CN116306061A - Determination and evaluation method considering stress deformation of support structure of asymmetric loaded foundation pit group - Google Patents
Determination and evaluation method considering stress deformation of support structure of asymmetric loaded foundation pit group Download PDFInfo
- Publication number
- CN116306061A CN116306061A CN202211087908.1A CN202211087908A CN116306061A CN 116306061 A CN116306061 A CN 116306061A CN 202211087908 A CN202211087908 A CN 202211087908A CN 116306061 A CN116306061 A CN 116306061A
- Authority
- CN
- China
- Prior art keywords
- wall
- deformation
- soil
- matrix
- stress
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000011156 evaluation Methods 0.000 title description 3
- 239000002689 soil Substances 0.000 claims abstract description 136
- 238000000034 method Methods 0.000 claims abstract description 56
- 238000005452 bending Methods 0.000 claims abstract description 48
- 230000008878 coupling Effects 0.000 claims abstract description 26
- 238000010168 coupling process Methods 0.000 claims abstract description 26
- 238000005859 coupling reaction Methods 0.000 claims abstract description 26
- 238000004364 calculation method Methods 0.000 claims abstract description 25
- 238000009412 basement excavation Methods 0.000 claims abstract description 18
- 238000013461 design Methods 0.000 claims abstract description 12
- 238000011158 quantitative evaluation Methods 0.000 claims abstract description 7
- 239000011159 matrix material Substances 0.000 claims description 89
- 238000006073 displacement reaction Methods 0.000 claims description 36
- 230000008569 process Effects 0.000 claims description 15
- 238000010008 shearing Methods 0.000 claims description 9
- 238000010276 construction Methods 0.000 claims description 8
- 238000009933 burial Methods 0.000 claims description 6
- 230000006835 compression Effects 0.000 claims description 5
- 238000007906 compression Methods 0.000 claims description 5
- 238000009434 installation Methods 0.000 claims description 5
- 230000037396 body weight Effects 0.000 claims description 3
- 238000005457 optimization Methods 0.000 abstract description 7
- 238000012937 correction Methods 0.000 description 2
- 238000011161 development Methods 0.000 description 2
- 239000004973 liquid crystal related substance Substances 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 230000009471 action Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000008859 change Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000010354 integration Effects 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 238000012502 risk assessment Methods 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 239000007858 starting material Substances 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
- 238000013519 translation Methods 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
-
- E—FIXED CONSTRUCTIONS
- E02—HYDRAULIC ENGINEERING; FOUNDATIONS; SOIL SHIFTING
- E02D—FOUNDATIONS; EXCAVATIONS; EMBANKMENTS; UNDERGROUND OR UNDERWATER STRUCTURES
- E02D17/00—Excavations; Bordering of excavations; Making embankments
- E02D17/02—Foundation pits
- E02D17/04—Bordering surfacing or stiffening the sides of foundation pits
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
- G06F17/12—Simultaneous equations, e.g. systems of linear equations
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Physics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Computational Mathematics (AREA)
- General Engineering & Computer Science (AREA)
- Geometry (AREA)
- Data Mining & Analysis (AREA)
- Computer Hardware Design (AREA)
- Databases & Information Systems (AREA)
- Evolutionary Computation (AREA)
- Mining & Mineral Resources (AREA)
- Civil Engineering (AREA)
- Algebra (AREA)
- Software Systems (AREA)
- Structural Engineering (AREA)
- Architecture (AREA)
- Life Sciences & Earth Sciences (AREA)
- Computing Systems (AREA)
- Operations Research (AREA)
- General Life Sciences & Earth Sciences (AREA)
- Paleontology (AREA)
- Testing Of Devices, Machine Parts, Or Other Structures Thereof (AREA)
Abstract
The invention provides a method for determining stress deformation of a foundation pit group support structure considering asymmetric stress, which comprises the following steps: establishing an improved elastic foundation beam integral analysis model; determining a calculation parameter and a coupling relation between soil pressure and wall deformation based on the improved elastic foundation beam integral analysis model; and (3) changing boundary conditions to simulate foundation pit excavation, establishing a ground continuous wall stress balance equation set through the coupling relation between the soil pressure and wall deformation, and iteratively solving to determine the final deformation value of the wall bodies at two sides. The method fully considers the influence of asymmetric load on the deformation of the wall bodies at two sides, can quickly solve the stress deformation characteristics of the wall bodies more in line with the actual situation, calculates the safety margin of the bending moment of the wall bodies and realizes the quantitative evaluation of risks, thereby providing theoretical support for engineering practice and design optimization.
Description
Technical Field
The invention relates to the field of geotechnical engineering calculation, in particular to a method for determining and evaluating stress deformation of a foundation pit group support structure considering asymmetric loading.
Background
Foundation pit engineering plays a vital role in the rapid development process of urban underground space. And the determination of the soil pressure load borne by the enclosure structure is a key link in the foundation pit engineering design. The value of the soil pressure load not only affects the safety of the whole foundation pit engineering, but also plays a key role in controlling the construction cost.
The elastic foundation beam method is a classical method for calculating the deformation of the diaphragm wall. The method simplifies the underground diaphragm wall into an elastic beam, simplifies the support into a spring, simplifies the soil body in the pit into a soil spring, and is also commonly called as an'm method'. When the soil body widths at two sides are different or one side has overload effect, asymmetric loading can be caused. The traditional elastic foundation beam method regards the enclosure wall with calculated width as a vertical foundation beam, the support (or anchor rod) is simplified into an elastic support related to the cross section area and the elastic modulus of the support (or anchor rod), and the counterforce of soil to the foundation beam below the excavation face is simulated by using a soil spring. The calculated length of the support is taken as one half of the distance between foundation pits, namely, the support center is assumed to be unchanged, and two sides are compressed symmetrically. Under asymmetric load, the support has a displacement mode of 'translation+compression', and the whole stress analysis of the support structure is needed. The existing elastic foundation beam method is only a simplified model, only the stress and deformation of the foundation pit under the condition of symmetrical load can be considered, and the condition of asymmetrical load cannot be considered.
