CN112329122B - Method for determining transverse deformation and internal force of shield tunnel caused by excavation of side foundation pit - Google Patents
Method for determining transverse deformation and internal force of shield tunnel caused by excavation of side foundation pit Download PDFInfo
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Abstract
The invention relates to a method for determining transverse deformation and internal force of a shield tunnel caused by excavation of a side foundation pit, which specifically comprises the following steps: s1: determining design parameters and geological condition information of a foundation pit and a tunnel; s2: obtaining horizontal displacement and vertical displacement of a soil body of a free field at the side of the foundation pit caused by horizontal deformation of the foundation pit support structure by a source-sink method; s3: extracting horizontal displacement and vertical displacement at each point on the circumference of the tunnel, calculating convergence at different positions of the tunnel, and determining the maximum convergence and the position thereof; s4: obtaining a pressure distribution mode around the tunnel; s5: and obtaining the structural load variable quantity Δ p3 of the segment, and further obtaining the transverse deformation and the corresponding internal force of the shield tunnel. The method can better reflect the deformation rule of the shield tunnel caused by excavation of the side foundation pit, so that the safety state of the shield tunnel under the disturbance of excavation of the foundation pit can be more accurately evaluated.
Description
Technical Field
The invention relates to a method in the technical field of constructional engineering, in particular to a method for determining cross section deformation and internal force of a shield tunnel caused by excavation of a side foundation pit.
Background
The urban subway is used as a main artery of modern urban underground traffic, and the safety of the urban subway is directly related to the life safety of vast passengers. In recent years, with the continuous progress of urbanization, the underground space in large and medium-sized cities in China gradually shows the characteristics and the trend of 'deep, large, near and miscellaneous', and the underground space development around the existing subways is inevitably carried out. The subway shield tunnel is formed by splicing prefabricated pipe pieces, the pipe pieces are connected through bolts, the overall rigidity of the structure is weak, and the deformation resistance is poor. Disturbance can be caused to the soil body on every side in the excavation process, and the peripheral subway tunnel structure can produce additional load to lead to the shield tunnel to appear the diseases such as section of jurisdiction mistake platform, fracture, percolating water, slight will influence the normal operation of tunnel and driving comfort, serious can cause the incident and influence the long-term performance of being in service of tunnel.
Through the search of documents in the prior art, the existing research method for the transverse deformation rule of the shield tunnel under the disturbance of the construction of the side foundation pit mainly adopts numerical simulation. The numerical simulation calculation process is relatively complex, and the constitutive model of the simulation material and the parameters thereof are not easy to determine. Yang Yu Bing is 2016. Plaxis is adopted in research on transverse deformation and cracking characteristic of shield tunnel under construction of adjacent foundation pit published in the journal of rock mechanics and engineering to perform inverse analysis on the deformation of shield tunnel in Ningbo area under disturbance of adjacent foundation pit, and the result shows that the tunnel deformation is the integral displacement towards the foundation pit and the section deformation in the mode of 'transverse duck egg'. The research of calculating the deformation rule of the shield tunnel based on the analytic method mainly focuses on the longitudinal direction of the tunnel, and a determination method aiming at the transverse deformation and the internal force of the tunnel is lacked. Under the normal condition, the cross section of the shield tunnel presents a 'transverse duck egg' mode under the self-weight stress of soil body, namely, the shield tunnel is horizontally elongated and vertically compressed. Stress release is caused by excavation of the side foundation pit, horizontal unloading is mainly used on the side of the foundation pit, and then the existing shield tunnel is further compressed in the vertical direction. The tunnel lateral deformation continues to increase, and the internal force of the tunnel structure also increases, and when exceeding the allowable stress of concrete or bolts, the tunnel lining may generate cracks, leakage and other diseases, and the normal operation of the tunnel engineering can be influenced in serious cases. Therefore, the research on the interaction of the excavation of the side foundation pit and the existing tunnel needs to consider the transverse characteristic of the shield tunnel, and an analysis method is provided for researching the influence of the transverse characteristic.
Disclosure of Invention
The invention aims to provide a method for determining the cross section deformation and the internal force of a shield tunnel caused by side foundation pit excavation, which can better reflect the deformation rule of the shield tunnel caused by the side foundation pit excavation, so that the safety state of the shield tunnel under foundation pit excavation disturbance can be more accurately evaluated.
