CN109783947B - Water-mining type ground crack numerical simulation method - Google Patents
Water-mining type ground crack numerical simulation method Download PDFInfo
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Abstract
The invention discloses a numerical simulation method of water-collecting type ground fractures, which adopts a passivated fracture zone model to represent ground fractures, divides soil body destruction into three stages of integrity, micro-fracture generation and macro-fracture generation, and in the simulation calculation process, if small main strain of a unit reaches critical strain between the integrity stage and the micro-fracture generation stage, the unit enters a softening stage, and in the softening stage, the stress is reduced along with the increase of the strain; and if the small main strain of the unit reaches the critical strain between the softening stage and the macro-crack stage, reducing the rigidity of the unit in the normal direction of the crack, thereby correcting the stress-strain matrix of the damaged unit. The method of the invention does not need to give the position of the ground fissure and the expansion direction of the ground fissure after the ground fissure occurs in advance, can objectively and truly simulate and predict the ground fissure caused by underground water exploitation, does not need to divide the grid again after the ground fissure occurs and expands, and has small calculation workload.
Description
Technical Field
The invention relates to a numerical simulation method in the field of geological engineering, in particular to a numerical simulation method for ground cracks caused by underground water exploitation.
Background
Underground water mining changes the stress state of the soil layer, and if the stress state of one point in the soil meets a certain condition, the point can generate shear failure or tensile fracture failure. When more and more damage points are formed in the soil, the damage points are connected into a piece and are exposed out of the ground surface, and the ground cracks can be further expanded after being formed. It can be seen that the water-mining type ground fissure is formed through a development process from none to all and from small to large. Formation of ground fractures can cause severe damage to surface structures, underground pipelines, and the like. In order to scientifically prevent and treat the occurrence of ground fissure disasters, numerical simulation and prediction of the occurrence and development of ground fissures are necessary. However, after the formation of the ground fissure, a significant discontinuous surface exists in the soil body, and the conventional finite element method is based on a continuum problem, so that if the finite element method is adopted to simulate the ground fissure, the ground fissure is required to be used as a unit boundary. However, since the position of the ground fracture is unknown before the ground fracture occurs due to the exploitation of the ground water and the direction of the ground fracture is unknown after the ground fracture occurs, when the finite element simulation is used, the mesh needs to be continuously re-divided according to the occurrence and the development of the ground fracture, which makes the calculation work huge and is difficult to be actually performed. Meanwhile, due to the fact that the grids are divided again, topological structures of the grids in adjacent computing steps are different, and therefore data transmission of displacement, pore water pressure, stress and the like in two adjacent time steps is difficult. On the other hand, the water-mining type ground fracture simulation not only involves the coupling calculation of underground water seepage and soil deformation, but also involves a space scale and a time scale which are much larger than those of the common engineering problem (such as a concrete structure), so that the finite unit size and the time increment step length in the ground fracture numerical simulation are large. For these reasons, the current water-mining type ground fracture numerical simulation is slow in progress, and the position and the propagation direction of the ground fracture are mostly given in advance, which is far from the requirements of the actual ground fracture simulation.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defect that the prior art is used for simulating the ground cracks caused by underground water exploitation, the invention provides the water-exploitation ground crack numerical simulation method, the method does not need to give the position of the ground cracks and the expansion direction of the ground cracks after the ground cracks occur in advance, the ground cracks caused by the underground water exploitation can be objectively and truly simulated and predicted, meanwhile, the method does not need to divide grids again after the ground cracks occur and expand, the calculation workload is small, and the method can be conveniently applied to the simulation of the water-exploitation ground cracks.