At present, numerical methods are mostly adopted for researching soil pressure and deformation under the action of asymmetric load, but a method for theoretically solving the deformation of the enclosure structure under the asymmetric load is rarely proposed. Meanwhile, stress deformation analysis and risk assessment of the envelope under asymmetric loading are important links for ensuring engineering safety construction.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a method for determining and evaluating stress deformation of an enclosure structure of an asymmetric loaded foundation pit group.
According to one aspect of the invention, a method for determining stress deformation of an enclosure structure of an asymmetric loaded foundation pit group is provided, which comprises the following steps:
establishing an improved elastic foundation beam integral analysis model;
determining a calculation parameter and a coupling relation between soil pressure and wall deformation based on the improved elastic foundation beam integral analysis model;
and (3) changing boundary conditions to simulate foundation pit excavation, establishing a ground continuous wall stress balance equation set through the coupling relation between the soil pressure and wall deformation, and iteratively solving to determine the final deformation value of the wall bodies at two sides.
Preferably, the improved elastic foundation beam whole analysis model comprises:
the earth continuous walls on two sides are used as elastic beams, the support is used as a spring unit with two ends compressed freely, soil in a pit is used as a soil spring unit, and a non-limiting soil pressure model is adopted for the soil pressure load behind the walls; wherein the non-limiting soil pressure model is
Wherein p is z Is a horizontal counterforce of the enclosure wall; k is the side pressure coefficient of the active soil pressure; gamma is the soil body weight; h is the depth of the wall; z is the calculated depth; alpha is the inclination angle formed by the sliding fracture surface and the horizontal plane;
is the internal friction angle of the soil body; delta is the wall soil friction angle.
Preferably, the determining the coupling relation between the calculated parameters and the soil pressure and the wall deformation based on the improved elastic foundation beam integral analysis model comprises the following steps:
determining calculation parameters, wherein the calculation parameters comprise a two-side ground connecting wall stiffness matrix, a support stiffness matrix and a soil spring stiffness matrix;
and determining the coupling relation between the soil pressure and the wall deformation, namely the coupling relation between the wall soil friction angle, the soil internal friction angle and the wall deformation based on the wall connecting stiffness matrix, the supporting stiffness matrix and the soil spring stiffness matrix and by combining the improved elastic foundation beam integral analysis model.
Preferably, the two-side ground continuous wall integral rigidity matrix [ K 1 ]、[K 2 ]The acquisition process of (1) comprises:
assuming infinite vertical rigidity of the wall body, neglecting vertical compression deformation of the wall body, and considering only the relation between the transverse displacement of the rod end and the force of the rod end and the corner;
substituting the wall body elastic modulus, the moment of inertia and the calculated unit length of the improved elastic foundation beam integral analysis model into a matrix to obtain a diaphragm wall unit stiffness matrix:
wherein F is Yi Shear force at node i; m is M i Bending moment at the node i; f (F) Yj Shear force at node j; m is M j Bending moment at the joint j; e is the elastic modulus of the wall body, I is the moment of inertia of the wall body, l is the length of the calculation unit, v i For horizontal deformation of node i, θ i Is the corner of node i; v j For horizontal deformation of node j, θ j Is the corner of node j; the wall body is divided into a plurality of rod units, and the connection points between the adjacent rod units are called nodes;
gradually arranging the stiffness matrix of the diaphragm wall unit along the depth of the wall bodyThe two layers are overlapped to obtain a matrix [ K ] of the overall rigidity of the two-side wall 1 ]、[K 2 ]；
The supporting rigidity matrix [ K ] s ]The acquisition process of (1) comprises:
the support is regarded as a spring unit related to the support cross-sectional area, the wall elastic modulus and the calculated length by the formula [ K ] s ]Calculating single support stiffness=ea/LS, wherein E is support elastic modulus, a is support cross-sectional area, L is support equivalent length, S is support equivalent spacing;
according to the number of supports corresponding to the construction stage, obtaining a support rigidity matrix [ K ] in a superposition manner s ]；
The soil spring stiffness matrix [ K ] m ]The acquisition process of (1) comprises:
calculating the corresponding soil spring stiffness according to the dividing units and the excavation depth, wherein the soil spring stiffness is related to the soil body characteristics and the burial depth by using a formula K m ＝k h bh、k h =mz calculation; k (K) m For earth spring rate, k h Calculating the width of a soil spring for the horizontal foundation bed coefficient, wherein b is the calculated width of the soil spring, h is the calculated width of the soil spring, m is the proportional coefficient of the foundation bed coefficient, and z is the burial depth of the soil body;
the stiffness of the single soil spring is overlapped and integrated into a soil spring integral stiffness matrix [ K ] m ]。
Preferably, the friction angle delta and the internal friction angle of the soil body are determined according to the non-limiting soil pressure model
The relation with the deformation s of the wall,
wherein delta m Correcting the friction angle in order to consider the coupling relation between the friction angle and the wall deformation;
to consider the coupling relation between the internal friction angle of the soil body and the deformation of the wall bodyCorrecting the internal friction angle of the soil body; s is the displacement of the wall body, s c Wall body limit displacement s for wall soil friction angle a Wall body limit displacement of friction angle in soil body, < + >>
