CN112733412B - Speed equivalent characterization method for hydrodynamic force action landslide motion mechanism research - Google Patents
Speed equivalent characterization method for hydrodynamic force action landslide motion mechanism research Download PDFInfo
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Abstract
The invention discloses a speed equivalent characterization method for hydrodynamic force action landslide motion mechanism research, which comprises the following steps: carrying out zoning on the landslide according to the engineering geological data; dividing the motion of the landslide body into two parts, namely wading and non-wading; based on Pan Guzheng striping algorithm, dividing a slip mass into a plurality of blocks, establishing a block discrete element model, applying a seepage field change rule caused by hydrodynamic factors to the discrete model by using an equivalent force method, and performing stress analysis on discrete units forming the blocks; analyzing the stress of a single discrete unit, and converting the underground water evolution and mechanical deterioration caused by hydrodynamic factors into the change of the speed of a sliding body; finally, boundary condition integral is given to obtain the equivalent sliding speed of each divided landslide body, so that the landslide motion mechanism under the action of hydrodynamic force can be intuitively and simply analyzed. The method can be applied to landslide numerical calculation and can also be used for landslide geomechanical physical model tests.
Description
Technical Field
The invention relates to a landslide motion mechanism analysis method, in particular to a speed equivalent characterization method for hydrodynamic force landslide motion mechanism research, and belongs to the field of hydraulic engineering, geotechnical engineering and geological disaster prevention and control engineering.
Background
The hydrodynamic landslide refers to a slope rock-soil body instability disaster which occurs under the driving of hydrodynamic factors. The hydrodynamic action is mainly caused by factors such as reservoir water level scheduling (especially sudden drop), rainfall (rainstorm and long-term rain) and the like during reservoir operation. Generally, the mechanisms of hydrodynamic forces acting on landslides are classified into the following three categories:
(1) During large-scale rainfall, surface runoff infiltration causes the underground water level to rise continuously, pores in rock and soil bodies are saturated with water, the volume weight is increased, and the gliding component force is increased. Meanwhile, the pore water pressure is increased, the effective stress is reduced, and the shearing strength is reduced. Moreover, the dry-wet alternation effect caused by the water level change of a long-time reservoir promotes the development and disintegration of cracks in the rock-soil body, seriously damages the integrity of the rock-soil body and is not beneficial to the stability;
(2) When the reservoir water level suddenly drops, the water level outside the slope body quickly drops, and the falling rate of the underground water level in the slope is difficult to follow the falling rate of the reservoir water level, so that a large water head difference is formed. Therefore, the groundwater in the slope can generate hydrodynamic pressure along the sliding direction in the dissipation process, and the sliding of the slope body is accelerated;
(3) The reservoir water level continuously erodes the slope body structure in the change process, and the rock and soil body and water generate physical and chemical actions to cause the deterioration of the physical and mechanical properties of the landslide body, so that the strength of the rock and soil body and the structural plane is obviously reduced.
For example, in late 6 months in 2019, in the normal operation process of a reservoir area of a hydropower station in a watershed, as the reservoir water level amplitude is large, the geological conditions of the reservoir bank are complex, and the stability of part of the bank slope is poor, a plurality of obvious landslide and slide collapse phenomena occur along the whole reservoir area close to a dam, so that disasters of different degrees, such as house cracking, foundation subsidence, river and highway interruption, are caused.
Therefore, the research on the landslide motion mechanism under the action of the hydrodynamic force is particularly necessary.
The existing landslide motion mechanism research method under hydrodynamic force comprises a numerical calculation method and a physical model test method. When the landslide motion mechanism is researched by adopting the two methods, hydrodynamic force action is generally converted into force or acceleration. Taking a physical model test as an example, a sliding body is usually set at a certain height by a given slope, and then slides along a sliding surface by generating a downward sliding force under the action of self weight. However, in the test, the sliding process of the sliding body is difficult to control, the problems that the sliding component force is too small, the friction coefficient of the sliding surface is too large, and the sliding slope cannot slide or does not slide completely often occur, and in addition, the movement form, the sliding sequence and the water entering speed of the sliding body in the sliding process cannot be accurately controlled by changing the slope size to change the water entering speed of the sliding body.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems of the existing landslide motion mechanism research method under hydrodynamic action, the invention provides a speed equivalence characterization method for the landslide motion mechanism research under hydrodynamic action.