The technical scheme is as follows: in order to solve the difficulty of numerical simulation of water-mining type ground fractures, the numerical simulation method of the ground fractures caused by underground water mining adopts a passivation fracture zone model to represent the ground fractures, the passivation fracture zone model divides soil body destruction into three stages of integrity, micro-fracture generation and macro-fracture generation, and two critical strain are used for generating the ground fractures
And
dividing the three phases; wherein f istIs the tensile strength of the soil, E is the tensile modulus of the soil, GfCritical value of fracture energy release rate, wcThe width of the fracture belt is related to the size of the soil body unit; the simulation method comprises the following specific steps:
(1) establishing a stratum moving model caused by underground water exploitation, and setting initial conditions and boundary conditions according to the specific simulated conditions;
(2) carrying out finite element mesh subdivision on the simulation area to obtain a discrete form of a finite element of the stratum moving model:
wherein K is a global stiffness matrix, K' is a coupling matrix of global node pore water pressure and node displacement,
is an integral infiltration matrix, delta w and delta p are respectively integral node displacement increment and integral node pore water pressure increment, F is integral node external load, w ist-1And pt-1Respectively the displacement of the whole node and the pore water pressure of the whole node at the end of the previous time step, wherein Q is a source and sink term, and delta t is a time step increment;
(3) considering initial conditions and boundary conditions, solving the equation set in the step (2), and obtaining the strain increment and the stress increment of each unit by the integral node displacement increment and the integral pore water pressure increment of the current time step so as to obtain the accumulated strain and stress of each unit;
(4) judging whether a small main strain of the unit reaches a critical strain0If so, the cell enters a softening stage in which the stress decreases with increasing strain; judging whether a small main strain of the unit reaches a critical strainfIf this is the case, the cell is destroyed and macroscopic cracks occur perpendicular to the direction of the small principal strainThe seam, after the macroscopic crack appears, the rigidity of the unit in the normal direction of the crack is reduced, so that the stress strain matrix of the failure unit is corrected;
(5) and (5) returning to the step (2), and calculating the next time step until the simulation of all the time steps is finished.
In a specific embodiment, in step (3), the strain increment { Δ } ═ B of each unit is determined]{Δw}eStress increment { Δ σ } - [ D ═ D]{ Δ }, cumulative strain { }t＝{}t-1+ { Delta }, cumulative stress { σ }, andt＝{σ}t-1+ { Δ σ }; wherein [ D ] is]Is a stress-strain matrix of the cell, [ B]For the cell strain matrix, { Δ w }eDisplacing the incremental column vectors for the cell nodes, { }t-1、{}tCell strain, { σ } at time t-1 and time t, respectivelyt-1、{σ}tThe cell stress at time t-1 and time t, respectively.
In particular embodiments, the stress decreases with increasing strain after the cell enters the softening stage by: finding out the stress corresponding to the current strain of the unit on the whole process curve, and obtaining the unbalanced stress of the unit by calculating the difference with the current stress of the unit; if the unbalanced stress is larger than the convergence threshold value, the stress of the unit is adjusted to the corresponding stress on the whole process curve, the load corresponding to the unbalanced stress is reversely loaded on the node of the unit, and corresponding strain and stress are calculated; this process is repeated until the unbalanced stress of the cell does not exceed the converged threshold.
In a specific embodiment, after the macro-cracking of the cell occurs, the stress-strain matrix of the cell is modified to:
[D]cs＝[D]s-[D]s[N]([D]c+[N]T[D]s[N])-1[N]T[D]s
wherein the content of the first and second substances,
[D]csis cracks ofStress-strain matrix of the seam earth, [ D ]]sIs the stress-strain matrix of the uncracked soil body, [ D]cIs the stress-strain matrix of the crack, [ N ]]Is a coordinate transformation matrix between a local coordinate system and a global coordinate system which are established in the directions vertical and parallel to the crack, n, s and t are three coordinate axis directions of the local coordinate system at the crack, n is vertical to the crack direction, s and t are parallel to the crack direction, DnnNormal stiffness for cracks, Dns、DntIs the tangential stiffness of the fracture; the normal stiffness and the tangential stiffness are calculated as:
wherein E, G is the tensile and shear modulus of soil, respectivelysThe slope of the stress-strain softening section line is a negative value, and beta is a shear transfer coefficient.