Preferably, the changing boundary condition simulates excavation of a foundation pit, and the building of the underground continuous wall stress balance equation set through the coupling relation between the soil pressure and the wall deformation comprises the following steps:
soil spring stiffness matrix [ K ] based on various working conditions m ]Building a force balance equation set of the diaphragm wall through the coupling relation of the soil pressure and the wall deformation:
solving the equation set to obtain a deformation matrix of the wall body:
wherein [ P ] e1 ]、[P e2 ]For the earth pressure load matrix outside the pit born by the walls on two sides [ K ] 1 ]、[K 2 ]Is the rigidity matrix of the wall bodies at two sides [ delta ] 1 ]、[Δ 2 ]Refers to the whole displacement matrix of the wall bodies on two sides [ K ] m ]Is the earth spring stiffness matrix [ delta ] m1 ]、[Δ m2 ]: supporting and installing an initial deformation matrix of the pit bottom soil body before pit bottom installation; [ K ] s ]For supporting the stiffness matrix, [ delta ] s1 ]、[Δ s2 ]The whole deformation matrix at the two ends of the finger support; [ delta ]' s1 ]、[Δ′ s2 ]Initial deformation matrix of two ends before support installation, [ K ] s ]·[Δ′ s1 ]、[K s ]·[Δ′ s2 ]To support the stress compensation matrix caused by construction hysteresis [ delta ] 10 ]＝[P e1 ]·([K 1 ]+[K m0 ]) -1 、[Δ 20 ]＝[P e2 ]·([K 2 ]+[K m0 ]) -1 As unexcavated primaryInitial equilibrium displacement [ K ] m0 ]Is the initial support stiffness matrix.
Preferably, the iterative solving includes:
judging whether the deformation errors of the front and the rear times are converged to a set value or not:
wherein [ delta ] 1 ]、[Δ 2 ]，[Δ′ 1 ]、[Δ′ 2 ]The wall body displacement is carried out twice in front and behind, and beta is a set error;
if the error requirement is not met, then ([ delta ] will be 1 ]+[Δ′ 1 ]) 2 and ([ delta ] 2 ]+[Δ′ 2 ]) Substituting/2 as a new initial displacement matrix into [ delta ] 10 ]、[Δ 20 ]And then, continuing to iterate until the error requirement is met, and obtaining the final deformation value of the wall bodies at the two sides.
According to a second aspect of the present invention, there is provided a method for evaluating stress deformation of a foundation pit group enclosure structure in consideration of asymmetric loading, comprising:
obtaining final deformation values of the wall bodies at two sides by adopting any method;
determining bending moment, shearing force and earth pressure distribution behind the wall body based on the final deformation values of the wall bodies at the two sides;
and determining the safety allowance of the wall bending moment based on the bending moment, the shearing force and the distribution of the earth pressure behind the wall, and realizing the safety quantitative evaluation of the wall in the excavation process.
Preferably, the bending moment of the wall body and the shearing force are solved by adopting an interpolation method,
wherein E is w The modulus of elasticity of the wall body; i w The moment of inertia of the wall body; [ M ]]Is a wall bending moment matrix; [ Q]Is a wall shear matrix; k is a finite element number; Δl is the finite element unit length, i.e., the total wall length divided by the finite elementNumber of divisions; [ delta ]] k+1 、[Δ] k-1 、[Δ] k The wall displacement at the k+1, k-1 and k nodes is respectively referred to; [ M ]] k+1 、[M] k Respectively refers to the bending moment of the wall body at the k+1 and k nodes, and the bending moment is represented by the formula [ M ]]Is obtained by solving;
and the post-wall soil pressure distribution is obtained by substituting the final deformation values of the two side walls into the non-limiting soil pressure formula for solving.
Preferably, the safety margin of the wall bending moment is calculated as follows:
wherein M is the maximum value of the bending moment of the wall body; mu is a wall bending moment design limit value; s is the safety margin of the bending moment of the wall body;
when the safety margin S of the wall bending moment is lower than the set threshold value, judging that the safety margin S of the wall bending moment is insufficient and risks exist.
Compared with the prior art, the invention has the following beneficial effects:
according to the method for determining and evaluating the stress deformation of the enclosure structure of the foundation pit group taking the asymmetric stress into consideration, the influence of the asymmetric load on the deformation of the wall bodies at two sides is fully considered, the stress deformation characteristics of the wall bodies which are more in line with the actual situation can be rapidly solved, the safety margin of the bending moment of the wall bodies is calculated, the quantitative evaluation of risks is realized, and theoretical support is provided for engineering practice and design optimization.
Drawings
Other features, objects and advantages of the present invention will become more apparent upon reading of the detailed description of non-limiting embodiments, given with reference to the accompanying drawings in which:
FIG. 1 is a schematic diagram of a computing model according to a preferred embodiment of the present invention;
FIG. 2 is a flow chart of a method for determining and evaluating stress deformation of a foundation pit cluster enclosure in consideration of asymmetric loading in accordance with a preferred embodiment of the present invention;
FIG. 3 is a graph showing the calculated values of wall deformation and the calculated values and engineering actual measured values of the stars (deep foundation pit excavation supporting design software in the prior art) according to another preferred embodiment of the present invention.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the present invention, but are not intended to limit the invention in any way. It should be noted that variations and modifications could be made by those skilled in the art without departing from the inventive concept. These are all within the scope of the present invention.
