Method for calculating passive soil pressure of soil retaining structure influenced by seepage in all directions

Abstract

The invention relates to a method for calculating passive soil pressure of a soil retaining structure influenced by seepage in all directions, which adopts a composite failure surface hypothesis, simulates a sliding surface through a composite surface formed by combining a logarithmic spiral curved surface and a plane, considers the influence of the anisotropic seepage in the calculation process, and calculates the passive soil pressure of the soil retaining structure by utilizing a modified # imgabs0 # equation and a two-dimensional Laplace equation. The resultant force of the effective counter-acting force of the soil body and the pore water pressure is obtained, passive soil pressure and pore water pressure distribution are analyzed, and the passive soil pressure of the soil retaining structure and the distance from the acting position of the passive soil pressure to the wall toe under the extreme rainstorm infiltration working condition are accurately calculated; theta v is solved through iterative trial and error according to component results in the horizontal direction and the vertical direction, efficient calculation of passive soil pressure distribution and pore water pressure distribution is achieved, only a single independent variable is needed for single circulation, multi-layer circulation is avoided, solving is easier and more convenient, the circulation efficiency of the iterative trial and error method is improved, and the calculation efficiency of the calculation method is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of geotechnical engineering, and in particular relates to a method for calculating the passive earth pressure of a retaining structure affected by isotropic seepage. Background Art

[0002] Retaining structures are structures that support roadbed fill, hillside soil, etc., and prevent fill and soil from deforming and becoming unstable. With the rapid development of coastal urban construction, the extreme climatic conditions faced by retaining structures have increased, and the seepage caused by heavy rain has posed new challenges to the bearing capacity of retaining structures.

[0003] The traditional soil pressure calculation method lacks consideration of the influence of anisotropic seepage, and the position of the passive soil pressure resultant force is preset in the calculation, which deviates from the actual project. On the other hand, the traditional passive soil pressure calculation method assumes the sliding surface as a curved surface, which does not fully conform to the actual project situation, and the simulation accuracy is not high under extreme rainstorm infiltration conditions. Summary of the invention

[0004] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a method for calculating the passive earth pressure of a retaining structure affected by isotropic seepage.

[0005] The method for calculating the passive earth pressure of a retaining structure affected by isotropic seepage includes the following steps:

[0006] Step 1: Simplify the sliding surface into a two-dimensional structure including straight line segments and curve segments, and preset θ v The value is used as the geometric distribution control parameter to control the sliding surface;

[0007] Step 2: The water head distribution h(x, y) in the backfill behind the retaining wall is obtained by series expansion, and the pore water pressure U is calculated along the sliding surface;

[0008] Step 3: Solve the horizontal and vertical components of the backfill reaction force R′ on the straight and curved segments respectively; calculate the deadweight of the sliding body and the passive earth pressure P on the straight and curved segments respectively. P The horizontal component of force P P1 and the vertical force P P2 ;

[0009] Step 4: Adjust θ v Repeat steps 2 to 4 until Determine θ v ;

[0010] Step 5: Calculate the distance T from the position where the passive earth pressure resultant acts to the wall toe based on the moment equilibrium equation.

[0011] As a preference, there is a fifth step after the fourth step, and the fifth step is specifically: determining θv and passive earth pressure P P Then, the equilibrium equation of the sliding body force on the wall toe is obtained according to the moment balance, and the passive earth pressure P is calculated. P The distance T from the action position to the wall toe.

[0012] Preferably, the sliding surface is a composite surface composed of a logarithmic spiral surface and a plane. After the sliding surface is simplified to a two-dimensional structure, the plane is simplified to a straight line segment, and the logarithmic spiral surface is simplified to a curve segment.

[0013] As a preferred method, before implementing step 1, the effective internal friction angle of the backfill soil is obtained through in-situ geotechnical tests and indoor geotechnical tests. The friction angle δ of the wall-soil interface, the height H of the retaining wall and the anisotropy coefficient ξ of seepage, ξ is the vertical permeability coefficient k y and horizontal permeability k x ratio.

[0014] Preferably, in step 2, the Fourier series expansion of the two-dimensional Laplace equation is used to obtain the water head distribution h(x, y) in the backfill soil behind the retaining wall under the xy coordinate axis, and the horizontal component and vertical component of the pore water pressure U on the straight segment and the curved segment are calculated based on the water head distribution h(x, y).