The technical scheme is as follows: the invention relates to a speed equivalent characterization method for hydrodynamic force action landslide motion mechanism research, which comprises the following steps of:
s1, collecting a time-dependent change rule of a water level of a project scheduling operation reservoir, carrying out zoning on a landslide according to project geological data, and acquiring an average deformation parameter and an average strength parameter of a landslide body of each zone;
s2, solving according to Boussinesq of a differential equation of the unstable motion of underground water to obtain a space-time equation h (x, t) of a saturation line in the landslide body, and dividing the motion of the landslide body into two parts, namely wading and non-wading;
s3, dividing the whole landslide body into a plurality of blocks based on Pan Guzheng segmentation algorithm, establishing a block discrete element model, applying a seepage field change rule brought by hydrodynamic factors to the discrete model by using an equivalent force method, and performing stress analysis on the blocks by taking the stress of the blocks as a boundary condition;
s4, taking the separation body to perform stress analysis on the single discrete unit, and converting underground water evolution and mechanical deterioration caused by hydrodynamic factors into change of the speed of the sliding body through a kinetic equation;
and S5, finally, obtaining the sliding speed equivalence of the landslide body of each zone by giving boundary condition integration, and representing the landslide motion mechanism under the action of hydrodynamic force.
In the step S1, the basis of zoning includes topography, stratigraphic property and hydrological condition.
In the step S2, the space-time equation h (x, t) of the saturation line in the landslide body is:
wherein h is the groundwater level and t is the time; k is the permeability coefficient, mu is the fluid viscosity coefficient; x is the position coordinate of the saturation line, and H is the thickness of the stratum water layer;
assuming that the thickness H of the aquifer is approximately constant, the average H of the thickness of the initial and final submerged flows over a period of time is used m Instead, the space-time equation is simplified to:
wherein h is m Is the average thickness of the aqueous layer;
and determining a wetting line of the landslide body according to the equation, wherein the non-wading part is above the wetting line, and the wading part is below the wetting line, so that the motion of the landslide body is divided into two parts, namely wading and non-wading.
In the step S3, assuming that all the bars undergo rigid body displacement, and the interaction force between the bars is along the sliding surface direction, ignoring the acceleration perpendicular to the sliding surface direction, and performing stress analysis on the blocks to obtain:
W i sinα i +(U i+1 -U i )cosα i -T i +ΔF i ＝M i a i
T i ＝C i,t L i +N i ·tanΦ i,t
wherein, W i Is severe in bulk, U i Pore water pressure, T, to which the block is laterally subjected i For tangential forces to which the bottom of the block is subjected, E i As inter-strip forces, M i Is mass of block, a i Acceleration of the block along the sliding surface, N i Normal force applied to the bottom of the block, L i Is the length of the sliding surface; c i,t As a function of the change in cohesion with time, phi i,t The function of the change of the friction angle along with time is that the water is continuously weakened along with the erosion of the water to the landslide body in the reservoir water level change process.
In step S4, the changes of the speed of the sliding body are converted from the groundwater evolution and the mechanical deterioration caused by hydrodynamic factors according to the following formula:
non-wading part:
wading part: for the section without a hydraulic gradient,
/>
in the case of the presence of a hydraulic gradient section,
wherein m is i And v is the mass and average velocity of the discrete unit, t is the motion time of the discrete unit, F c For contact forces between discrete units, F d And F b For drag and buoyancy of the fluid on the discrete units, G i For discrete unit gravity, J is the hydraulic gradient force.
In particular, the discrete unit gravity G i Comprises the following steps:
G i ＝γ·V i (ii) a Wherein γ is the weight of the discrete unit, V i Is the volume of a discrete unit;
non-wading parts, G i By using natural heavy gamma 1 Calculating;
a wading part: for the part without the hydraulic gradient, the gravity of the water discrete unit adopts natural gravity gamma 2 Calculating, the gravity of the underwater discrete unit adopts saturated gravity gamma sat Calculating; for the part with hydraulic gradient, the gravity of the water discrete unit adopts natural gravity gamma 2 Calculating, wherein the gravity of the underwater discrete unit is calculated by adopting the buoyancy gamma';
wherein, γ sat ＝γ'+γ w ，γ w Indicates the severity of the water;
the natural weight gamma of the discrete units on the wading portion, taking into account the change in weight of the discrete units caused by reservoir level changes 2 Calculated according to the following formula:
γ 2 ＝γ d +ω x,t ·γ w ；
wherein, γ d Is the dry weight of the discrete unit; omega x,t As discrete sheetsVolume water content of the element. Here, the volume water content ratio ω x,t As a function of time and location; the volume water content of the slip-band soil at different positions is different, and the water content is changed along with the change of the reservoir water level (the moisture content in the soil body is changed along with the change of the wetting line due to the change of the reservoir water position, so that the water content is changed along with the time).