In order to achieve the purpose, the method for determining the transverse deformation and the internal force of the shield tunnel caused by excavation of the side foundation pit comprises the following steps:
s1: determining design parameters and geological condition information of a foundation pit and a tunnel;
s2: the horizontal deformation of the foundation pit support structure caused by foundation pit excavation is regarded as stratum loss, and the horizontal displacement of the soil body of the free field at the side of the foundation pit caused by the horizontal deformation of the foundation pit support structure is obtained by integrating along the depth direction by a source-sink methodu(x, z) And vertical displacements(x, z)；
S3: extracting the horizontal displacement of each point on the circumference of the tunnel through the obtained horizontal displacement field and vertical displacement field of the soil body of the free field at the side of the foundation pitu ϕ And vertical displacements ϕ Calculating the convergence at different positions of the tunnel∆h ϕ And recording the maximum convergence amount respectively∆h max And the corresponding angleϕ max ；
S4: determining the external soil layer pressure distribution of the cross section of the shield tunnel under the initial condition to obtain a pressure distribution mode;
s5: the main stress direction of the side soil body rotates after the foundation pit is excavated, the main stress direction is assumed to be consistent with the directions of the long axis and the short axis of the changed elliptical tunnel, the pressure distribution mode of the step S4 is adopted to calculate the convergence deformation and the internal force distribution of the tunnel, and the foundation pit excavation is assumed to only cause the tunnel loadp 3Alternatively, the maximum convergence amount of the tunnel obtained in step S3 is used∆h max Determining the corresponding segment structure load variable quantity by force methodp 3Further obtain the neighborAnd the shield tunnel transversely deforms and correspondingly generates internal force under the action of near foundation pit construction.
As a further improvement of the method for determining the transverse deformation and the internal force of the shield tunnel caused by excavation of the side foundation pit, in step S1,
the design parameters of the foundation pit comprise: the excavation depth of the foundation pit, the embedding depth of the enclosure structure and the horizontal deformation distribution of the foundation pit enclosure structure;
the design parameters of the tunnel include: the method comprises the following steps of (1) tunnel burial depth, segment inner diameter, segment thickness, concrete segment elastic modulus, number and positions of segment longitudinal joints, bending rigidity reduction coefficient of the longitudinal joints and horizontal distance from a tunnel to a foundation pit;
the geological condition information includes: the soil layer weight, the cohesion, the internal friction angle and the soil resistance coefficient.
As a further improvement of the method for determining the transverse deformation and the internal force of the shield tunnel caused by excavation of the side foundation pit, in the step S2, the horizontal displacement of the soil body of the free field at the side of the foundation pit is adoptedu(x, z) And vertical displacements(x, z) The following formula is satisfied:
Wherein the content of the first and second substances,Hexcavating depth for the foundation pit;Dthe depth of the enclosure wall in the soil is determined; (x, z) Coordinates of any point beside the foundation pit are obtained;r 1、r 2the following formula is satisfied for the parameters related to the relative position of the foundation pit:
and
；a(h) Is depth ofhEquivalent radius of formation lossAnd at any depth, according to area equivalence, the stratum loss corresponding to each micro-segment is equivalent to a circle, and the following formula is satisfied:
；δ(h) Is depth ofhAnd the horizontal deformation of the enclosure.
As a further improvement of the method for determining the transverse deformation and the internal force of the shield tunnel caused by excavation of the side foundation pit, in step S3, the convergence quantity is determined∆h ϕ The calculation formula of (a) is as follows:
Wherein the content of the first and second substances,ϕthe included angle between the connecting line of the displacement calculation point on the circumference of the tunnel and the axle center of the tunnel and the vertical direction is more than or equal to 0ϕ＜πBefore and after the side foundation pit is excavated, the cross section of the shield tunnel is changed from a circle to an ellipse, and the angle corresponding to the maximum convergence is consideredϕ max I.e. in the direction of the minor or major axis of the ellipse.
As a further improvement of the method for determining the transverse deformation and the internal force of the shield tunnel caused by excavation of the side foundation pit, in step S4, the pressure distribution mode at least comprises:
vertical load at top of tunnelp 1The following formula is satisfied:
Wherein p is0Is a ground load; q. q.s1For the vertical pressure of the soil layer at the top of the tunnel, the following formula is satisfied:
，γiand hiRespectively the weight and the thickness of the ith soil layer, and n is the number of the soil layers; q. q.s2For the vertical pressure of the soil layer in the tunnel arch shoulder range, the following formula is satisfied:
and r is the radius of the tunnel,
the average soil layer weight in the tunnel arch shoulder range is obtained;
vertical load at tunnel bottomp 2The following formula is satisfied:
Wherein the content of the first and second substances,tandγ c the thickness and the weight of the tube piece respectively;
horizontal load at top of tunnelp 3The following formula is satisfied:
Wherein the content of the first and second substances,candφrespectively the cohesion and the internal friction angle of the soil layer;
horizontal loading in the deep range of a tunnelp 4The following formula is satisfied:
average dead weight of shield segmentp 5：
soil layer resistance of two sides of shield segmentp 6：
Wherein, the assumed soil layer resistance only has the included angles between the two sides of the tunnel segment and the vertical directionϕIs in the range of 45-135 degrees;p h for the soil layer resistance at the arch waist of the tunnel, the following formula is satisfied:
，k s is the modulus of the foundation.