Referring to fig. 1 and 2, the present invention provides an embodiment of a method for determining stress deformation of an enclosure structure of an asymmetrically loaded foundation pit group, which includes:
s100, an improved elastic foundation beam integral analysis model is established, and parameters required by the model are acquired according to engineering actual conditions;
s200, determining a calculation parameter and a coupling relation between soil pressure and wall deformation based on the improved elastic foundation beam integral analysis model established in the S100;
s300, changing boundary conditions to simulate foundation pit excavation, establishing a force balance equation set of the diaphragm wall through the parameters in S200 and the coupling relation between the soil pressure and the wall deformation, and carrying out iterative solution to obtain final deformation values of the walls at two sides.
The method is based on an improved elastic foundation beam integral analysis model, combines the research results of a finite element method and non-limiting soil pressure, fully considers the influence of asymmetric load on deformation of the wall bodies at two sides, rapidly solves the deformation characteristics of the wall bodies under stress more in line with actual conditions, can be applied to quantitative evaluation of bending moment risks of the enclosure structures, and provides theoretical support for engineering practice and design optimization.
In a preferred embodiment of the present invention, S100 is implemented, and an improved elastic foundation beam integral analysis model is built according to the actual working conditions. Wherein, the two sides are the wall and simplify to the elastic beam, support and simplify to the spring unit that both ends freely compress, and the soil body is simplified to the soil spring unit in the hole, and the earth pressure load adopts the simulation of non-limit earth pressure model behind the wall. The solving formula of the soil pressure is as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,
the improved elastic foundation beam analysis model considers the stress deformation of the foundation pit under the asymmetric load condition, and simultaneously adopts an unlimited soil pressure model to calculate the soil pressure behind the wall.
Wherein p is z The horizontal counter force of the enclosure wall is calculated by solving the above method; k is the side pressure coefficient of the active soil pressure and is obtained through a direct shear test; gamma is the soil body weight, and is obtained by measuring the mass and the volume of a soil block; h is the depth of the wall body, and is known by design; z is the calculated depth, and is obtained according to the calculation conditions; alpha is the inclination angle formed by the sliding fracture surface and the horizontal plane;
is the internal friction angle of the soil body; delta is the wall soil friction angle, and is obtained through a correction formula of the wall soil friction angle and the soil internal friction angle.
The method for determining and evaluating the stress deformation of the support structure of the asymmetric stressed foundation pit group is determined, the influence of the wall-soil coupling theory and the asymmetric load on the deformation of the wall bodies at two sides is fully considered, the stress deformation characteristics of the wall bodies which are more in line with the actual conditions can be rapidly solved, and theoretical support is provided for engineering practice and design optimization.
In another preferred embodiment of the present invention, S200 is implemented based on the improved elastic foundation beam ensemble analysis model established in S100. Specifically, the method comprises the following steps:
s201, assuming that the vertical rigidity of the wall is infinite, neglecting the vertical compression deformation of the wall, and only considering the relation between the transverse displacement of the rod end and the rod end force of the corner. Substituting S100 related data, namely wall body elastic modulus, inertia moment and calculated unit length, to obtain a wall-connected unit stiffness matrix, and then stacking unit elements one by one along the depth of the wall body to obtain a wall-connected integral stiffness matrix [ K ] 1 ]、[K 2 ]。
The elastic modulus, the moment of inertia and the length of the computing unit of the wall body are the inherent properties of the elastic foundation beam analysis model, are related to the wall body material, and are not obtained through calculation. E is the wall elastic modulus; i is the moment of inertia of the wall; l is the length of the calculation unit; v i For horizontal deformation of node i, θ i Is the corner of node i; v j For horizontal deformation of node j, θ j Is the corner of node j; f (F) Yi Shear force at node i; m is M i Bending moment at the node i; f (F) Yj Shear force at node j; m is M j Bending moment at the joint j; the node refers to the connection point between the adjacent rod units when the wall body is divided into a plurality of rod units.
S202, simplifying the support to a spring unit related to the sectional area, the elastic modulus and the calculated length by using the formula [ K ] s ]Individual support stiffness was calculated =ea/LS. And then according to the number of supports corresponding to the construction stage, the support rigidity matrix [ K ] is formed by superposition and integration s ]. Wherein [ K ] s ]Is a supporting rigidity matrix; e is the supporting elastic modulus; a is the supporting sectional area; l is the equivalent length of the support; s is the equivalent spacing of the supports.
S203, according to dividing units (dividing units refer to dividing a wall body into a plurality of units along the depth direction, each unit is called a rod member finite element unit, the rigidity of each rod member unit is calculated by the matrix formula, then the rigidity matrix of the whole wall body is obtained by superposition), and the excavation depth, the corresponding soil spring rigidity is calculated, the elastic compression rigidity is related to the soil body characteristics and the burial depth, and the formula K can be used m ＝k h bh、k h Calculated =mz. And then integrating the calculated single soil spring stiffness into a soil spring integral stiffness matrix [ K ] m ]. Wherein K is m The stiffness of the soil spring is the same; k (k) h Is the horizontal bed coefficient; b is the calculated width of the soil spring; h is the calculated width of the soil spring; m is the proportionality coefficient of the foundation bed coefficient; z is the burial depth of the soil body.