Wherein the contact force F between the discrete unit cells c Involving contact normal forces
And contact tangential force>
The calculation formula is as follows:
in the above formula,. DELTA.U n And Δ U t Normal relative displacement and tangential relative displacement respectively; k n And K t Normal stiffness of each of the two discrete units A and B
And tangential stiffness
And (3) obtaining in parallel:
drag force F of fluid on discrete unit d Calculated according to the following formula:
wherein, C d Is the drag coefficient, p w Is the density of water; v. of w And v i Respectively the water flow speed and the movement speed of the discrete units, A d Is the projection of the contact area of the water and the discrete units in the water flow direction.
Buoyancy F of fluid to discrete units b Calculated according to the following formula:
F b ＝ρ w gV；
where ρ is w Is the density of water; g is gravity acceleration; v is the discrete unit volume.
The method for calculating the hydraulic gradient force J along the water surface gradient caused by reservoir water level change comprises the following steps:
J＝J x +J y ；
wherein, J x ＝γ w iV，J y ＝γ w jV；J x Is a hydraulic gradient force in the x direction, J y Is the hydraulic gradient force in the y direction, i is the hydraulic gradient in the x direction, and j is the hydraulic gradient in the y direction.
Has the beneficial effects that: compared with the prior art, the invention has the advantages that: (1) According to the analysis method, firstly, the landslide body is subjected to blocking treatment and then discrete unit dispersion, a continuous-discontinuous coupling calculation mode is applied to the fluid-solid coupling analysis of the landslide on the bank, and the landslide body underground water evolution law under the reservoir water level change working condition is well converted into the landslide body speed, so that the landslide motion mechanism under the hydrodynamic action can be analyzed intuitively and simply; (2) The analysis method can realize multi-factor equivalence, defines a processing method for converting hydrodynamic factors into discrete element particle speed change under the working condition of reservoir water level change, and can be applied to numerical calculation of landslide motion analysis; the method can also be applied to a landslide physical model test, after the speed of the sliding body of each subarea zone is calculated by adopting the method, the landslide body can be controlled to be static by converting a reference system, and the sliding belt movement is simulated by utilizing the conveyor belt to realize the different-speed and different-type sliding of the subarea zone of the sliding body, so that the sliding process is accurate and controllable, and the test precision is high.
Drawings
FIG. 1 is a schematic view of a discrete unit fill block;
FIG. 2 is a schematic diagram of a block under force;
FIG. 3 is a schematic diagram of forces exerted by the interaction between discrete units;
FIG. 4 is a schematic diagram of the buoyancy and drag forces experienced by a discrete unit;
FIG. 5 is a schematic diagram of a discrete cell subjected to a hydraulic gradient force.
Detailed Description
The technical solution of the present invention is further explained with reference to the drawings and the embodiments.
The invention relates to a speed equivalent characterization method for a hydrodynamic force action landslide motion mechanism research, which adopts an equivalent force method and an equivalent velocity method to convert underground water evolution and mechanical action caused by hydrodynamic force factors into change of a sliding body speed, and specifically comprises the following steps:
s1, collecting a time-dependent change rule of a water level of a project scheduling operation reservoir, carrying out zoning on a landslide according to project geological data, and acquiring an average deformation parameter and an average strength parameter of a landslide body of each zone;
wherein, the subregion divides the area basis to include: the method comprises the following steps of (1) topographic and geomorphic (2) stratigraphic lithology (3) hydrological conditions.
The deformation parameters obtained in the S1 are macro deformation parameters of the sliding mass, and normal stiffness and tangential stiffness can be calculated according to the macro deformation parameters and are used for calculating contact force in the S4.
The acquired strength parameters comprise a cohesion parameter and a friction angle parameter, and are used in the stress analysis process in the step S3.