As a further improvement of the method for determining the transverse deformation and the internal force of the shield tunnel caused by excavation of the side foundation pit, in step S5, determining the corresponding tube piece structure horizontal load change amount by a force methodp 3Further, the concrete steps of obtaining the vertical convergence amount and the corresponding internal force of the shield tunnel under the construction action of the adjacent foundation pit are as follows:
the control equation is used as follows:
Wherein the content of the first and second substances,x 1andx 2respectively assuming virtual bending moment and axial force acting on the vault of the tunnel;δ ii is unit forcex i Edge generated by position of applied forcex i The deformation in the direction of the force is,i=1，2；δ ij is unit forcex j In thatx i Edge generated by position of applied forcex i The deformation in the direction of the force is,i，j=1，2；∆ ip the pressure of the soil is inx i Edge generated by position of applied forcex i The deformation in the direction of the force is,i=1，2。
in unit virtual bending momentx 1Or axial forcex 2Under the action, the shield segments determine models respectivelyThe following boundary conditions are satisfied:
As a further improvement of the method for determining the transverse deformation and the internal force of the shield tunnel caused by excavation of the side foundation pit, in step S1, a deformation mode of the foundation pit enclosure structure is determined.
As a further improvement of the method for determining the transverse deformation and the internal force of the shield tunnel caused by excavation of the side foundation pit, the deformation mode of the foundation pit enclosure structure is a parabolic mode, and the enclosure structure deformation has the following expression:
Wherein the content of the first and second substances,h 0indicating maximum deformation of the building envelopeδ maxThe depth of the buried part is greater than the depth of the buried part,δ max=A+B. A. B and C are constant coefficients and can be obtained by fitting field data.
As a further improvement of the method for determining the transverse deformation and the internal force of the shield tunnel caused by excavation of the side foundation pit, in step S5, different distances between the tunnel and the foundation pit are takenL t And obtaining the tunnel convergence, bending moment and axial force changes caused by the construction of the side foundation pit.
The method can better reflect the deformation rule of the shield tunnel caused by excavation of the side foundation pit, so that the safety state of the shield tunnel under the disturbance of excavation of the foundation pit can be more accurately evaluated. The method is simple and practical, is convenient to popularize and has a high application value.
Drawings
FIG. 1 is a schematic diagram of lateral free field soil displacement caused by horizontal deformation of a foundation pit support structure.
Fig. 2 is a schematic diagram of shield tunnel deformation under the excavation action of a side foundation pit.
Fig. 3 is a schematic diagram of a shield tunnel cross-section external load distribution model.
Fig. 4 is a schematic deformation diagram of the enclosure structure in the embodiment.
FIG. 5 is a schematic diagram of horizontal displacement and vertical displacement of soil bodies at different depths in the embodiment.
Fig. 6 is a schematic diagram of the influence of the distance between the existing tunnel and the newly-built foundation pit on the convergence amount, the bending moment and the axial force of the tunnel.
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.