[0015] As a preferred method, in step three, The equation is integrated to solve the reaction stress P of the backfill soil in the straight line segment, using the modified The numerical solution of the equation calculates the effective reaction stress P′ of the backfill soil in the curved segment.

[0016] As a preferred embodiment, in step 4, θ v The cycle range is from 0° to 90°, with each cycle increasing by the same angle.

[0017] The beneficial effects of the present invention are:

[0018] 1) The present invention adopts the composite failure surface hypothesis, and simulates the sliding surface by combining a logarithmic spiral surface and a plane. The influence of anisotropic seepage is taken into account in the calculation process. The equation and the two-dimensional Laplace equation are used to obtain the effective reaction force of the soil and the resultant force of the pore water pressure, analyze the distribution of passive earth pressure and pore water pressure, and accurately calculate the passive earth pressure of the retaining structure under extreme rainstorm infiltration conditions and the distance from its action position to the wall toe.

[0019] 2) The present invention solves θ by iterative trial and error based on the component results in the horizontal and vertical directions v, to achieve efficient calculation of passive earth pressure distribution and pore water pressure distribution, only a single independent variable is needed for a single loop, avoiding multi-layer loops, making the solution simpler, improving the loop efficiency of the iterative trial and error method, and improving the computational efficiency of the calculation method. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a flow chart of a method for calculating the passive earth pressure of a retaining structure affected by isotropic seepage in the present invention;

[0021] Figure 2 It is the composite sliding surface shape and sliding body force analysis diagram adopted by the present invention;

[0022] Figure 3 is a comparison diagram of the passive earth pressure calculated by the method of the present invention and the existing research results;

[0023] Figure 4 is a comparison diagram of the pore water pressure calculated by the method of the present invention and the finite element simulation result;

[0024] Figure 5 It is a diagram showing the position variation of the passive earth pressure resultant force action point calculated by the method of the present invention. DETAILED DESCRIPTION

[0025] The present invention is further described below in conjunction with embodiments. The description of the following embodiments is only used to help understand the present invention. It should be noted that for ordinary persons in the art, without departing from the principle of the present invention, the present invention can also be modified in some ways, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

[0026] Embodiment 1

[0027] As an example, Figure 1 and Figure 2 As shown in the figure, this method of calculating the passive earth pressure of retaining structures affected by isotropic seepage considers the thickness of the backfill behind the retaining wall to be infinite, so the sliding surface can be simplified to a two-dimensional sliding line, and the curved surface and plane are simplified to the curved and straight segments of the sliding line in the analytical calculation. W 、M U 、M R are the sliding body deadweight, pore water pressure and soil reaction force. Figure 2 The moment at point O, the center of the helix.

[0028] This method for calculating the passive earth pressure of a retaining structure affected by isotropic seepage is based on an iterative trial-and-error cycle calculation and specifically includes the following steps:

[0029] Step 1: Obtain the effective internal friction angle of backfill soil through in-situ geotechnical tests and indoor geotechnical tests The friction angle δ of the wall-soil interface, the height of the retaining wall H and the anisotropy coefficient of seepage ξ, where ξ is the vertical permeability k y and horizontal permeability k x The ratio of

[0030] Step 2: First, preset a θ v The value is used as the geometric distribution control parameter of the geometric sliding surface to start the iterative trial and error cycle. The calculation steps in each cycle are steps 3 to 7.

[0031] Step 3: Calculate the pore water pressure U along the sliding surface. Use the Fourier series expansion of the two-dimensional Laplace equation to obtain the water head distribution h(x, y) in the backfill soil behind the retaining wall under the xy coordinate axis. Based on the water head h(x, y), the pore water pressure distribution on the composite sliding surface can be calculated. The sliding surface is divided into curved segments and straight segments for calculation.

[0032] Step 4: Calculate the soil reaction force R'. For the straight line segment, use The equation is integrated and solved, and the reaction stress of the backfill soil is For curved segments, the modified The effective reaction stress p′ of backfill soil is calculated by numerical solution of the equation; The equation is:

[0033]

[0034] Step 5: Calculate the self-weight of the sliding body in each curved segment and straight segment partition respectively;

[0035] Step 6: Calculate the passive earth pressure P in the horizontal direction of each curved segment and straight segment partition P1 =(R h +U h ) / cosδ and the vertical passive earth pressure P P2 =(R v +U h -W) / sinδ;

[0036] Step 7: Make a judgment, if The calculation is terminated and the process goes to step 8. Otherwise, the preset value θ is modified. v , enter the next cycle.