Has the advantages that: the numerical simulation method of the water-collecting type ground fissure can simulate the ground fissure caused by underground water exploitation, and predict the position of the ground fissure under the underground water exploitation condition and the subsequent expansion direction, as well as the horizontal displacement and the vertical displacement of the soil body on two sides of the ground fissure. Compared with the prior art, the method has the following advantages:
(1) the position of the ground fissure and the expansion direction of the ground fissure do not need to be given in advance, and the generation and the expansion of the ground fissure completely depend on the stress change and the damage of the soil body, so that the ground fissure simulation in the true sense is realized.
(2) The method can be modified properly on the basis of the existing ground settlement simulation finite element software considering the nonlinear coupling effect of water flow and soil deformation, and the grid does not need to be divided again in the calculation process, so that the calculation workload is small.
(3) Simulation of multiple cracks can be achieved.
Drawings
FIG. 1 is a schematic representation of the passivated fracture zone model constitutive relation in the process of the present invention;
FIG. 2 is an iterative diagram of stress and strain at the softening stage of the method of the present invention;
FIG. 3 is a schematic diagram of a generalized geologic model in an experimental example of the present invention;
FIG. 4 is a schematic diagram of meshing of a simulation area according to an example of the present invention;
FIG. 5 is a schematic view showing the distribution of small principal stresses in the soil layer and the development of ground cracks during the pumping process of the experimental example of the present invention;
FIG. 6 is a graph showing the shear strain before initiation of a fracture in an experimental example of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings and examples.
The embodiment of the invention discloses a water-mining type ground fracture numerical simulation method, which adopts a passivated fracture zone model to represent ground fractures, and comprises the following steps:
(1) and establishing a stratum moving model caused by underground water exploitation, and setting initial conditions and boundary conditions according to the specific conditions of simulation. In the step, a fully-coupled stratum movement model caused by underground water exploitation is established according to the soil framework balance condition and the water flow continuity condition and in consideration of the nonlinear characteristic of soil deformation
Wherein G is the shear modulus of the soil framework; ν is the poisson ratio of the soil framework;
the volume strain of the soil framework is defined, and the pressure is positive; u and v are displacements in the x and y directions, respectively; p is the pore water pressure; gamma is the soil gravity; gamma raywIs the severity of the water; k is the permeability coefficient; q is the source and sink item.
According to the specific situation of simulation, giving initial condition u & ltu & gtt＝0＝0
v|t＝0＝0
p|t＝0＝p0(x,y)
And the boundary condition is
Wherein n is the outer normal direction of the boundary; p is the known pore water pressure; q is the derivative of the known pore water pressure in the direction of the boundary normal; u and v are respectively known horizontal displacement and vertical displacement; p is a radical of0(x, y) is the pore water pressure distribution before pumping;1a boundary for which the pore water pressure is known;2a boundary for which the normal derivative of pore water pressure is known; s1Is displacing a known boundary.
(2) And carrying out finite element mesh generation on the simulation area. And dispersing the simulation area into quadrilateral isoparametric units, and performing unit analysis. For cell e, its cell stiffness matrix
The coupling matrix of the pore water pressure and the node displacement of the unit nodes is
The cell penetration matrix is
Wherein [ D ]]A stress-strain matrix that is a cell; [ B ]]Is a cell strain matrix; { M } - [ 110 ]]T；[N′]＝[N1N2 N3 N4]，Ni(i ═ 1,2,3,4) is a shape function; Δ t is the time step increment.
The stiffness matrix, the coupling matrix and the penetration matrix of all the units are collected to obtain the discrete form of the finite element of the formula (1)
Wherein K is a global stiffness matrix; k' is a coupling matrix of the pore water pressure and the node displacement of the whole node;
is an integral infiltration matrix; Δ w ═ Δ u Δ v]TThe integral node displacement increment is obtained; delta p is the integral node pore water pressure increment; f is the integral node external load; w is at-1And pt-1The displacement of the whole node and the pore water pressure of the whole node at the end of the last time step are respectively.
