under the current supporting pressure is the minimum.
According to the invention, based on the characteristic of high permeability of the sandy gravel stratum, water and soil are adopted for calculating the supporting pressure of the excavation surface, when underground water exists in the stratum, the supporting pressure required by the excavation surface needs to balance the lateral pressure of the soil body and the pressure of the underground water level, and the calculation formula of the pressure of the underground water level is as follows:
Figure 12223DEST_PATH_IMAGE055
in the formula:
Figure 49449DEST_PATH_IMAGE056
is the density of water; g is the acceleration of gravity；
Figure 265667DEST_PATH_IMAGE057
The height difference between the underground water level and the excavation surface position is obtained;
the supporting pressure of the excavation surface is the sum of the lateral pressure of the soil body and the pressure of the underground water, and is obviously known by the formula: g.
Figure 476068DEST_PATH_IMAGE056
is constant, the groundwater pressure is only equal to
Figure 359710DEST_PATH_IMAGE057
And is relevant and not affected by other factors. Therefore, only the influence of various factors on the side pressure of the soil body is considered when the influence factors of the supporting pressure of the excavation surface are analyzed.
In the invention, as shown in fig. 17, the ultimate supporting pressure of the excavation face is analyzed by an ultimate balance method, the soil body is considered to be a rigid body in the analysis, and the slip bodies (the prism soil body and the wedge soil body) are not deformed due to the change of the state. When the support pressure of the excavation surface is the original side pressure of the stratum, the soil body is not disturbed, so that deformation does not occur. And when the excavation face supporting pressure is the lower limit supporting pressure, the sliding body is in the ultimate balance state, at the moment, the stress state of the sliding body is changed, certain vertical displacement exists in different positions inside the sliding body, and the displacement at the earth surface is 0. When the supporting pressure is within the range of the original stress of the stratum and the lower limit supporting force, the isosurface with the vertical displacement of 0 is positioned in the sliding body (the soil body above the isosurface can be considered not to be disturbed by the shield construction), and the difference of the isosurface exists when the supporting pressure is different, namely the difference of the influence range of the shield construction on the surrounding soil body also exists.
Based on the above summary and combined with the shield construction experience, the excavation face support pressure control follows the following principle:
(1) the excavation face supporting pressure is set within the range of the lower limit supporting pressure and the original side pressure, a certain safety factor is considered on the basis of the lower limit supporting pressure for the lower limit supporting pressure of the supporting pressure control, namely 20kPa is added on the basis of the calculation result to be used as the lower limit control.
(2) During shallow earthing construction, under the condition that the power of shield equipment allows, the support pressure is greater than the lower limit support pressure plus 20kPa and less than the upper limit support pressure minus 20kPa, and is close to the original side pressure as much as possible, so that the ground surface settlement is not over-limited;
(3) when the shield tunnel passes through the existing structure in the stratum in a close-connection mode, the supporting pressure is close to the original lateral pressure as much as possible, and the displacement in the stratum is guaranteed within a controllable range through subsequent auxiliary measures (filling of a gap outside a shield shell, synchronous grouting filling, secondary grout supplementing filling and the like).
The invention establishes a shield excavation face ultimate support pressure calculation model, deduces a calculation formula of the excavation face ultimate support pressure, determines the optimal support pressure of the excavation face and the support pressure of the excavation face considering underground water, and provides a shield construction soil pressure control principle. The method can improve the safety of shield construction, provide basis for the pressure control of the earth bin in shield construction, reduce the influence of earth pressure balance shield construction on the surrounding environment, and play an important role in promoting urban subway construction.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (10)

1. A sand and gravel stratum earth pressure balance shield earth bin pressure design and control method is characterized by comprising the following steps:
the method comprises the following steps: constructing a soil body loose soil pressure calculation model in an active limit balance state of a sandy gravel stratum above an interface, and calculating the interface loose soil pressure;
step two: constructing a soil body passive damaged soil pressure calculation model under a sand-gravel stratum passive limit balance state above the interface, and calculating the interface passive damaged soil pressure;
step three: constructing an excavation face ultimate support pressure calculation model, and calculating excavation face ultimate support pressures in different ultimate balance states according to the interface soil pressure calculation result;
step four: calculating the optimal supporting pressure of the excavation surface;
step five: calculating the underground water level pressure to obtain the ultimate supporting pressure of the excavation surface considering the underground water;
step six: and determining the control principle of the supporting pressure of the excavation surface, and designing and controlling the pressure of the shield construction soil bin.