[0037] Step 8: Determine θ v and passive earth pressure P P After that, the equilibrium equations of the sliding body forces on the wall toe are listed according to the moment balance, and the distance T from the position of the passive earth pressure resultant force to the wall toe can be calculated:

[0038] The above iterative trial-and-error cycle method and calculation steps are written into a MATLAB program to realize automatic calculation.

[0039] Embodiment 2

[0040] As another embodiment, this embodiment 2 proposes, based on the embodiment 1, a more specific method for calculating the passive earth pressure of the retaining structure affected by isotropic seepage, θ v The cycle range is 0° to 90°, with each cycle increasing by 0.1°. v The specific method of the iterative trial and error cycle is:

[0041] Step 3: Calculate the pore water pressure U along the sliding surface, and use the Fourier series expansion of the two-dimensional Laplace equation to obtain the water head distribution h(x,y) in the backfill behind the retaining wall under the xy coordinate axis:

[0042]

[0043] Among them, the anisotropy coefficient of seepage ξ=k y / k x , m is the number of terms in the Fourier series expansion, m = 0, 1, 2, ...; M = (2m+1)π / 2.

[0044] Step 4: The pore water pressure distribution on the composite slip surface can be calculated based on the water head h(x,y), where the straight line segment and the curve segment are:

[0045]

[0046] Among them, U CDh , U CDv are the horizontal and vertical components of the pore water pressure in the straight line segment, U ACh , U ACv are the horizontal and vertical components of the pore water pressure in the curve segment, r0 is the starting radius of the logarithmic spiral, y c and D U is the ordinate of the starting point and the terminal point of the straight line segment. v =U ACv +U CDv , U h =U ACh +U CDh .

[0047] The shape of the sliding surface and the force on the sliding body within the step are as follows Figure 2 As shown, where θ m1is the angle between the starting radius and the ending radius of the spiral curve, r0 is the length of the starting radius of the spiral curve, point O is the vertex of the spiral curve, and θ is the angle required for the spiral curve to rotate from the starting radius to any point on the curve.

[0048] R is the radius of curvature along the spiral curve, and the reaction force R' of the backfill straight and curved segments is:

[0049]

[0050]

[0051] Among them, R CDh , R CDv are the horizontal and vertical components of the pore water pressure in the straight line segment, R ACh , R ACv are the horizontal and vertical components of the pore water pressure in the curve segment, R h =R ACh +R CDh , R v =R ACv +R CDv

[0052] Step 5: Calculate the weight of the sliding body by partition. The gravity on the sliding body is W = W1-W2+W3, where:

[0053]

[0054] Among them, γ sat It is the buoyant density of soil.

[0055] It should be noted that the parts in this embodiment that are the same or similar to those in the first embodiment can be referenced to each other and will not be described in detail in this application.

[0056] Embodiment 3

[0057] As another embodiment, this embodiment 2 proposes, on the basis of the embodiment 1, a more specific method for calculating the passive earth pressure of a retaining structure affected by isotropic seepage.

[0058] In step 8, the calculation formula for the distance T from the position where the passive earth pressure resultant force acts to the wall toe is:

[0059]

[0060] P v and P h are the horizontal and vertical components of the passive earth pressure, respectively. L1 to L5 are the force arms from each force to the toe of the wall, which are calculated as follows:

[0061]

[0062] Where CD is the length of the straight line segment of the slip surface, BD is the horizontal distance from the top of the wall to the end point of the slip surface, and n1 and n2 can be calculated by the following formula:

[0063]

[0064] It should be noted that the parts in this embodiment that are the same or similar to those in Embodiments 1 and 2 can be referenced to each other and will not be described in detail in this application.

[0065] Embodiment 4

[0066] As another embodiment, this embodiment 4 compares the method for calculating the passive earth pressure of the retaining structure affected by isotropic seepage with the existing calculation method on the basis of embodiments 1 to 3:

[0067] The method of the present invention is compared with the passive earth pressure calculation results using the spiral surface as the failure surface. Figure 3 As shown, through and Four cases are simulated and calculated. It can be seen that the calculation results of the present invention are in good agreement with the existing research results, which verifies the reliability of the present method. Except for the case of , the calculation result obtained by the present invention is smaller than that obtained by the traditional passive earth pressure calculation method.