In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of description and simplicity of description, but do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be construed as limiting the present invention; the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance; furthermore, unless expressly stated or limited otherwise, the terms "mounted," "connected," and "connected" are to be construed broadly, as they may be fixedly connected, detachably connected, or integrally connected, for example; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
Example 1
A method for determining transverse deformation and internal force of a shield tunnel caused by excavation of a side foundation pit specifically comprises the following steps:
s1: determining design parameters and geological condition information of a foundation pit and a tunnel;
s2: the horizontal deformation of the foundation pit support structure caused by foundation pit excavation is regarded as stratum loss, and the horizontal displacement of the soil body of the free field at the side of the foundation pit caused by the horizontal deformation of the foundation pit support structure is obtained by integrating along the depth direction by a source-sink methodu(x, z) And vertical displacements(x, z)；
S3: extracting the horizontal displacement of each point on the circumference of the tunnel through the obtained horizontal displacement field and vertical displacement field of the soil body of the free field at the side of the foundation pitu ϕ And vertical displacements ϕ Calculating the convergence at different positions of the tunnel∆h ϕ And recording the maximum convergence amount respectively∆h max And the corresponding angleϕ max ；
S4: determining the external soil layer pressure distribution of the cross section of the shield tunnel under the initial condition to obtain a pressure distribution mode;
s5: the main stress direction of the side soil body rotates after the foundation pit is excavated, the main stress direction is assumed to be consistent with the directions of the long axis and the short axis of the changed elliptical tunnel, the pressure distribution mode of the step S4 is adopted to calculate the convergence deformation and the internal force distribution of the tunnel, and the foundation pit excavation is assumed to only cause the tunnel loadp 3Alternatively, the maximum convergence amount of the tunnel obtained in step S3 is used∆h max Determining the corresponding segment structure load variable quantity by force methodp 3And further obtaining the transverse deformation of the shield tunnel and the corresponding internal force under the construction action of the adjacent foundation pit.
In the present embodiment, in step S1,
the design parameters of the foundation pit comprise: the excavation depth of the foundation pit, the embedding depth of the enclosure structure and the horizontal deformation distribution of the foundation pit enclosure structure;
the design parameters of the tunnel include: the method comprises the following steps of (1) tunnel burial depth, segment inner diameter, segment thickness, concrete segment elastic modulus, number and positions of segment longitudinal joints, bending rigidity reduction coefficient of the longitudinal joints and horizontal distance from a tunnel to a foundation pit;
the geological condition information includes: the soil layer weight, the cohesion, the internal friction angle and the soil resistance coefficient.
In this embodiment, in step S2, the free-field soil body on the lateral side of the foundation pit is horizontally displacedu(x, z) And vertical displacements(x, z) The following formula is satisfied:
Wherein the content of the first and second substances,Hexcavating depth for the foundation pit;Dthe depth of the enclosure wall in the soil is determined; (x, z) Coordinates of any point beside the foundation pit are obtained;r 1、r 2the following formula is satisfied for the parameters related to the relative position of the foundation pit:
and
；a(h) Is depth ofhAnd (3) equivalent radius of the stratum loss, wherein the stratum loss corresponding to each micro-segment is equivalent to a circle according to area equivalence at any depth, and the following formula is satisfied:
；δ(h) Is depth ofhAnd the horizontal deformation of the enclosure.
In the present embodiment, in step S3, the amount of convergence∆h ϕ The calculation formula of (a) is as follows:
Wherein the content of the first and second substances,ϕthe included angle between the connecting line of the displacement calculation point on the circumference of the tunnel and the axle center of the tunnel and the vertical direction is more than or equal to 0ϕ＜πBefore and after the side foundation pit is excavated, the cross section of the shield tunnel is changed from a circle to an ellipse, and the angle corresponding to the maximum convergence is consideredϕ max I.e. in the direction of the minor or major axis of the ellipse.
In this embodiment, in step S4, the pressure distribution pattern includes:
vertical load at top of tunnelp 1The following formula is satisfied:
Wherein p is0Is a ground load; q. q.s1For the vertical pressure of the soil layer at the top of the tunnel, the following formula is satisfied:
，γiand hiRespectively the weight and the thickness of the ith soil layer, and n is the number of the soil layers; q. q.s2For the vertical pressure of the soil layer in the tunnel arch shoulder range, the following formula is satisfied:
r is the radius of the tunnel and the average soil layer weight in the range of the arch shoulder of the tunnel;
vertical load at tunnel bottomp 2The following formula is satisfied:
Wherein the content of the first and second substances,tandγ c the thickness and the weight of the tube piece respectively;
horizontal load at top of tunnelp 3The following formula is satisfied:
Wherein the content of the first and second substances,candφrespectively the cohesion and the internal friction angle of the soil layer;
horizontal loading in the deep range of a tunnelp 4The following formula is satisfied:
average dead weight of shield segmentp 5：
soil layer resistance of two sides of shield segmentp 6：
Wherein, the assumed soil layer resistance only has the included angles between the two sides of the tunnel segment and the vertical directionϕIs in the range of 45-135 degrees;p h for the soil layer resistance at the arch waist of the tunnel, the following formula is satisfied:
，k s is the modulus of the foundation.