2. The sandy gravel stratum earth pressure balance shield earth bin pressure design and control method as claimed in claim 1, wherein:
the first step specifically comprises the following steps:
(1) assumptions of the calculation model
Assuming that the slip surface is a vertical surface, the width of a slip body is the diameter of a tunnel and is defined as 2B, and meanwhile, defining the lateral pressure coefficient K of a soil body as the ratio of the normal stress of the soil body on the slip surface to the average vertical stress;
(2) sand cobble stratum soil loose soil pressure calculation
According to the assumption of the model, the corner distribution formula of the maximum principal stress on the differential soil strips around the horizontal direction is as follows:
Figure 403836DEST_PATH_IMAGE001
in the formula:
Figure 638509DEST_PATH_IMAGE002
is the principal stress rotation angle at the slip plane; b is half of the width of the sliding body; x is the horizontal distance from the differential soil strips to the center of the tunnel;
Figure 59126DEST_PATH_IMAGE003
is the principal stress rotation angle at x;
the included angle between the large main stress on the sliding surface and the normal direction of the sliding surface is
Figure 62854DEST_PATH_IMAGE004
Then, then
Figure 645145DEST_PATH_IMAGE002
Is composed of
Figure 570376DEST_PATH_IMAGE004
The following can be obtained:
Figure 591421DEST_PATH_IMAGE005
further we can differentiate the stress at different x on the soil strip as:
Figure 449656DEST_PATH_IMAGE006
Figure 468427DEST_PATH_IMAGE007
Figure 880954DEST_PATH_IMAGE008
in the formula: kaThe active soil pressure coefficient is the active soil pressure coefficient,
Figure 440111DEST_PATH_IMAGE009
；
Figure 356115DEST_PATH_IMAGE010
is the horizontal pressure at x;
Figure 342525DEST_PATH_IMAGE011
is the vertical pressure at x;
Figure 242348DEST_PATH_IMAGE012
is the maximum principal stress at x;
Figure 103732DEST_PATH_IMAGE013
is the minimum principal stress at x;
Figure 874242DEST_PATH_IMAGE014
is the shear stress at x;
the vertical stress of the horizontal micro-segment dx on the micro-divided soil strip is:
Figure 31553DEST_PATH_IMAGE015
after the horizontal integration of the vertical stress on the differential soil strips, dividing the horizontal integration by the width 2B to obtain the average vertical stress on the differential soil strips, namely:
Figure 215410DEST_PATH_IMAGE016
the soil body lateral pressure coefficient K is:
Figure 319632DEST_PATH_IMAGE017
the following formula can be obtained according to the stress balance of the micro soil strips in the vertical direction:
Figure 210228DEST_PATH_IMAGE018
solving the differential equation to obtain
Figure 804020DEST_PATH_IMAGE019
The expression of (a) is:
Figure 944015DEST_PATH_IMAGE020
considering the boundary conditions: z =0, σv=p0The following can be obtained:
Figure 117507DEST_PATH_IMAGE021
in the formula:
Figure 862609DEST_PATH_IMAGE019
i.e. loosening of soil pressure, P0Is the earth surface load; gamma is the volume weight of the soil body; b is half of the width of the sliding body; k is the lateral pressure coefficient at the slip plane; phi is the internal friction angle of the soil body.
3. The sandy gravel stratum earth pressure balance shield earth bin pressure design and control method as claimed in claim 1, wherein:
the second step specifically comprises:
(1) assumptions of the calculation model
Assuming that a slip surface is a vertical surface, and the width of a slip body is the diameter of the tunnel and is defined as 2B;
(2) pebble stratum soil passive damage soil pressure calculation
Taking K as the lateral pressure coefficient of the slip surface when the soil body is passively damagedp=Ka，KaThe active soil pressure coefficient is the active soil pressure coefficient,
Figure 627303DEST_PATH_IMAGE022
；
when the slider is in ultimate balance state, carry out the atress analysis to the inside differential soil strip of slider, the vertical direction atress of soil body is balanced, then has:
Figure 254593DEST_PATH_IMAGE023
the above formula is modified to obtain:
Figure 700618DEST_PATH_IMAGE024
the solution of this first order non-homogeneous linear differential equation is:
Figure 565806DEST_PATH_IMAGE025
bringing in a boundary condition, when z =0,
Figure 501401DEST_PATH_IMAGE026
=P0c is obtained, and when z = H, the pressure on the slider is:
Figure 84829DEST_PATH_IMAGE027
in the formula (I), the compound is shown in the specification,
Figure 68965DEST_PATH_IMAGE028
i.e. passively breaking the earth pressure, P0Is the earth surface load;K a the active soil pressure coefficient is the active soil pressure coefficient,
Figure 86862DEST_PATH_IMAGE029
(ii) a B is half of the width of the sliding body; gamma is the volume weight of the soil body; phi is the internal friction angle of the soil body.