S2, solving according to Boussinesq of the differential equation of the unstable motion of the underground water to obtain a space-time equation h (x, t) of a saturation line in the landslide body, and dividing the motion of the landslide body into two parts, namely wading and non-wading;
the space-time equation h (x, t) of the infiltration line in the landslide body is as follows:
wherein h is the groundwater level and t is the time; k is the permeability coefficient, mu is the fluid viscosity coefficient; x is the position coordinate of the wetting line, and H is the thickness of the stratum water-containing layer;
assuming that the thickness H of the aquifer is approximately constant, the average value H of the thickness of the submerged flow at the beginning and at the end of a certain period of time is used m Instead, the space-time equation is simplified to:
wherein h is m Is the average thickness of the aqueous layer;
and determining a saturation line of the sliding mass according to the equation, wherein the non-wading part is above the saturation line, and the wading part is below the saturation line, so that the movement of the sliding mass is divided into two parts, namely wading and non-wading.
S3, based on Pan Guzheng segmentation algorithm, dividing the whole slip mass into a plurality of blocks, establishing a block discrete element model, wherein each block is formed by contacting a plurality of discrete particle units, applying a seepage field change rule caused by hydrodynamic factors to the discrete model by using an equivalent force method as shown in figure 1, and performing stress analysis on the blocks by using the stress of the blocks as boundary conditions;
assuming that all the strips generate rigid body displacement, the interaction force between the strips is along the direction of the sliding surface, the acceleration perpendicular to the direction of the sliding surface is ignored, and the stress analysis is carried out on the blocks, as shown in fig. 2, the following steps are obtained:
W i sinα i +(U i+1 -U i )cosα i -T i +ΔF i ＝M i a i
T i ＝C i,t L i +N i ·tanΦ i,t
wherein, W i Is severe in bulk, U i Pore water pressure, T, to which the block is laterally subjected i For tangential forces to which the bottom of the block is subjected, E i As force between the bars, M i Is a block bodyAmount a i Acceleration of the block along the sliding surface, N i Normal force applied to the bottom of the block, L i Is the length of the sliding surface; c i,t As a function of the change in cohesion with time, phi i,t The function of the change of the friction angle along with time is that the water is continuously weakened along with the erosion of the water to the landslide body in the reservoir water level change process.
S4, taking the separation body to perform stress analysis on the single discrete unit, and converting underground water evolution and mechanical deterioration caused by hydrodynamic factors into change of the speed of the sliding body through a kinetic equation;
taking the detachment body to analyze the stress of the single discrete unit, considering the contact force between particles of the discrete unit (see figure 3) and the buoyancy and drag force when the discrete unit is contacted with fluid (see figures 4 and 5) for the movement of the single discrete unit, and simultaneously, the variation of reservoir water level can also cause the hydraulic gradient force with the gradient varying along the water surface. Then there are:
1) Non-wading part:
2) A wading part:
for the section without a hydraulic gradient,
in the case of the presence of a hydraulic gradient section,
wherein m is i And v is the mass and average velocity of the discrete unit, t is the motion time of the discrete unit, F c For contact forces between discrete units, F d And F b For drag and buoyancy of the fluid on the discrete units, G i For discrete unit gravity, J is the hydraulic gradient force.
(1) Discrete unit gravity calculation:
G i ＝γ·V i (ii) a Wherein γ is the weight of a discrete unit, V i Is the volume of a discrete unit;
non-wading parts, G i By natural severe gamma 1 Calculating;
wading part: for the part without the hydraulic gradient, the gravity of the water discrete unit adopts natural gravity gamma 2 Calculating, the gravity of the underwater discrete unit adopts saturated gravity gamma sat Calculating; for the part with hydraulic gradient, the gravity of the water discrete unit adopts natural gravity gamma 2 Calculating, wherein the gravity of the underwater discrete unit is calculated by adopting the buoyancy gamma'; wherein, γ sat ＝γ'+γ w ，γ w Indicates the severity of the water;
the natural weight gamma of the discrete units over the wading section of water takes into account the change in weight of the discrete units caused by reservoir level changes 2 Calculated according to the following formula:
γ 2 ＝γ d +ω x,t ·γ w ；
wherein, γ d Is the dry weight of the discrete unit; omega x,t Is the volumetric water content of the discrete cell. Here, the volume water content ratio ω x,t As a function of time and location; the volume water content of the slip-band soil at different positions is different, and the water content is changed along with the change of the reservoir water level (the moisture content in the soil body is changed along with the change of the wetting line due to the change of the reservoir water position, so that the water content is changed along with the time).