In this embodiment, in step S5, the corresponding tube sheet structure horizontal load change amount is determined by the force methodp 3Further, the concrete steps of obtaining the vertical convergence amount and the corresponding internal force of the shield tunnel under the construction action of the adjacent foundation pit are as follows:
the control equation is used as follows:
Wherein the content of the first and second substances,x 1andx 2respectively assuming virtual bending moment and axial force acting on the vault of the tunnel;δ ii is unit forcex i Edge generated by position of applied forcex i The deformation in the direction of the force is,i=1，2；δ ij is unit forcex j In thatx i Edge generated by position of applied forcex i The deformation in the direction of the force is,i，j=1，2；∆ ip the pressure of the soil is inx i Edge generated by position of applied forcex i The deformation in the direction of the force is,i=1，2。
in unit virtual bending momentx 1Or axial forcex 2Under the action, the shield segment determines the bending moment in the modelMAxial forceNAnd shear forceQThe following boundary conditions are satisfied:
In this embodiment, in step S1, the deformation mode of the foundation pit enclosure is determined.
In this embodiment, the deformation mode of the foundation pit enclosure is a parabolic mode, and the deformation of the enclosure has the following expression:
Wherein the content of the first and second substances,h 0indicating maximum deformation of the building envelopeδ maxThe depth of the buried part is greater than the depth of the buried part,δ max=A+B. A. B and C are constant coefficients and can be obtained by fitting field data.
In this embodiment, in step S5, different distances between the tunnel and the foundation pit are takenL t And obtaining the tunnel convergence, bending moment and axial force changes caused by the construction of the side foundation pit.
Example 2
Fig. 1 to 6 show a method for determining lateral deformation and internal force of a shield tunnel caused by excavation of a side foundation pit, which can obtain displacement of a soil body of a free field at the side of the foundation pit after determining deformation information of a foundation pit enclosure structure, establish a model capable of considering a longitudinal seam of the tunnel, and further determine deformation and internal force of the tunnel.
The invention is realized by the following technical scheme, which comprises the following steps:
the method comprises the following steps of firstly, determining design parameters and geological condition information of a foundation pit and a tunnel.
The design parameters of the foundation pit comprise: the excavation depth of the foundation pit, the embedding depth of the enclosure structure and the horizontal deformation distribution of the foundation pit enclosure structure.
The tunnel design parameters include: the tunnel buries deeply, section of jurisdiction internal diameter, section of jurisdiction thickness, concrete segment elastic modulus, the number and the position of section of jurisdiction longitudinal joint, longitudinal joint bending rigidity reduction factor, the horizontal distance of tunnel apart from the foundation ditch.
The geological condition information comprises: the soil layer weight, the cohesion, the internal friction angle and the soil resistance coefficient.
And secondly, regarding the horizontal deformation of the foundation pit support structure caused by foundation pit excavation as stratum loss, and obtaining the horizontal displacement of the soil body of the free field at the side of the foundation pit caused by the horizontal deformation of the foundation pit support structure by integrating along the depth direction through a source-sink methodu(x, z) And vertical displacements(x, z) The following formula is satisfied:
Wherein the content of the first and second substances,Hexcavating depth for the foundation pit;Dthe depth of the enclosure wall in the soil is determined; (x, z) Coordinates of any point beside the foundation pit are obtained;r 1、r 2the following formula is satisfied for the parameters related to the relative position of the foundation pit:
and
；a(h) Is depth ofhAnd (3) equivalent radius of the stratum loss, wherein the stratum loss corresponding to each micro-segment is equivalent to a circle according to area equivalence at any depth, and the following formula is satisfied:
；δ(h) Is depth ofhAnd the horizontal deformation of the enclosure.
Thirdly, extracting the horizontal displacement of each point on the circumference of the tunnel through the obtained horizontal displacement field and vertical displacement field of the soil body of the free field at the side of the foundation pitu ϕ And vertical displacements ϕ Calculating the amount of convergence (stretch) at different positions of the tunnel∆h ϕ And recording the maximum convergence (stretch) amount, respectively∆h max And the corresponding angleϕ max 。
Wherein the content of the first and second substances,ϕthe included angle between the connecting line of the displacement calculation point on the circumference of the tunnel and the axle center of the tunnel and the vertical direction is more than or equal to 0ϕ＜πAs shown in FIG. 2Shown in the figure. Assuming that the cross section of the shield tunnel is changed from a circle to an ellipse before and after the excavation of the side foundation pit, the angle corresponding to the maximum convergence (stretching) amount is consideredϕ max I.e. in the direction of the minor (major) axis of the ellipse. And fourthly, determining the external soil layer pressure distribution of the cross section of the shield tunnel under the initial condition, wherein the pressure distribution mode is shown in figure 3.