S204，Determining a friction angle delta and an internal friction angle of the soil body according to the non-limiting soil pressure model in S100
Relationship with wall deformation s:
wherein s is wall displacement, s c Wall body limit displacement s for wall soil friction angle a Is the wall body limit displacement of the internal friction angle of the soil body,
in the embodiment, in the implementation of S201, the wall is discretized into a plurality of rod sub-units by adopting a finite element method, and the force and displacement relationship of each unit rod is solved by using structural mechanics, so that the rigidity matrix of the whole wall is obtained by superposition. The calculation accuracy is higher, and the efficiency is faster. When S202 is implemented, the single supporting member acting on the wall body is overlapped and integrated into the integral supporting rigidity matrix, so that the stress and deformation calculation of the wall body is facilitated. In the implementation of S203, the pit bottom soil pressure acting on the wall is converted Cheng Tu to a spring global stiffness matrix. The method can embody the resistance of the pit bottom soil body to the deformation of the wall body, and adopts the form of the integral stiffness matrix of the soil spring to calculate by utilizing the matrix, so as to obtain the stress and the deformation of the wall body. In the implementation of S204, a friction angle and soil internal friction angle correction formula based on wall-soil coupling is established in consideration of the fact that the development process of non-limiting soil pressure is related to the process that the wall-soil friction angle and the soil internal friction angle deform along with the wall body. The calculation method is more in line with the stress deformation characteristics of the wall body in actual conditions, and theoretical support is provided for engineering practice and design optimization.
In another preferred embodiment of the present invention, the friction angle delta in the S200 is based on the friction angle delta in the soil body
Relation with wall deformation S, implementing S300, changing boundary stripsThe member simulates the excavation of a foundation pit, and the coupling relation between the supporting axial force and the deformation of the wall bodies at two sides (namely the friction angle delta and the internal friction angle of soil body +.>
Relationship with wall deformation s), building a force balance equation set of the diaphragm wall, and carrying out iterative solution, and obtaining final deformation values of the wall bodies at two sides when the current and the later deformation calculation converges to the error set value. Here, changing the boundary condition means: the stress condition of asymmetric load is considered. Under the conventional symmetrical condition, the stress deformation is calculated, and only one half model is needed to be adopted to establish a stress balance equation; when the asymmetric condition is considered, a symmetric model cannot be selected for calculation, stress boundaries on two sides of a foundation pit are respectively considered, and the following underground continuous wall stress balance equation is jointly established. S300, a specific implementation process comprises the following steps:
s301, determining a soil spring stiffness matrix under each excavation working condition based on the formula of S203.
S302, according to the formula in S200, solving a soil pressure load matrix, if the soil pressure load matrix is solved for the first time, assuming that the wall deformation is zero, and establishing a ground continuous wall stress balance equation set through the coupling relation between the supporting axial force and the wall deformation at two sides:
s303, solving the deformation of the wall in the step S302:
wherein, [ P ] e1 ]、[P e2 ]For the earth pressure load matrix outside the pit born by the walls on two sides [ K ] 1 ]、[K 2 ]Is the rigidity matrix of the wall bodies at two sides [ delta ] 1 ]、[Δ 2 ]Refers to the whole displacement matrix of the wall bodies on two sides [ K ] m ]Is the earth spring stiffness matrix [ delta ] m1 ]、[Δ m2 ]: initial change of pit bottom soil body before support installationA shape matrix; [ K ] s ]For supporting the stiffness matrix, [ delta ] s1 ]、[Δ s2 ]The whole deformation matrix at the two ends of the finger support; [ delta ]' s1 ]、[Δ′ s2 ]Initial deformation matrix of two ends before support installation, [ K ] s ]·[Δ′ s1 ]、[K s ]·[Δ′ s2 ]To support the stress compensation matrix caused by construction hysteresis [ delta ] 10 ]＝[P e1 ]·([K 1 ]+[K m0 ]) -1 、[Δ 20 ]＝[P e2 ]·([K 2 ]+[K m0 ]) -1 For initial equilibrium displacement without excavation, [ K ] m0 ]Is the initial support stiffness matrix.
S304, comparing errors of two wall deformations before and after:
wherein [ delta ] 1 ]、[Δ 2 ]，[Δ′ 1 ]、[Δ′ 2 ]For the displacement of the wall body twice, beta is a set error.
If the error requirement is not satisfied, to ensure convergence of the calculation result, the method will ([ delta ] is performed 1 ]+[Δ′ 1 ]) 2 and ([ delta ] 2 ]+[Δ′ 2 ]) And 2, reversely substituting the new initial displacement matrix into a relation between the friction angle and the displacement in the step 204, solving the distribution value of the soil pressure under the displacement, and repeating the solving processes in the steps 200 to 300 until the displacement is solved twice before and after the wall body and is smaller than the set error.
In another embodiment of the present invention, a method for evaluating stress deformation of a foundation pit group enclosure structure considering asymmetric loading is provided, which specifically includes the following steps:
(1) According to engineering actual parameters, final deformation values of the two side walls are obtained, and the final deformation values can be obtained by adopting the method for determining the stress deformation of the foundation pit group support structure considering asymmetric stress in any one embodiment;
(2) Determining bending moment, shearing force and earth pressure distribution behind the wall according to final deformation values of the wall bodies at two sides;
(3) And determining the safety allowance of the wall bending moment based on the bending moment, the shearing force and the earth pressure distribution behind the wall, and realizing the safety quantitative evaluation of the wall in the excavation process.
The obtained final deformation value is applied to engineering safety evaluation, so that early warning of engineering safety can be realized.