(3) Considering initial condition and boundary condition, solving equation set (2) to obtain node displacement increment and pore water pressure increment of current time step, and calculating strain increment of each unit
{Δ}＝[B]{Δw}e (3)
And stress increment
{Δσ}＝[D]{Δ} (4)
Further, the accumulated strain of each cell can be calculated
{}t＝{}t-1+{Δ} (5)
And accumulated stress
{σ}t＝{σ}t-1+{Δσ} (6)
Wherein, { Δ w }eDisplacing the incremental column vectors for the cell nodes, { }t-1、{}tCell strain, { σ } at time t-1 and time t, respectivelyt-1、{σ}tThe cell stress at time t-1 and time t, respectively.
(4) And characterizing the ground fracture by adopting a passivated fracture zone model. The passivation fracture zone model soil destruction is divided into three stages of integrity, microcrack generation (softening) and macrocrack generation (figure 1). If in the t step, the small principal strain of the unit reaches the critical strain
The cell enters a softening phase where the stress decreases with increasing strain. In the formula (7), the reaction mixture is,0critical strain between the complete stage and the micro-crack generation stage of the soil unit; f. oftThe tensile strength of the soil body; e is the tensile modulus of the soil body. In this case, the iterative calculation shown in fig. 2 can be adopted, and the iterative process is as follows:
firstly, a certain unit stress exceeds a tensile strength value ftTo reach A (sigma)1，1) Found on the full process curve of FIG. 21Corresponding point B (σ)2，1) At this time, the unbalanced stress of the cell is σ1-σ2。
② if the unbalance stress is larger than the threshold value of convergence (preset to 0.1kPa), the unit stress is adjusted to the point B, and the unbalance stress sigma is adjusted1-σ2A corresponding load is applied back to the junction of the cell, representing the stress relief process, and the cell is labeled as a softened cell and its modulus is set to a small positive value, such as 1e-10 kPa.
And thirdly, returning to the step (2) to perform calculation again (second iteration). The load in the calculation is only the reverse load corresponding to the stress release of the previous step, and the modulus of the softening unit is small, so that no obvious stress is generatedIncrease, but significant increase in strain, to C (σ)2，2) Then again using the strain at point C2Calculating the stress sigma on the whole process curve3(point D) when the unbalanced stress of the cell is σ2-σ3。
And fourthly, returning to the step II until the unbalanced stress of the two iterative calculations does not exceed a given threshold value.
If the small principal strain of the cell reaches the critical strain
The cell fails and macro-cracks occur perpendicular to the direction of the small principal strain. In the formula (8), the reaction mixture is,fcritical strain between the microcrack initiation (softening) phase and the macrocracks initiation phase; gfIs fracture energy release rate critical value; w is acThe width of the rupture zone is related to the cell size. After the macro cracks appear, the rigidity of the unit in the normal direction of the cracks is reduced based on the principle of strain additivity, so that the stress-strain matrix of the failure unit is corrected
[D]cs＝[D]s-[D]s[N]([D]c+[N]T[D]s[N])-1[N]T[D]s (9)
Wherein the content of the first and second substances,
wherein [ D ]]csThe stress strain matrix is a crack-containing soil body; [ D ]]sThe stress strain matrix is the uncracked soil body; [ D ]]cA stress-strain matrix for the crack; [ N ]]A coordinate transformation matrix between a local coordinate system and a global coordinate system which are established in the directions vertical and parallel to the crack; n, s and t are three coordinate axis directions of a local coordinate system at the crack, n is perpendicular to the crack direction, and s and t are parallel to the crack direction. DnnNormal stiffness for the crack; dns、DntIs the tangential stiffness of the crack. Normal stiffness and tangential stiffness are calculated as
Wherein E, G is the tensile and shear modulus of soil, respectivelysThe slope of the stress-strain softening section line is a negative value, and beta is a shear transfer coefficient.