p 1For the vertical load of tunnel top, satisfy following formula:
Wherein the content of the first and second substances,p 0is a ground load;q 1for the vertical pressure of the soil layer at the top of the tunnel, the following formula is satisfied:
，γ i and h i are respectively the firstiThe weight and thickness of the subsoil layer,nthe number of soil layers;q 2for the vertical pressure of the soil layer in the tunnel arch shoulder range, the following formula is satisfied:
，rin order to be the radius of the tunnel,
the average soil layer weight in the range of the tunnel arch shoulder.
p 2For the vertical load of tunnel bottom, satisfy following formula:
Wherein the content of the first and second substances,tandγ c the thickness and the weight of the tube piece respectively;
p 3in order to horizontally load the top of the tunnel,the following formula is satisfied:
Wherein the content of the first and second substances,candφrespectively the cohesion and the internal friction angle of the soil layer;
p 4for the horizontal load in the deep range of the tunnel, the following formula is satisfied:
p 5The average dead weight of the shield segment is as follows:
p 6The soil layer resistance of the two sides of the shield segment is as follows:
Wherein, the assumed soil layer resistance only has the included angles between the two sides of the tunnel segment and the vertical directionϕIs in the range of 45-135 degrees;p h for the soil layer resistance at the arch waist of the tunnel, the following formula is satisfied:
，k s is the modulus of the foundation.
And fifthly, after the foundation pit is excavated, the main stress direction of the side soil body rotates, and assuming that the main stress direction is consistent with the direction of the long axis and the short axis of the changed elliptical tunnel, the load mode shown in fig. 3 is adopted to calculate the convergence deformation and the internal force distribution of the tunnel. Suppose that excavation of a foundation pit causes only horizontal loading of a tunnelp 3Varying, according to the maximum convergence (stretch) of the tunnel obtained in the third step∆ h max The corresponding tube segment structure horizontal load variable quantity can be determined by a force methodp 3And further obtaining the vertical convergence of the shield tunnel and corresponding internal forces (bending moment, axial force and shearing force) under the construction action of the adjacent foundation pit. The control equation is as follows:
Wherein the content of the first and second substances,x 1andx 2respectively assuming virtual bending moment and axial force acting on the vault of the tunnel;δ ii is unit force (bending moment)x i Edge generated by position of applied forcex i The deformation in the direction of the force is,i=1，2；δ ij is unit force (bending moment)x j In thatx i Edge generated by position of applied forcex i The deformation in the direction of the force is,i，j=1，2；∆ ip the pressure of the soil is inx i Edge generated by position of applied forcex i The deformation in the direction of the force is,i=1，2。
in unit virtual bending momentx 1Or axial forcex 2Under the action, the shield segment determines the bending moment in the modelMAxial forceNAnd shear forceQThe following boundary conditions are satisfied:
Example 3
The method comprises the following steps of firstly, determining design parameters and geological condition information of a foundation pit and a tunnel.
The soil, tunnel and foundation pit parameters selected in this case are shown in table 1. In this case, if the foundation pit support structure is deformed into a parabolic mode, the support structure deformation has the following expression:
Wherein the content of the first and second substances,h 0indicating maximum deformation of the building envelopeδ maxThe depth of the buried part is greater than the depth of the buried part,δ max=A+B. Taking in caseh 0=15 m，A=3，B=33，C=8, variation diagram is shown in fig. 3.
TABLE 1 soil, Tunnel and Foundation pit parameter Table
And secondly, determining the displacement of the soil body of the free field at the side of the foundation pit. According to the formulas 1 and 2, the soil deformation at any position on the side of the foundation pit can be determined, and the relation between the horizontal deformation and the vertical deformation of the soil at different depths along with the change of the distance between the tunnel and the foundation pit is shown in fig. 5.
Thirdly, calculating the horizontal displacement and the vertical displacement of each point on the circumference of the tunnel, and further calculating the maximum convergence (stretching) quantity through a formula 3∆h max And the corresponding angleϕ max 。
Fourthly, determining the external soil layer pressure distribution of the cross section of the shield tunnel under the initial condition, wherein the result is as follows:p 1=316.2 kPa；p 2=343.7 kPa；p 3=133.2kPa；p 4=57.8 kPa；p 5=8.7 kPa；p h =177.5kPa。
fifthly, according to the formula 10-13, taking different horizontal distances between the tunnel and the foundation pitL t To obtainThe tunnel convergence, bending moment and axial force changes caused by the construction of the side foundation pit are shown in figure 6.