[0068] The comparison results between the water head distribution along the sliding surface inside the backfill soil calculated by the method of the present invention and the finite element simulation results are as follows: Figure 4 As shown, by simulating the three cases of y=x, y=x / 2 and y=x / 4, it can be seen that the two are highly consistent, which further verifies the reliability of the method of the present invention and indicates that the method can also provide a theoretical basis and technical support for calculating the distribution of pore water pressure along the sliding surface.

[0069] Furthermore, in this embodiment, by changing the value of the anisotropy coefficient ξ of the seepage, the method is used to calculate ξ=1 / 3 and ξ=1, and The results of the change of the ratio of the distance T between the passive earth pressure resultant force position and the wall toe and the retaining wall height H under eight conditions are shown, and the resultant force position is represented by the value of T / H. Figure 5 As shown in the figure, the increase of the effective internal friction angle δ and the seepage anisotropy coefficient ξ of the soil will increase the overall T / H of the resultant force action position. It can be seen that this method can provide a theoretical basis and technical support for calculating the resultant force action position of passive earth pressure.

[0070] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

Claims

1. A method for calculating the passive earth pressure of a retaining structure affected by isotropic seepage, characterized in that: The calculation method includes the following steps: Step 1: Simplify the sliding surface into a two-dimensional structure including straight line segments and curve segments, and preset θ v The value is used as the geometric distribution control parameter to control the sliding surface; Step 2: The water head distribution h(x, y) in the backfill behind the retaining wall is obtained by series expansion, and the pore water pressure U is calculated along the sliding surface; Step 3: Solve the horizontal and vertical components of the backfill reaction force R′ on the straight and curved segments respectively; calculate the deadweight of the sliding body and the passive earth pressure P on the straight and curved segments respectively. P The horizontal component of force P P1 and the vertical force P P2 ; Step 4: Adjust θ v Repeat steps 2 to 4 until Determine θ v .

2. The method for calculating the passive earth pressure of a retaining structure affected by isotropic seepage according to claim 1, characterized in that: After step 4, there is step 5, which is as follows: determine θ v and passive earth pressure P P Then, the equilibrium equation of the sliding body force on the wall toe is obtained according to the moment balance, and the passive earth pressure P is calculated. P The distance T from the action position to the wall toe.

3. The method for calculating the passive earth pressure of a retaining structure affected by isotropic seepage according to claim 1, characterized in that: The sliding surface is a composite surface composed of a logarithmic spiral surface and a plane. After the sliding surface is simplified to a two-dimensional structure, the plane is simplified to a straight line segment and the logarithmic spiral surface is simplified to a curve segment.

4. The method for calculating the passive earth pressure of a retaining structure affected by isotropic seepage according to claim 1, characterized in that: Before implementing step 1, the effective internal friction angle of the backfill soil is obtained through in-situ geotechnical tests and indoor geotechnical tests. The friction angle δ of the wall-soil interface, the height H of the retaining wall and the anisotropy coefficient ξ of seepage, ξ is the vertical permeability coefficient k y and horizontal permeability k x ratio.

5. The method for calculating the passive earth pressure of a retaining structure affected by isotropic seepage according to claim 1, characterized in that: In step 2, the Fourier series expansion of the two-dimensional Laplace equation is used to obtain the water head distribution h(x, y) in the backfill soil behind the retaining wall under the xy coordinate axis. According to the water head distribution h(x, y), the horizontal component and vertical component of the pore water pressure U on the straight segment and the curved segment are calculated respectively.

6. The method for calculating the passive earth pressure of a retaining structure affected by isotropic seepage according to claim 1, characterized in that: In step three, use The equation is integrated to solve the reaction stress P of the backfill soil in the straight line segment, using the modified The numerical solution of the equation calculates the effective reaction stress P′ of the backfill soil in the curved segment.

7. The method for calculating the passive earth pressure of a retaining structure affected by isotropic seepage according to claim 1, characterized in that: In step 4, θ v The cycle range is from 0° to 90°, with each cycle increasing by the same angle.

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