In a preferred embodiment, the bending moment and shearing force of the wall can be solved by adopting the following formula:
wherein E is w The modulus of elasticity of the wall body is given by a design unit; i w The moment of inertia of the wall body is given by a design unit; [ M ]]Is a wall bending moment matrix; [ Q]Is a wall shear matrix; k is a finite element number; Δl is the length of a finite element unit, i.e. the total length of the wall divided by the dividing number of the finite element unit (the finite element unit refers to dividing the whole foundation pit enclosure wall into a plurality of units along the depth direction, and each wall unit is called a rod member finite unit); [ delta ]] k+1 、[Δ] k-1 、[Δ] k Respectively refers to wall displacement [ delta ] at k+1, k-1 and k nodes] k+1 、[Δ] k-1 、[Δ] k The wall displacement at the k+1, k-1 and k nodes is respectively referred to; wherein [ delta ]]The final deformation matrix of the wall body is obtained, and the displacement value at the node is extracted from the matrix; [ M ]] k+1 、[M] k Respectively refers to the bending moment of the wall body at the k+1 and k nodes, and the bending moment is represented by the formula [ M ]]Is obtained by solving.
And the post-wall soil pressure distribution is obtained by substituting the final deformation values of the two side walls into the non-limiting soil pressure formula for solving. Specifically, the calculated wall deformation value (displacement matrix [ delta ]]) Substituting the friction angle delta and the internal friction angle of the soil body
In two related formulas of the wall deformation s, calculating to obtain a corrected friction angle and a corrected internal friction angle delta of the soil body m 、/>
And then delta is added m 、/>
Substituting and solving PZ, C1 and C2 to obtain the final non-limiting soil pressure.
In a preferred embodiment, the formula for determining the safety margin of the wall bending moment is as follows:
wherein M is the maximum value of the bending moment of the wall body; m is M u Designing a limit value for the bending moment of the wall body; s is the safety margin of the bending moment of the wall body;
specifically, when the wall safety quantitative evaluation is performed in the digging process, the safety margin of the bending moment of the wall can be compared with a set safety threshold value according to the obtained safety margin of the bending moment of the wall, if the safety margin is smaller than the set safety threshold value, the risk is evaluated, and an alarm or a treatment can be given. For example, in one embodiment, the safety threshold is set to be 0.3, and when S is less than or equal to 0.3, the safety margin of the bending moment of the wall is evaluated to be insufficient, risks exist, and optimization measures should be adopted.
Because the overall calculated amount is large, the embodiment of the invention is suitable for being realized by combining software programming, and next, the comparison result of the deformation and the stress value of the underground continuous wall calculated by the embodiment of the invention and the actual measured value of the actual engineering is shown through a case of the actual engineering. The case is a foundation pit engineering of a certain land block, and the field actual measurement data comprise deformation of the underground continuous walls at two sides of the foundation pit under different working conditions. The results of the calculations corresponding to the conditions three, four, five are shown in fig. 3. As shown in the figure, compared with the traditional elastic foundation Liang Jiefa (the starter), the displacement calculated value of the diaphragm wall solved by the embodiment of the invention can be better matched with the measured value, and the accurate calculated result is achieved. Therefore, the calculation result of the embodiment of the invention can fully consider the influence of the asymmetric load on the deformation of the wall body, and provides theoretical support for engineering practice and design optimization.
The foregoing describes specific embodiments of the present invention. It is to be understood that the invention is not limited to the particular embodiments described above, and that various changes and modifications may be made by one skilled in the art within the scope of the claims without affecting the spirit of the invention. The above-described preferred features may be used in any combination without collision.
Claims (10)
1. The method for determining the stress deformation of the foundation pit group enclosure structure by considering the asymmetric stress is characterized by comprising the following steps of:
establishing an improved elastic foundation beam integral analysis model;
determining a calculation parameter and a coupling relation between soil pressure and wall deformation based on the improved elastic foundation beam integral analysis model;
and (3) changing boundary conditions to simulate foundation pit excavation, establishing a ground continuous wall stress balance equation set through the coupling relation between the soil pressure and wall deformation, and iteratively solving to determine the final deformation value of the wall bodies at two sides.
2. The method for determining the stress deformation of the foundation pit group enclosure structure considering the asymmetric loading according to claim 1, wherein the improved elastic foundation beam integral analysis model comprises the following steps:
the earth continuous walls on two sides are used as elastic beams, the support is used as a spring unit with two ends compressed freely, soil in a pit is used as a soil spring unit, and a non-limiting soil pressure model is adopted for the soil pressure load behind the walls; wherein the non-limiting soil pressure model is
Wherein p is z Is a horizontal counterforce of the enclosure wall; k is the side pressure coefficient of the active soil pressure; gamma is the soil body weight; h is the depth of the wall; z is the calculated depth; alpha is slip crackThe inclination angle formed by the surface and the horizontal plane;
is the internal friction angle of the soil body; delta is the wall soil friction angle.
3. The method for determining the stress deformation of the enclosure structure of the foundation pit group considering the asymmetric loading according to claim 1, wherein the determining the coupling relation between the calculation parameters and the soil pressure and the wall deformation based on the improved elastic foundation beam integral analysis model comprises the following steps:
determining calculation parameters, wherein the calculation parameters comprise a two-side ground connecting wall stiffness matrix, a support stiffness matrix and a soil spring stiffness matrix;
and determining the coupling relation between the soil pressure and the wall deformation, namely the coupling relation between the wall soil friction angle, the soil internal friction angle and the wall deformation based on the wall connecting stiffness matrix, the supporting stiffness matrix and the soil spring stiffness matrix and by combining the improved elastic foundation beam integral analysis model.