(2) Contact force calculation
When the discrete unit particles interact with each other, corresponding contact normal force is generated
And a tangential force->
Then there are:
wherein, K n And K t Contact normal stiffness and contact tangential stiffness, Δ U, respectively n And Δ U t Normal and tangential relative displacements, respectively. And the contact normal stiffness and the contact tangential stiffness in the linear contact model are obtained by respectively connecting the normal stiffness and the tangential stiffness of the two contact bodies in parallel, and the method comprises the following steps:
wherein the superscripts A and B denote two discrete units in contact,
for the respective normal stiffness of the two contacting discrete units A and B, < >>
Is the tangential stiffness of each of the two contacting discrete units a and B.
(3) Drag force calculation
Wherein, C d Is the drag coefficient, ρ w Is the density of water; v. of w And v i Respectively the water flow speed and the movement speed of the discrete units, A d Is the projection of the contact area of the water and the discrete units in the water flow direction.
(4) Buoyancy calculation
F b ＝ρ w gV
Where ρ is w Is the density of water; g is the acceleration of gravity; v is the discrete unit volume.
(5) Calculation of hydraulic gradient force
Because reservoir water level changes to cause hyperstatic pore water pressure in a landslide body, the particle unit is subjected to hydraulic gradient force J, and the calculation method comprises the following steps:
J＝J x +J y ；
wherein, J x ＝γ w iV，J y ＝γ w jV；J x Is a hydraulic gradient force in the x direction, J y Is the hydraulic gradient force in the y direction, i is the hydraulic gradient in the x direction, and j is the hydraulic gradient in the y direction.
In conclusion, the underground water evolution and the mechanical action caused by hydrodynamic factors are converted into the change of the speed of the landslide body through a kinetic equation.
And S5, finally, integrating boundary conditions to obtain the equivalent sliding speed of the landslide body of each zone, and representing the landslide motion mechanism under the action of hydrodynamic force.
Claims (9)
1. A speed equivalent characterization method for hydrodynamic force action landslide motion mechanism research is characterized by comprising the following steps:
s1, collecting a time-dependent change rule of a water level of a project scheduling operation reservoir, carrying out zoning on a landslide according to project geological data, and acquiring an average deformation parameter and an average strength parameter of a landslide body of each zone;
s2, solving according to Boussinesq of an underground water unstable motion differential equation to obtain a space-time equation h (x, t) of a wetting line in the landslide body, wherein x is a position coordinate of the wetting line, t is time, and the landslide body motion is divided into two parts, namely wading and non-wading;
s3, dividing the whole landslide body into a plurality of blocks based on Pan Guzheng segmentation algorithm, establishing a block discrete element model, applying a seepage field change rule brought by hydrodynamic factors to the discrete model by using an equivalent force method, and performing stress analysis on the blocks by taking the stress of the blocks as a boundary condition;
s4, taking the separation body to perform stress analysis on the single discrete unit, and converting underground water evolution and mechanical deterioration caused by hydrodynamic factors into change of the speed of the sliding body through a kinetic equation; the specific process is as follows:
non-wading part:
wading part: for the section without a hydraulic gradient,
in the case of the presence of a hydraulic gradient section,
wherein m is i And v is the mass and average velocity of the discrete units, t is the motion time of the discrete units, fc is the contact force between the discrete units, F d And F b For drag and buoyancy of the fluid on the discrete units, G i Is a discrete unit gravity, and J is a hydraulic gradient force;
and S5, finally, obtaining the sliding speed equivalence of the landslide body of each zone by giving boundary condition integration, and representing the landslide motion mechanism under the action of hydrodynamic force.
2. The method for speed equivalent characterization of hydrodynamic force landslide motion mechanism studies according to claim 1 wherein in step S1, the zonal basis comprises topographical features, stratigraphic lithology and hydrological conditions.