4. The sandy gravel stratum earth pressure balance shield earth bin pressure design and control method as claimed in claim 1, wherein:
and in the third step, when constructing the excavation face limit supporting pressure calculation model, the excavation face limit supporting pressure comprises excavation face lower limit supporting pressure and excavation face upper limit supporting pressure, and when calculating the excavation face limit supporting pressure, the wedge body is divided into n differential soil strips in an inclined mode in the direction consistent with the inclined plane of the wedge body.
5. The sandy gravel stratum earth pressure balance shield earth bin pressure design and control method as claimed in claim 4, wherein:
(1) the calculation model of the lower limit support pressure of the excavation surface is as follows:
determining the horizontal plane as the maximum main stress plane and the angle between the slip plane and the horizontal planeαIs composed of
Figure 193359DEST_PATH_IMAGE030
(ii) a The wedge-shaped body is degenerated into a triangular differential soil strip 1 at the right-angle vertex of the right-angle triangular slider, and the rest positions are trapezoidal differential soil strips i;
(2) the upper limit support pressure calculation model of the excavation surface is as follows:
determining the shield excavation surface as the maximum main stress surface, wherein the angle between the slip surface and the excavation surface is
Figure 264083DEST_PATH_IMAGE030
And further the angle between the slip plane and the horizontal planeαIs composed of
Figure 51910DEST_PATH_IMAGE031
(ii) a The wedge-shaped body is degenerated into a triangular differential soil strip 1 at the right-angle peak of the right-angle triangular slider, and the rest positions are trapezoidal differential soil strips i.
6. The sandy gravel stratum earth pressure balance shield earth bin pressure design and control method as claimed in claim 5, wherein:
the lower limit support pressure of the excavation face is calculated as follows:
the force balance equation in the normal direction of the excavation surface of the soil strip i is as follows:
Figure 688428DEST_PATH_IMAGE032
vertical force balance equation of soil i:
Figure 169088DEST_PATH_IMAGE033
in the formula：
Figure 992687DEST_PATH_IMAGE034
Supporting pressure (N) of the excavation surface to which the soil strips are subjected;
Figure 584206DEST_PATH_IMAGE035
the friction force (N) borne by each side surface of the soil strip is related to the soil loosening pressure of the upper soil body borne by the wedge-shaped body and the side surface area of the soil strip when the lower limit supporting force is calculated;
Figure 278492DEST_PATH_IMAGE036
the soil strips are subjected to the normal supporting force (N) of the next soil strip;
Figure 257949DEST_PATH_IMAGE037
subjecting the soil strip to the normal pressure (N) of the previous soil strip;
Figure 37687DEST_PATH_IMAGE038
the coefficient of friction between the soil strips;
Figure 229634DEST_PATH_IMAGE039
the upper load (N) to the soil strip, and
Figure 778427DEST_PATH_IMAGE019
related, equal to the loose soil pressure
Figure 600889DEST_PATH_IMAGE019
The product of the area of the horizontal plane on the soil strip;
Figure 399081DEST_PATH_IMAGE040
is the gravity (N) of the soil strip;
according to the above formula, F when i =1gp0=0, the above equation can be changed to force balance equation for soil bar 1;
force balance equation of normal direction of excavation surface of simultaneous soil strips i and force balance equation of vertical direction of soil body i are calculatedCalculating the lower limit support pressure of the excavation face
Figure 332402DEST_PATH_IMAGE034
：
Figure 296553DEST_PATH_IMAGE041
In summary, the following function is used to represent
Figure 289917DEST_PATH_IMAGE042
：
Figure 309826DEST_PATH_IMAGE043
In the formula (I), the compound is shown in the specification,
Figure 312417DEST_PATH_IMAGE019
in order to loosen the pressure of the soil,
Figure 632540DEST_PATH_IMAGE038
is the friction coefficient between the soil strips, K is the lateral pressure coefficient at the slip surface,iis a differential soil strip, gamma is the volume weight of the soil body, D is the diameter of the tunnel,αis the angle between the slip plane and the horizontal plane.