The method mainly comprises the following steps: s1: determining design parameters and geological condition information of a foundation pit and a tunnel; s2: obtaining horizontal displacement and vertical displacement of a soil body of a free field at the side of the foundation pit caused by horizontal deformation of the foundation pit support structure by a source-sink method; s3: extracting horizontal displacement and vertical displacement at each point on the circumference of the tunnel, calculating convergence at different positions of the tunnel, and determining the maximum convergence and the position thereof; s4: obtaining a pressure distribution mode around the tunnel; s5: and obtaining the structural load variable quantity Δ p3 of the segment, and further obtaining the transverse deformation and the corresponding internal force of the shield tunnel.
Compared with the prior art, the method for determining the transverse deformation and the internal force of the shield tunnel caused by the excavation of the side foundation pit can better reflect the deformation rule of the shield tunnel caused by the excavation of the side foundation pit, so that the safety state of the shield tunnel under the disturbance of the excavation of the foundation pit can be more accurately evaluated. The method is simple and practical, is convenient to popularize and has a high application value.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several equivalent substitutions or obvious modifications can be made without departing from the spirit of the invention, and all the properties or uses are considered to be within the scope of the invention.
Claims (6)
1. A method for determining transverse deformation and internal force of a shield tunnel caused by excavation of a side foundation pit is characterized by comprising the following steps:
s1: determining design parameters and geological condition information of a foundation pit and a tunnel;
s2: the horizontal deformation of the foundation pit support structure caused by foundation pit excavation is regarded as stratum loss, and the horizontal displacement of the soil body of the free field at the side of the foundation pit caused by the horizontal deformation of the foundation pit support structure is obtained by integrating along the depth direction by a source-sink methodu(x, z) And vertical displacements(x, z)；
S3: extracting the horizontal displacement of each point on the circumference of the tunnel through the obtained horizontal displacement field and vertical displacement field of the soil body of the free field at the side of the foundation pitu ϕ And vertical displacements ϕ Calculating the convergence at different positions of the tunnel∆h ϕ And recording the maximum convergence amount respectively∆h max And the corresponding angleϕ max ；
S4: determining the external soil layer pressure distribution of the cross section of the shield tunnel under the initial condition to obtain a pressure distribution mode;
s5: the main stress direction of the side soil body rotates after the foundation pit is excavated, the main stress direction is assumed to be consistent with the directions of the long axis and the short axis of the changed elliptical tunnel, the pressure distribution mode of the step S4 is adopted to calculate the convergence deformation and the internal force distribution of the tunnel, and the foundation pit excavation is assumed to only cause the tunnel loadp 3Alternatively, the maximum convergence amount of the tunnel obtained in step S3 is used∆h max Determining the corresponding segment structure load variable quantity by force methodp 3Further acquiring transverse deformation of the shield tunnel and corresponding internal force under the construction action of the adjacent foundation pit;
in the step S1, in the step S,
the design parameters of the foundation pit comprise: the excavation depth of the foundation pit, the embedding depth of the enclosure structure and the horizontal deformation distribution of the foundation pit enclosure structure;
the design parameters of the tunnel include: the method comprises the following steps of (1) tunnel burial depth, segment inner diameter, segment thickness, concrete segment elastic modulus, number and positions of segment longitudinal joints, bending rigidity reduction coefficient of the longitudinal joints and horizontal distance from a tunnel to a foundation pit;
the geological condition information includes: the soil layer weight, cohesion, internal friction angle and soil resistance coefficient;
in step S2, the soil body of the free field at the side of the foundation pit is horizontally displacedu(x, z) And vertical displacements(x, z) The following formula is satisfied:
Wherein the content of the first and second substances,Hexcavating depth for the foundation pit;Dthe depth of the enclosure wall in the soil is determined; (x, z) Coordinates of any point beside the foundation pit are obtained;r 1、r 2the following formula is satisfied for the parameters related to the relative position of the foundation pit:
and
；a(h) Is depth ofhAnd (3) equivalent radius of the stratum loss, wherein the stratum loss corresponding to each micro-segment is equivalent to a circle according to area equivalence at any depth, and the following formula is satisfied:
；δ(h) Is depth ofhThe horizontal deformation of the enclosure structure is controlled;
in step S3, the convergence amount∆h ϕ The calculation formula of (a) is as follows:
Wherein the content of the first and second substances,ϕthe included angle between the connecting line of the displacement calculation point on the circumference of the tunnel and the axle center of the tunnel and the vertical direction is more than or equal to 0ϕ＜πBefore and after the side foundation pit is excavated, the cross section of the shield tunnel is changed from a circle to an ellipse, and the angle corresponding to the maximum convergence is consideredϕ max I.e. in the direction of the minor or major axis of the ellipse.