The stress-strain relationship of the crack-containing cell is { Δ σ } - [ D { (Δ σ }) ]]cs{Δ} (11)
Wherein, { Δ σ } represents a stress increment; { Δ } is the strain increment.
(5) And (4) returning to the step (2), and calculating the next time step until the simulation of all the time steps is finished.
The present invention is further illustrated below with reference to specific experimental examples to verify the effect of the method of the present invention. According to the cause and the burying condition of loose sediments, a quaternary soil layer in the Sutin region can be divided into a diving aquifer and three bearing aquifers, and a weak permeable layer consisting of clay and silty clay is arranged between the aquifers. Since the last 70 s, the areas in the society of stannum have mined large amounts of groundwater, and the mined amount mainly comes from the second confined aquifer. The exploitation of a large amount of groundwater causes not only severe ground settlement but also the occurrence of ground cracks in the area. Since the first ground fissure was discovered in 1989, 26 ground fissures have been commonly found in the Sutin region so far, and most ground fissures occur in tin-free western regions, wherein the thickness of a quaternary soil layer is small, the burial depth of a bedrock is relatively shallow, the surface of the bedrock is greatly fluctuated, and a third confined aquifer is absent. According to field investigation, the cracks in the susvi area develop mostly in relation to underburden elevations, mostly near above the elevation area of the bedrock. According to the geological conditions of the crack development area in the Suxi region, a geological model shown in figure 3 can be generalized, and figure 4 is the grid division of a simulation area.
Before the ground crack appears, the soil body can be used as a continuum, and a ground settlement model caused by the fully-coupled underground water exploitation as shown in the formula (1) can be obtained by considering the nonlinear characteristics of the deformation of the soil body according to the soil framework balance condition and the water flow continuity condition. Its initial condition is u-t＝0＝0
v|t＝0＝0
p|t＝0＝10y
The boundary condition is
p|s1＝10y
u|s1，s3，s4＝0
v|s2，s3＝0
The boundaries S1, S2, S3, and S4 are shown in fig. 2, n is the outer normal direction of the boundary, and the origin of coordinates is located at the lower left corner of the simulation area.
FIG. 5 shows the simulation results, from which it can be seen that after pumping water for 10 days, tensile stress occurred above the bedrock swell area and near the surface at the side boundary, and a ground fracture occurred above the bedrock swell area (FIG. 5-b); after pumping water for 40 days, the tensile stress distribution area near the surface of the earth increased, the length of the first fracture also increased, and a second fracture appeared to the left of the first fracture (fig. 5-c). Under the influence of the second crack, the width of the tensile stress area near the ground surface is further reduced, but the depth is increased, the tensile stress area extends to the deep part and is intensively distributed near the two parallel cracks, and the compressive stress of the sand layer below the cracks begins to be reduced. Along with the stable pumping, the cracks and the tensile stress areas continue to develop to deep parts (figure 5-d), the overall development direction is vertical downwards, the tensile stress areas further approach to the two cracks, and a certain compressive stress area is formed on the ground surface between the two cracks. The simulation results are basically consistent with the field investigation conditions. Fig. 6 is a shear strain distribution diagram of the ground surface before two ground cracks appear, and it can be seen that the two ground cracks do not occur at a place where the shear stress is large, but instead occur at a place where the shear strain is zero, that is, the local ground settlement unevenness at the place is not high, but the minimum principal stress is the pulling force, and the maximum value of the pulling force in the area can be reached. After the first crack occurred, the two disks of the crack were significantly dislocated due to the interruption of the stress transmission.