4. The method for determining stress deformation of foundation pit group enclosure structure considering asymmetric loading according to claim 3, wherein the two-sided wall-connected integral stiffness matrix [ K ] 1 ]、[K 2 ]The acquisition process of (1) comprises:
assuming infinite vertical rigidity of the wall body, neglecting vertical compression deformation of the wall body, and considering only the relation between the transverse displacement of the rod end and the force of the rod end and the corner;
substituting the wall body elastic modulus, the moment of inertia and the calculated unit length of the improved elastic foundation beam integral analysis model into a matrix to obtain a diaphragm wall unit stiffness matrix:
wherein F is Yi Shear force at node i; m is M i Bending moment at the node i; f (F) Yj Shear force at node j; m is M j At node jBending moment; e is the elastic modulus of the wall body, I is the moment of inertia of the wall body, l is the length of the calculation unit, v i For horizontal deformation of node i, θ i Is the corner of node i; v j For horizontal deformation of node j, θ j Is the corner of node j; the wall body is divided into a plurality of rod units, and the connection points between the adjacent rod units are called nodes;
the stiffness matrixes of the diaphragm wall units are stacked one by one along the depth of the wall body to obtain a two-sided diaphragm wall integral stiffness matrix [ K ] 1 ]、[K 2 ]；
The supporting rigidity matrix [ K ] s ]The acquisition process of (1) comprises:
the support is regarded as a spring unit related to the support cross-sectional area, the wall elastic modulus and the calculated length by the formula [ K ] s ]Calculating single support stiffness=ea/LS, wherein E is support elastic modulus, a is support cross-sectional area, L is support equivalent length, S is support equivalent spacing;
according to the number of supports corresponding to the construction stage, obtaining a support rigidity matrix [ K ] in a superposition manner s ]；
The soil spring stiffness matrix [ K ] m ]The acquisition process of (1) comprises:
calculating the corresponding soil spring stiffness according to the dividing units and the excavation depth, wherein the soil spring stiffness is related to the soil body characteristics and the burial depth by using a formula K m ＝k h bh、k h =mz calculation; k (K) m For earth spring rate, k h Calculating the width of a soil spring for the horizontal foundation bed coefficient, wherein b is the calculated width of the soil spring, h is the calculated width of the soil spring, m is the proportional coefficient of the foundation bed coefficient, and z is the burial depth of the soil body;
the stiffness of the single soil spring is overlapped and integrated into a soil spring integral stiffness matrix [ K ] m ]。
5. The method for determining stress deformation of foundation pit group enclosure structure with asymmetric load according to claim 4, wherein the friction angle delta and the internal friction angle of soil body are determined according to an unlimited soil pressure model
The relation with the deformation s of the wall,
wherein delta m Correcting the friction angle in order to consider the coupling relation between the friction angle and the wall deformation;
correcting the internal friction angle of the soil body by considering the coupling relation between the internal friction angle of the soil body and the deformation of the wall body; s is the displacement of the wall body, s c Wall body limit displacement s for wall soil friction angle a Wall body limit displacement of friction angle in soil body, < + >>
6. The method for determining the stress deformation of the enclosure structure of the foundation pit group considering asymmetric loading according to claim 1, wherein the changing boundary condition simulates excavation of the foundation pit, and the establishing of the stress balance equation set of the diaphragm wall through the coupling relation between the soil pressure and the wall deformation comprises the following steps:
soil spring stiffness matrix [ K ] based on various working conditions m ]Building a force balance equation set of the diaphragm wall through the coupling relation of the soil pressure and the wall deformation:
solving the equation set to obtain a deformation matrix of the wall body:
wherein [ P ] e1 ]、[P e2 ]Is the pressure load of earth outside the pit applied to the walls at two sidesMatrix [ K 1 ]、[K 2 ]Is the rigidity matrix of the wall bodies at two sides [ delta ] 1 ]、[Δ 2 ]Refers to the whole displacement matrix of the wall bodies on two sides [ K ] m ]Is the earth spring stiffness matrix [ delta ] m1 ]、[Δ m2 ]: supporting and installing an initial deformation matrix of the pit bottom soil body before pit bottom installation; [ K ] s ]For supporting the stiffness matrix, [ delta ] s1 ]、[Δ s2 ]The whole deformation matrix at the two ends of the finger support; [ delta ]' s1 ]、[Δ′ s2 ]Initial deformation matrix of two ends before support installation, [ K ] s ]·[Δ′ s1 ]、[K s ]·[Δ′ s2 ]To support the stress compensation matrix caused by construction hysteresis [ delta ] 10 ]＝[P e1 ]·([K 1 ]+[K m0 ]) -1 、[Δ 20 ]＝[P e2 ]·([K 2 ]+[K m0 ]) -1 For initial equilibrium displacement without excavation, [ K ] m0 ]Is the initial support stiffness matrix.
7. The method for determining stress deformation of a foundation pit cluster enclosure taking into account asymmetric loading of claim 6, wherein the iteratively solving comprises:
judging whether the deformation errors of the front and the rear times are converged to a set value or not:
wherein [ delta ] 1 ]、[Δ 2 ]，[Δ 1 ′]、[Δ′ 2 ]The wall body displacement is carried out twice in front and behind, and beta is a set error;
if the error requirement is not met, then ([ delta ] will be 1 ]+[Δ 1 ′]) 2 and ([ delta ] 2 ]+[Δ′ 2 ]) Substituting/2 as a new initial displacement matrix into [ delta ] 10 ]、[Δ 20 ]And then, continuing to iterate until the error requirement is met, and obtaining the final deformation value of the wall bodies at the two sides.
8. The method for evaluating the stress deformation of the foundation pit group enclosure structure by considering the asymmetric stress is characterized by comprising the following steps of:
obtaining a final deformation value of the two side walls by the method of any one of claims 1-7;
determining bending moment, shearing force and earth pressure distribution behind the wall body based on the final deformation values of the wall bodies at the two sides;
and determining the safety allowance of the wall bending moment based on the bending moment, the shearing force and the distribution of the earth pressure behind the wall, and realizing the safety quantitative evaluation of the wall in the excavation process.