3. The method for characterizing the speed equivalence of the research on the kinetic mechanism of hydrodynamic landslide of claim 1, wherein in step S2, the spatiotemporal equation h (x, t) of the saturation line in the landslide body is:
wherein h is the groundwater level and t is the time; k is the permeability coefficient, mu is the fluid viscosity coefficient; x is the position coordinate of the wetting line, and H is the thickness of the stratum water-containing layer;
assuming that the thickness H of the aquifer is approximately constant, the average H of the thickness of the initial and final submerged flows over a period of time is used m Instead, the space-time equation reduces to:
wherein h is m Is the average thickness of the aqueous layer;
and determining a wetting line of the landslide body according to the equation, wherein the non-wading part is above the wetting line, and the wading part is below the wetting line, so that the motion of the landslide body is divided into two parts, namely wading and non-wading.
4. The method for characterizing speed equivalence in research of hydrodynamic force landslide motion mechanism according to claim 1, wherein in step S3, assuming that all the bars are subjected to rigid body displacement and interaction force between the bars is along the sliding surface direction, neglecting acceleration perpendicular to the sliding surface direction, and performing force analysis on the bars:
W i sinα i +(U i+1 -U i )cosα i -T i +(E i+1 -E i )＝M i a i
T i ＝C i，t L i +N i ·tanΦ i，t
wherein, W i Is severe in bulk, U i Pore water pressure, T, to which the block is laterally subjected i For tangential forces to which the bottom of the block is subjected, E i As force between the bars, M i Is mass of block, a i Acceleration of the block along the sliding surface, α i Toe being a slip surface, N i Normal force applied to the bottom of the block, L i Is the length of the sliding surface; c i，t As a function of the change in cohesion with time, phi i，t Is to massageWipe angle as a function of time.
5. The method for speed-equivalent characterization of hydrodynamic force landslide motion mechanism studies according to claim 1 wherein said discrete unit G gravity i Comprises the following steps:
G i ＝γ·V i
wherein γ is the weight of the discrete unit, V i Is the volume of a discrete unit;
for the non-wading part, G i By using natural heavy gamma 1 Calculating;
for the wading portion:
for the part without the hydraulic gradient, the gravity of the water discrete unit adopts natural gravity gamma 2 Calculating, the gravity of the underwater discrete unit adopts saturated gravity gamma sat Calculating;
for the part with hydraulic gradient, the gravity of the water discrete unit adopts natural gravity gamma 2 Calculating, wherein the gravity of the underwater discrete unit is calculated by adopting the buoyancy gamma'; wherein γ sat = γ' + γ w, γ w representing the water gravity;
considering that reservoir water level changes cause the discrete cell weight to change, the natural weight γ 2 of the discrete cells over the portion of water involved is calculated according to the following equation:
γ 2 ＝γ d +ω x，t ·γ W ；
wherein, γ d Is the dry weight of the discrete unit; omega x，t Is the volumetric water content of the discrete unit.
6. Method for the speed-equivalent characterization of the hydrodynamic landslide motion mechanism study according to claim 1 wherein the contact force between said discrete units F c Involving contact normal forces
And contact tangential force
The calculation formula is as follows:
wherein, delta U n And Δ U t Normal relative displacement and tangential relative displacement respectively; k is n And K t Normal stiffness of each of the two discrete units A and B
And tangential stiffness
And (3) obtaining in parallel:
7. the method for speed-equivalent characterization of hydrodynamic landslide motion engineering studies according to claim 1 wherein said fluid drag force F on discrete elements d Calculated according to the following formula:
where Cd is the drag coefficient, ρ w Is the density of water; vw and vi are the water flow rate and the speed of movement of the discrete unit, A, respectively d Is the projection of the contact area of the water and the discrete units in the water flow direction.
8. According toThe method for velocity equivalent characterization for hydrodynamic landslide motion mechanism studies according to claim 1 wherein the buoyancy F of the fluid to discrete units b Calculated according to the following formula:
F b ＝ρ w gV
where ρ is w Is the density of water; g is the acceleration of gravity; v is the discrete unit volume.
9. The method for speed equivalent characterization of hydrodynamic force landslide motion mechanism research according to claim 1, wherein the calculation of hydraulic gradient force J induced by reservoir level change along the slope of water surface is:
J＝J x +J y
wherein, J x ＝γ w iV，J y ＝γ w jV；J x Is a hydraulic gradient force in the x direction, J y Is hydraulic gradient force in the y direction, i is hydraulic gradient in the x direction, j is hydraulic gradient in the y direction, γ w Is the water gravity and V is the discrete unit volume.
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