Claims (3)
1. The method is characterized in that a passivation fracture zone model is adopted to represent the ground fractures, the passivation fracture zone model divides soil body destruction into three stages of integrity, micro-fracture generation and macro-fracture generation, and two critical strain are used for simulating the ground fracturesAnd
dividing the three phases; wherein f istIs the tensile strength of the soil, E is the tensile modulus of the soil, GfCritical value of fracture energy release rate, wcThe width of the fracture belt is related to the size of the soil body unit; the simulation method comprises the following specific steps:
(1) establishing a stratum moving model caused by underground water exploitation, and setting initial conditions and boundary conditions according to the specific simulated conditions;
(2) carrying out finite element mesh subdivision on the simulation area to obtain a discrete form of a finite element of the stratum moving model:
wherein K is a global stiffness matrix, K' is a coupling matrix of global node pore water pressure and node displacement,
is an integral infiltration matrix, delta w and delta p are respectively integral node displacement increment and integral node pore water pressure increment, F is integral node external load, w ist-1And pt-1Respectively the displacement of the whole node and the pore water pressure of the whole node at the end of the previous time step, wherein Q is a source and sink term, and delta t is a time step increment;
(3) considering initial conditions and boundary conditions, solving the equation set in the step (2) to obtain the integral node displacement increment and the integral pore water pressure increment of the current time step, thereby obtaining the strain increment and the stress increment of each unit and further obtaining the accumulated strain and stress of each unit;
(4) judging whether a small main strain of the unit reaches a critical strain0If so, the cell enters a softening stage in which the stress decreases with increasing strain; judging whether a small main strain of the unit reaches a critical strainfIf the cell is damaged, generating a macro crack vertical to the direction of small principal strain, and after the macro crack is generated, reducing the rigidity of the cell in the normal direction of the crack so as to correct the stress strain matrix of the damaged cell; after the macro cracks appear on the unit, the stress-strain matrix of the unit is corrected into:
[D]cs＝[D]s-[D]s[N]([D]c+[N]T[D]s[N])-1[N]T[D]s
wherein the content of the first and second substances,
[D]csis a stress-strain matrix of the soil body containing cracks, [ D ]]sIs the stress-strain matrix of the uncracked soil body, [ D]cIs the stress-strain matrix of the crack, [ N ]]Is a coordinate transformation matrix between a local coordinate system and a global coordinate system which are established in the directions vertical and parallel to the crack, n, s and t are three coordinate axis directions of the local coordinate system at the crack, n is vertical to the crack direction, s and t are parallel to the crack direction, DnnNormal stiffness for cracks, Dns、DntIs the tangential stiffness of the fracture; the normal stiffness and the tangential stiffness are calculated as:
wherein E, G is the tensile and shear modulus of soil, respectivelysThe slope of the stress-strain softening section line is a negative value, and beta is a shear transfer coefficient;
(5) and (5) returning to the step (2), and calculating the next time step until the simulation of all the time steps is finished.
2. The water-extraction-type ground fracture numerical simulation method according to claim 1, wherein in the step (3), the strain increment { Δ } ═ B of each unit is set to be [ B ]]{Δw}eStress increment { Δ σ } - [ D ═ D]{ Δ }, cumulative strain { }t＝{}t-1+ { Delta }, cumulative stress { σ }, andt＝{σ}t-1+ { Δ σ }; wherein [ D ] is]Is a stress-strain matrix of the cell, [ B]For the cell strain matrix, { Δ w }eDisplacing the incremental column vectors for the cell nodes, { }t-1、{}tCell strain, { σ } at time t-1 and time t, respectivelyt-1、{σ}tThe cell stress at time t-1 and time t, respectively.
3. The numerical simulation method of water-extraction-type ground fractures according to claim 1, wherein after the unit enters the softening stage, the stress is reduced along with the increase of strain by the following specific method: finding out the stress corresponding to the current strain of the unit on the whole process curve, and obtaining the unbalanced stress of the unit by calculating the difference with the current stress of the unit; if the unbalanced stress is larger than the convergence threshold value, the stress of the unit is adjusted to the corresponding stress on the whole process curve, the load corresponding to the unbalanced stress is reversely loaded on the node of the unit, and corresponding strain and stress are calculated; this process is repeated until the unbalanced stress of the cell does not exceed the converged threshold.
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