7. The sandy gravel stratum earth pressure balance shield earth bin pressure design and control method as claimed in claim 5, wherein:
the upper limit support pressure of the excavation face is calculated as follows:
the force balance equation in the normal direction of the excavation surface of the soil strip i is as follows:
Figure 531226DEST_PATH_IMAGE044
vertical force balance equation of soil i:
Figure 772851DEST_PATH_IMAGE045
in the formula:
Figure 110291DEST_PATH_IMAGE046
supporting pressure (N) of the excavation surface to which the soil strips are subjected;
Figure 19342DEST_PATH_IMAGE037
subjecting the soil strip to the normal pressure (N) of the previous soil strip;
Figure 354508DEST_PATH_IMAGE036
the soil strips are subjected to the normal supporting force (N) of the next soil strip;
Figure 817850DEST_PATH_IMAGE035
the friction force (N) borne by each side surface of the soil strip is related to the soil pressure of the passive damage of the upper soil body to the wedge-shaped body and the side surface area of the soil strip when the lower limit supporting force is calculated;
Figure 958982DEST_PATH_IMAGE039
the upper load (N) to the soil strip, and
Figure 988118DEST_PATH_IMAGE028
related, equal to passively damaging earth pressure
Figure 228606DEST_PATH_IMAGE028
The product of the area of the horizontal plane on the soil strip;
Figure 444824DEST_PATH_IMAGE040
is the gravity (N) of the soil strip;
Figure 858488DEST_PATH_IMAGE038
the coefficient of friction between the soil strips;
according to the above formula, when i =1Fgp0=0, the above equation can be changed to force balance equation for soil bar 1;
combining the force balance equation of the excavation surface normal direction of the soil strip i and the force balance equation of the soil body i in the vertical direction, and calculating the upper limit supporting pressure of the excavation surface
Figure 210972DEST_PATH_IMAGE046
：
Figure 920564DEST_PATH_IMAGE047
In summary, the following function is used to represent
Figure 155236DEST_PATH_IMAGE046
：
Figure 575853DEST_PATH_IMAGE048
In the formula (I), the compound is shown in the specification,
Figure 782844DEST_PATH_IMAGE028
in order to passively destroy the soil pressure,
Figure 693031DEST_PATH_IMAGE038
is the friction coefficient between the soil strips, K is the lateral pressure coefficient at the slip surface,iis a differential soil strip, gamma is the volume weight of the soil body, D is the diameter of the tunnel,αis the angle between the slip plane and the horizontal plane.
8. The sandy gravel stratum earth pressure balance shield earth bin pressure design and control method as claimed in claim 1, wherein:
the fourth step specifically comprises:
the original vertical pressure of different depths of stratum is produced by earth surface load and the earth pillar gravity of top, and is the same with the loose soil pressure of adopting full earthing theory to calculate, promptly:
Figure 680578DEST_PATH_IMAGE049
in the formula (I), the compound is shown in the specification,
Figure 904886DEST_PATH_IMAGE011
in order to be the vertical pressure of the formation,
Figure 763121DEST_PATH_IMAGE050
is used as the ground surface load,
Figure 781892DEST_PATH_IMAGE051
is the volume weight of the soil body,
Figure 928840DEST_PATH_IMAGE052
burying soil body deeply;
the original lateral pressure of the formation is related to the formation vertical pressure and the lateral pressure coefficient, namely:
Figure 753577DEST_PATH_IMAGE053
in the formula (I), the compound is shown in the specification,
Figure 669580DEST_PATH_IMAGE010
is the original lateral pressure;
Figure 124832DEST_PATH_IMAGE011
is the formation vertical pressure;
Figure 555813DEST_PATH_IMAGE054
is a lateral pressure coefficient;
and when the support pressure of the excavation surface is the same as the original side pressure of the stratum, the support pressure of the excavation surface is the optimal support pressure, and the stratum is minimally disturbed under the current support pressure.
9. The sandy gravel stratum earth pressure balance shield earth bin pressure design and control method as claimed in claim 1, wherein:
in the fifth step, the underground water level pressure calculation formula is as follows:
Figure 428916DEST_PATH_IMAGE055
in the formula:
Figure 465005DEST_PATH_IMAGE056
is the density of water; g is the acceleration of gravity;
Figure 825579DEST_PATH_IMAGE057
the height difference between the underground water level and the excavation surface position is obtained;
the ultimate supporting pressure of the excavation surface considering the underground water is the sum of the ultimate supporting pressure of the excavation surface and the underground water level pressure.
10. The sandy gravel stratum earth pressure balance shield earth bin pressure design and control method as claimed in claim 1, wherein:
in the sixth step, the control principle of the support pressure of the excavation surface is as follows:
(1) the excavation face supporting pressure is set in the range of the lower limit supporting pressure and the original side pressure, for the lower limit of the supporting pressure control, a certain safety coefficient is considered on the basis of the lower limit supporting pressure, and 20kPa is added on the basis of the calculation result to serve as the lower limit of the control;
(2) during shallow earthing construction, under the condition that the power of shield equipment allows, the support pressure is greater than the lower limit support pressure plus 20kPa and less than the upper limit support pressure minus 20kPa, and is close to the original lateral pressure as much as possible;
(3) when the shield tunnel passes through the existing structure in a close-up mode, the support pressure is controlled within the original side pressure range and is close to the original side pressure, and the displacement in the stratum is guaranteed within a controllable range through follow-up auxiliary measures.
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