2. The method for determining the lateral deformation and the internal force of the shield tunnel caused by excavation of the side foundation pit according to claim 1, wherein in step S4, the pressure distribution pattern at least comprises:
vertical load at top of tunnelp 1The following formula is satisfied:
Wherein p is0Is a ground load; q. q.s1For the vertical pressure of the soil layer at the top of the tunnel, the following formula is satisfied:
，γiand hiRespectively the weight and the thickness of the ith soil layer, and n is the number of the soil layers; q. q.s2For the vertical pressure of the soil layer in the tunnel arch shoulder range, the following formula is satisfied:
and r is the radius of the tunnel,
the average soil layer weight in the tunnel arch shoulder range is obtained;
vertical load at tunnel bottomp 2The following formula is satisfied:
Wherein the content of the first and second substances,tandγ c the thickness and the weight of the tube piece respectively;
horizontal load at top of tunnelp 3The following formula is satisfied:
Wherein the content of the first and second substances,candφrespectively the cohesion and the internal friction angle of the soil layer;
horizontal loading in the deep range of a tunnelp 4The following formula is satisfied:
average dead weight of shield segmentp 5：
soil layer resistance of two sides of shield segmentp 6：
Wherein, the assumed soil layer resistance only has the included angles between the two sides of the tunnel segment and the vertical directionϕIs in the range of 45-135 degrees;p h for the soil layer resistance at the arch waist of the tunnel, the following formula is satisfied:
，k s is the modulus of the foundation.
3. The method for determining the transverse deformation and the internal force of the shield tunnel caused by excavation of the side foundation pit according to claim 1, wherein in step S5, the change amount of the horizontal load of the corresponding segment structure is determined by the force methodp 3Further, the concrete steps of obtaining the vertical convergence amount and the corresponding internal force of the shield tunnel under the construction action of the adjacent foundation pit are as follows:
the control equation is used as follows:
Wherein the content of the first and second substances,x 1andx 2respectively assuming virtual bending moment and axial force acting on the vault of the tunnel;δ ii is unit forcex i Edge generated by position of applied forcex i The deformation in the direction of the force is,i=1，2；δ ij is unit forcex j In thatx i Edge generated by position of applied forcex i The deformation in the direction of the force is,i，j=1，2；∆ ip the pressure of the soil is inx i Edge generated by position of applied forcex i The deformation in the direction of the force is,i=1，2；
in unit virtual bending momentx 1Or axial forcex 2Under the action, the shield segment determines the bending moment in the modelMAxial forceNAnd shear forceQThe following boundary conditions are satisfied:
4. The method for determining the lateral deformation and the internal force of the shield tunnel caused by excavation of the side foundation pit according to claim 1, wherein in step S1, a deformation mode of the foundation pit enclosure structure is determined.
5. The method for determining the lateral deformation and the internal force of the shield tunnel caused by excavation of the side foundation pit according to claim 4, wherein the deformation mode of the foundation pit enclosure structure is a parabolic mode, and the deformation of the enclosure structure has the following expression:
Wherein the content of the first and second substances,h 0indicating maximum deformation of the building envelopeδ maxThe depth of the buried part is greater than the depth of the buried part,δ max=A+B；A、BandCis a constant coefficient and is obtained by fitting field data.
6. The method for determining the lateral deformation and the internal force of the shield tunnel caused by excavation of the lateral foundation pit according to claim 1, wherein in step S5, different distances between the shield tunnel and the foundation pit are takenL t And obtaining the tunnel convergence, bending moment and axial force changes caused by the construction of the side foundation pit.
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| CN116108543B (en) * | 2023-03-15 | 2023-06-27 | 湖南大学 | Method for determining additional internal force and deformation of shield tunnel caused by settlement of under-consolidated stratum |
| CN117216862B (en) * | 2023-11-09 | 2024-02-02 | 湖南大学 | Three-dimensional shield tunnel dynamic analysis model based on fiber beam unit |
| CN117951799A (en) * | 2024-03-26 | 2024-04-30 | 北京城建设计发展集团股份有限公司 | Long-term treatment method for transverse convergence deformation of subway shield tunnel |
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