9. The method for evaluating the stress deformation of the foundation pit group enclosure structure considering the asymmetric loading according to claim 8, wherein the bending moment of the wall body and the shearing force are solved by adopting an interpolation method,
wherein E is w The modulus of elasticity of the wall body; i w The moment of inertia of the wall body; [ M ]]Is a wall bending moment matrix; [ Q]Is a wall shear matrix; k is a finite element number; Δl is the finite element unit length, i.e., the total wall length divided by the finite element division number; [ delta ]] k+1 、[Δ] k-1 、[Δ] k The wall displacement at the k+1, k-1 and k nodes is respectively referred to; [ M ]] k+1 、[M] k Respectively refers to the bending moment of the wall body at the k+1 and k nodes, and the bending moment is represented by the formula [ M ]]Is obtained by solving;
and the post-wall soil pressure distribution is obtained by substituting the final deformation values of the two side walls into the non-limiting soil pressure formula for solving.
10. The method for evaluating stress deformation of foundation pit cluster enclosing structure considering asymmetric loading according to claim 9, wherein,
the safety margin of the wall bending moment is calculated as follows:
wherein M is the maximum value of the bending moment of the wall body; mu is a wall bending moment design limit value; s is the safety margin of the bending moment of the wall body;
when the safety margin S of the wall bending moment is lower than the set threshold value, judging that the safety margin S of the wall bending moment is insufficient and risks exist.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211087908.1A CN116306061A (en) | 2022-09-07 | 2022-09-07 | Determination and evaluation method considering stress deformation of support structure of asymmetric loaded foundation pit group |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211087908.1A CN116306061A (en) | 2022-09-07 | 2022-09-07 | Determination and evaluation method considering stress deformation of support structure of asymmetric loaded foundation pit group |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN116306061A true CN116306061A (en) | 2023-06-23 |
Family
ID=86791082
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202211087908.1A Pending CN116306061A (en) | 2022-09-07 | 2022-09-07 | Determination and evaluation method considering stress deformation of support structure of asymmetric loaded foundation pit group |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN116306061A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117763925A (en) * | 2024-02-22 | 2024-03-26 | 中铁建设集团华北工程有限公司 | Method for analyzing foundation pit support by using prestressed hollow pile |
-
2022
- 2022-09-07 CN CN202211087908.1A patent/CN116306061A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117763925A (en) * | 2024-02-22 | 2024-03-26 | 中铁建设集团华北工程有限公司 | Method for analyzing foundation pit support by using prestressed hollow pile |
| CN117763925B (en) * | 2024-02-22 | 2024-04-30 | 中铁建设集团华北工程有限公司 | Method for analyzing foundation pit support by using prestressed hollow pile |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108457311B (en) | A kind of deep base pit enclosure wall stress deformation quick calculation method considering the coupling of wall soil | |
| Keawsawasvong et al. | Undrained basal stability of braced circular excavations in non-homogeneous clays with linear increase of strength with depth | |
| JP5215649B2 (en) | Unit building structural analysis system, structural decision support system, and seismic performance evaluation system | |
| EP2866019A1 (en) | Air-water-soil skeleton coupled calculation device, coupled calculation method, and coupled calculation program | |
| Tradigo et al. | On the use of embedded pile elements for the numerical analysis of disconnected piled rafts | |
| Sapountzakis | Bars under torsional loading: a generalized beam theory approach | |
| Miao et al. | Three‐dimensional finite element analyses of passive pile behaviour | |
| CN109706940B (en) | Method for setting foundation pit servo support system | |
| CN116306061A (en) | Determination and evaluation method considering stress deformation of support structure of asymmetric loaded foundation pit group | |
| Park et al. | Development of component stiffness equations for bolted connections to RHS columns | |
| CN103886138A (en) | Seismic design method for external water tank structure of outer containment of nuclear power plant with fluid-structure interaction considered | |
| Won et al. | Nonlinear three-dimensional analysis of pile group supported columns considering pile cap flexibility | |
| Lee et al. | Structural analysis of pipe-framed greenhouses using interface elements for cross-over connections | |
| CN113283143A (en) | Method for correcting finite element model of superposed beam based on dynamic and static force data | |
| Ouyang et al. | Second-order analysis of steel sheet piles by pile element considering nonlinear soil-structure interactions | |
| Kazaz et al. | An alternative frame‐shear wall model: continuum formulation | |
| Al-Aukaily et al. | Response sensitivity for geometrically nonlinear displacement-based beam-column elements | |
| Topkaya et al. | Development of computational software for analysis of curved girders under construction loads | |
| CN115906572A (en) | Topological optimization design method of concrete filled steel tube sleeper structure based on APDL | |
| CN111985021B (en) | Safety analysis method for fluid-solid coupling of all-over joints of shield excavation surface | |
| CN115935465A (en) | Long-span bridge full-life cycle state evaluation method combined with digital twinning technology | |
| CN110866299B (en) | Method for calculating concrete partial load of heightened gravity dam based on finite element direct internal force method | |
| Hoenderkamp | Elastic analysis of asymmetric tall building structures | |
| CN112784332A (en) | K-m method based pile body internal force calculation method for foundation before pile of reinforced sheet wall | |
| de Araújo et al. | Exact structural-property matrices and Timoshenko’s shape functions for nonprismatic frame elements defined by noncentroidal axes |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |