Calculation method of active earth pressure of counterweight retaining wall in rotation mode around wall bottom

Abstract

This invention discloses a simple, reasonable, and easy-to-operate method for calculating the active earth pressure of a counterweight retaining wall under a rotation mode around the wall base. The method includes the following steps: Step 10: Along the slope direction, within the slope cross-section, project the lower wall back, platform, and upper wall back as segments AB, BC, and CD, respectively; project the top surface of the backfill behind the wall as a straight line or two broken-line segments (DY and YJ); project the overall slip surface as two broken-line segments (AQF); and project the local slip surface as a straight line segment (XBQ). Step 20: Divide the potential sliding soil wedge behind the wall into three zones under the two rotation modes: rotation around the wall toe (K) and rotation around the wall heel (A). Step 30: Establish equations for each zone according to mechanical equilibrium conditions to determine the earth pressure acting on segments AB, BC, and CD. Step 40: Using the condition that the backfill behind the wall reaches an active limit equilibrium state, use an optimization solution method to calculate the slip surface inclination angle and the active earth pressure acting on the wall under the two rotation modes.

Description

Technical Field

[0001] This invention relates to the technical field of soil retaining engineering, and more specifically, to a method for calculating the active earth pressure of a counterweight retaining wall under the rotation mode around the wall base. Background Technology

[0002] Earth pressure problems involving counterweight retaining walls are related to slope safety and settlement deformation of the top surface of embankments in embankment projects, covering many fields such as railways, highways, municipal works, and building construction. The focus is on calculating and analyzing the earth pressure on counterweight retaining walls to provide a fundamental basis for related engineering designs. Therefore, the reasonable calculation of active earth pressure on counterweight retaining walls is one of the key issues of concern in related engineering practice.

[0003] Methods for calculating active earth pressure on counterweight retaining walls generally fall into two categories: classical limit equilibrium theory analysis and numerical simulation methods. Among these, the approximate theoretical analysis method, represented by the limit equilibrium method, is the most commonly used method in practice. In particular, a commonly used limit equilibrium method in relevant Chinese technical manuals is the upper and lower wall slip surface method. This method includes the first and second rupture surfaces of the upper wall and the lower wall, all three of which are planar. It assumes that the inclination angle of the second rupture surface of the upper wall is a fixed value, and then calculates the earth pressure on the wall based on the condition of maximum active earth pressure. While this method is simple to operate, a significant drawback is that the location of the slip surface in the soil behind the wall differs considerably from the actual location, often leading to an unsafe situation where the calculated earth pressure is less than the actual value.

[0004] To address this issue, previous studies have relied on the traditional "first rupture surface of the upper wall, second rupture surface of the lower wall, and rupture surface of the lower wall" soil sliding model, reducing the internal friction angle of the soil behind the upper wall to calculate earth pressure. However, the relevant internal friction angle reduction value is closely related to the backfill properties, geometric characteristics, and wall geometry. Existing internal friction angle reduction methods rely on empirical values ​​for typical cases and lack broad applicability. Numerical simulation is generally a viable solution. However, reasonable numerical modeling involves a series of steps, including wall-soil interface simulation, model mesh generation, soil constitutive modeling, and boundary conditions. The calculation process is complex and time-consuming, making it unsuitable for rapid multi-parameter scheme comparison and design, and thus difficult to widely implement in practical engineering designs. Therefore, these methods cannot provide the fast, simple, reasonable, and widely applicable method required for calculating the active earth pressure of a counterweight retaining wall in practical engineering. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a simple, reasonable and easy-to-operate method for calculating the active earth pressure of a counterweight retaining wall under the rotation mode around the wall base. The technical solution is as follows:

[0006] A method for calculating the active earth pressure of a counterweight retaining wall under rotation mode around the wall base, wherein the contact surface between the counterweight retaining wall and the backfill soil includes the lower wall back, the platform, and the upper wall back; characterized in that the calculation method includes the following steps:

[0007] Step 10: Along the slope direction, within the slope cross section, project the lower wall back, platform, and upper wall back as segments AB, BC, and CD respectively; project the bottom surface of the wall as segment AK; project the top surface of the backfill behind the wall as a straight line or two broken line segments DYJ composed of segments DY and YJ; project the action surface of segment YJ and strip load as segment ZI; project the overall slip surface as two broken line segments AQF composed of segments AQ and QF; and project the local slip surface as a straight line segment XBQ composed of segments XB and BQ.

[0008] Step 20: Using segments AQF and XBQ, the potential sliding soil wedge ABCDXYFQ behind the wall under two rotation modes, rotating around the wall toe K point and rotating around the wall heel A point, is divided into three zones: the rear side zone XYFQ, the upper wall zone DXBC, and the lower wall zone ABQ.

[0009] Step 30: Establish equations for each zone according to the mechanical equilibrium conditions to determine the earth pressure acting on segments AB, BC and CD.

[0010] Step 40: Taking the wall as a condition for rotating around the wall toe point K or the wall heel point A and making the backfill behind the wall reach an active limit equilibrium state, the optimization solution method is used to calculate the overall slip surface inclination angle, the local slip surface inclination angle, and the active earth pressure acting on the upper back wall, platform, lower back wall, and the entire wall under the two rotation modes.

[0011] The outstanding advantages of the active earth pressure calculation method for a counterweight retaining wall under the rotation mode around the wall base in this invention are as follows: First, this invention reasonably considers the general combination morphology of the soil slip surface behind the wall, and uses two segments of broken-line slip surface to represent the overall slip surface, avoiding the irrationality of the previous method based on a single straight-line overall slip surface; Second, this invention defines the control condition for calculating the active earth pressure of a counterweight retaining wall by using the minimum wall stability coefficient to calculate the location of the soil slip surface and the active earth pressure of the counterweight retaining wall, breaking through the limitations and irrationality of the previous method that used the maximum active earth pressure condition. Furthermore, the mechanical concepts of this invention are clear, the principles are simple, the specific calculation operations and formulas are relatively simple, it is easy to implement computer calculations, and the calculation results are more reasonable. It can calculate and determine the inclination angles of the overall slip surface and local slip surface, as well as the earth pressure acting on the upper back, platform, lower back, and the entire wall of the counterweight retaining wall. It avoids the complex modeling and analysis steps and time-consuming calculation process of numerical simulation methods, and provides a convenient, effective, and more conceptually reasonable method for the calculation of active earth pressure on counterweight retaining walls and related engineering designs, taking into account both technical significance and engineering practical value.

[0012] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0013] The accompanying drawings, which form part of this invention, are used to aid in understanding the invention. The content provided in the drawings and their related descriptions can be used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0014] Figure 1 This is a schematic diagram of the structure of the wall and the backfill soil in the active earth pressure calculation method of the counterweight retaining wall under the rotation mode around the wall base of the present invention.

[0015] Figure 2 This is a force analysis diagram of the wall and the backfill soil in the active earth pressure calculation method of a counterweight retaining wall under the rotation mode around the wall base of the present invention.

[0016] Figure 3 This is a schematic diagram of the counterweight retaining wall supporting backfill in Embodiment 1 of the present invention.

[0017] Figure 4 This is a schematic diagram of the counterweight retaining wall supporting backfill in Embodiment 2 of the present invention.

[0018] The relevant markings in the above figures are:

[0019] 100 - counterweight retaining wall, 200 - backfill behind the wall, 300 - upper back of the wall, 400 - platform, 500 - lower back of the wall. Detailed Implementation

[0020] The present invention will now be clearly and completely described in conjunction with the accompanying drawings. Those skilled in the art will be able to implement the present invention based on these descriptions. Before describing the present invention in conjunction with the accompanying drawings, it should be particularly noted that:

[0021] The technical solutions and features provided in the various parts of this invention, including the following description, can be combined with each other without conflict.

[0022] Furthermore, the embodiments of the present invention described below are generally only some, not all, of the embodiments of the present invention. Therefore, all other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort should fall within the scope of protection of the present invention.

[0023] Regarding the terminology and units used in this invention: The terms "comprising," "having," and any variations thereof in the specification, claims, and related parts of this invention are intended to cover non-exclusive inclusion.

[0024] Figure 1 This is a schematic diagram of the structure of the wall and the backfill soil in the active earth pressure calculation method of the counterweight retaining wall under the rotation mode around the wall base of the present invention. Figure 2 This is a force analysis diagram of the wall and the backfill soil in the active earth pressure calculation method of a counterweight retaining wall under the rotation mode around the wall base of the present invention.

[0025] like Figure 1-2 As shown, the method for calculating the active earth pressure of a counterweight retaining wall under the rotation mode around the wall base according to the present invention includes the following steps:

[0026] Step 10: The contact surface between the counterweight retaining wall 100 and the backfill 200 includes the lower wall back 500, the platform 400, and the upper wall back 300. Along the slope direction, within the cross section of the slope, the lower wall back 500, the platform 400, and the upper wall back 300 are projected as segments AB, BC, and CD, respectively. The bottom surface of the wall is projected as segment AK. The top surface of the backfill 200 is projected as a straight line or two broken line segments DYJ composed of segments DY and YJ. The surface on which segment YJ interacts with the strip load is projected as segment ZI. The overall slip surface is projected as two broken line segments AQF composed of segments AQ and QF. The local slip surface is projected as a straight line segment XBQ composed of segments XB and BQ.

[0027] Step 20: For the counterweight retaining wall 100 under the action of the backfill 200 and the top surface load, the possible rotation modes around the bottom of the wall are mainly rotation around the wall toe K point and rotation around the wall heel A point. Using the AQF segment and XBQ segment, the potential sliding soil wedge ABCDXYFQ behind the wall under the two rotation modes is divided into 3 zones, namely the rear side zone XYFQ, the upper wall zone DXBC and the lower wall zone ABQ.

[0028] Step 30: Establish equations for each zone according to the mechanical equilibrium conditions to determine the earth pressure acting on segments AB, BC, and CD, including the resultant normal earth pressure E acting on segment CD. a1 The resultant normal earth pressure E acting on segment BC a2 The resultant normal earth pressure E acting on segment AB b1 The resultant force T of the tangential earth pressure acting on segment CD a1 The resultant force T of the tangential earth pressure acting on segment BC a2 The resultant force T of the tangential earth pressure acting on segment AB b1 The details are as follows:

[0029] For the rear lateral region XYFQ, the following can be derived from the mechanical equilibrium conditions:

[0030] (1)

[0031] According to the Coulomb strength criterion, we can obtain:

[0032] (2)

[0033] For the upper wall region DXBC, the following can be derived from the mechanical equilibrium conditions:

[0034] (3-1)

[0035] (3-2)

[0036] According to the Coulomb strength criterion, we can obtain:

[0037] (4)

[0038] For the lower wall region ABQ, the following can be derived from the mechanical equilibrium conditions:

[0039] (5)

[0040] According to the Coulomb strength criterion, we can obtain:

[0041] (6)

[0042] Therefore, the earth pressures acting on segments AB, BC, and CD can all be represented by four independent variables: the horizontal inclination angle θ1 of segment QF, the vertical inclination angle θ2 at point B, the endpoint of platform BC, the horizontal inclination angle θ3 of segment AQ, and the normal earth pressure E acting on segment XB. a .

[0043] Step 40: Taking the wall rotation around point K (toe) or point A (heel) as a condition, and ensuring that the backfill behind the wall reaches an active limit equilibrium state, an optimization solution method is used to calculate the overall slip surface inclination angle, the local slip surface inclination angle, and the active earth pressure acting on the upper back wall 300, platform 400, lower back wall 500, and the entire wall under the two rotation modes, as detailed below:

[0044] For the rotation mode of the wall about point K at the wall toe, the governing equation for its active limit state is:

[0045] (7)

[0046] The point of application of the resultant earth pressure acting on segment CD is taken as the height H above point C. a At point / 3, the point of application of the resultant earth pressure acting on segment BC is taken as the midpoint of segment BC, and the point of application of the resultant earth pressure acting on segment AB is taken as 5H above point A. b / 12 places.

[0047] In equation (7), the anti-tilting moment M of the wall rotating about point K at the wall toe is... r t and overturning moment M d t The expressions are as follows:

[0048] (8)

[0049] (9)

[0050] The moment M generated by the wall's self-weight on point K at the wall toe GK The expression is:

[0051] (10)

[0052] The rotation mode of the wall about its heel point A is mainly controlled by the bearing capacity of the foundation, and its active limit state governing equation is:

[0053] (11)

[0054] In the formula, the maximum compressive stress σ of the base is... max It can be calculated based on earth pressure using the static equilibrium condition of the wall, and its expression is:

[0055] (12)

[0056] The expression for the normal pressure N at the bottom of the wall is:

[0057] (13)

[0058] The vertical component E of the resultant earth pressure acting on the wall V The vertical component E of the resultant earth pressure on the back of the wall aV The vertical component E of the resultant earth pressure force of the platform mV The vertical component E of the resultant earth pressure on the back of the wall bV The expressions are as follows:

[0059] (14)

[0060] (15)

[0061] Wall self-weight G W The expression is:

[0062] (16)

[0063] The resultant moment M of earth pressure and the wall's self-weight b The moment M of the earth pressure on the back of the wall at the centroid of the bottom surface of the wall. rO The moment M of the wall's self-weight about the centroid of the wall's base. GO The expressions are as follows:

[0064] (17)

[0065] (18)

[0066] When the wall rotates around point K (the toe) or point A (the heel) and the backfill behind the wall reaches an active limit equilibrium state, the overall rotational stability of the wall has a minimum stability coefficient. Therefore, the corresponding optimization solution method is to mathematically transform the problem of solving the active earth pressure under the two rotation modes into solving for four independent variables θ1, θ2, θ3, and E under this minimum stability coefficient. a The optimized solution value includes the following two cases:

[0067] (1) For the rotation mode of the wall about the wall toe K point, the four independent variables θ1, θ2, θ3, and E corresponding to the minimum stability coefficient a The optimized solution value θ 1t θ 2t θ 3t E at The calculation expression is:

[0068] (19)

[0069] (2) For the rotation mode of the wall around the wall heel point A, the four independent variables θ1, θ2, θ3, and E corresponding to the minimum stability coefficient are a The optimized solution value θ 1h θ 2h θ 3h E ah The calculation expression is:

[0070] (20)

[0071] In equations (19) and (20), the four independent variables are θ1, θ2, θ3, and E. a The constraints that need to be satisfied are:

[0072] (twenty one)

[0073] Among them, K a c This is the Coulomb active earth pressure coefficient, and its expression is:

[0074] (twenty two)

[0075] Based on equations (19)-(22), θ1, θ2, θ3, and E are obtained under the two rotation modes respectively. a The optimized solution value θ 1t θ 2t θ 3t E at With θ 1h θ 2h θ 3h E ah Then, substituting these values ​​into equations (2) to (6), the active earth pressure E acting on segments CD, BC, and AB under the rotation modes around the wall toe K and around the wall heel A can be calculated respectively. a1 With T a1 E a2 With T a2 E b1 With T b1 Then, according to equations (14) and (15), the vertical component E of the resultant earth pressure acting on the entire wall can be calculated. V .

[0076] The horizontal component E of the resultant earth pressure acting on the entire wall H The horizontal component E of the resultant earth pressure on the back of the wall aH The horizontal component E of the resultant earth pressure force of the platformmH The horizontal component E of the resultant earth pressure on the back of the wall bH The expressions are as follows:

[0077] (twenty three)

[0078] (twenty four)

[0079] Therefore, the resultant earth pressure E acting on the entire wall can be calculated as follows:

[0080] (25)

[0081] The meanings of the relevant symbols in the diagram and the above formula are: E a1 E b1 The resultant normal earth pressures acting on segments CD and AB are T, respectively. a1 T b1 These are the resultant tangential earth pressures acting on segments CD and AB, respectively; E a2 T a2 These are the resultant forces of normal earth pressure and tangential earth pressure acting on segment BC, respectively; E a and T a These are the normal earth pressure and tangential earth pressure acting on segment XB, respectively; E b φ is the normal earth pressure acting on section BQ; φ is the internal friction angle of the backfill behind the wall; c is the cohesion of the backfill behind the wall; c w For wall-soil interface cohesion; δ CD δ BC δ AB θ represents the interface friction angles of segments CD, BC, and AB, respectively; q represents the strip load acting perpendicularly on segment YJ, with a distribution width of L and a distance b between its endpoint Z and point Y; l BX l CD l BC l AB l QF l ZF l BQ l AQ Let BX, CD, BC, AB, QF, ZF, BQ, and AQ be the lengths of the segments, respectively, where 0 ≤ l. ZF ≤L, if point F is located in segment IJ, then l ZF = L, if point F is located in segment ZY or segment YX, then l ZF = 0; α1 and α2 are the horizontal inclination angles of segments DY and YJ, respectively; θ1 is the horizontal inclination angle of segment QF; θ2 is the vertical inclination angle of point B, the endpoint of platform segment BC; θ3 is the horizontal inclination angle of segment AQ; γ s Unit weight of backfill soil behind the wall; Ha H b H and H represent the height of the upper wall back, the height of the lower wall back, and the total height of the retaining wall, respectively. H = H a +H b ;β a β b These are the vertical inclination angles of the upper and lower wall backs, respectively; b t b p b b These represent the top width, platform width, and bottom width of the retaining wall, respectively; η is the inclination angle of line segment DB; γ w γ represents the unit weight of the retaining wall; W, Gs1, and Gs2 represent the self-weight of the soil in the rear side zone XYFQ, the upper wall zone DXBC, and the lower wall zone ABQ, respectively, and are equal to the area of ​​the corresponding region multiplied by the unit weight γ of the backfill soil. s ;F s t M is the stability coefficient of the wall rotating about point K at the wall toe; r t With M d t These are the anti-tilting moment and overturning moment of the wall rotating about point K at the wall toe, respectively; F s h Let σ be the rotational stability coefficient of the wall about point A on its heel. u and σ max These are the ultimate bearing capacity of the foundation soil and the maximum compressive stress at the base of the wall, respectively; M GK G is the torque exerted by the wall's self-weight on the wall's toe K; N is the normal pressure on the wall's bottom surface; G W For the wall's own weight; K a c E is the Coulomb active earth pressure coefficient; E is the resultant active earth pressure acting on the entire wall; E V E is the vertical component of the resultant earth pressure acting on the entire wall. aV E mV E bV These are the vertical components of the resultant earth pressure on the upper wall back, platform, and lower wall back, respectively; E H E represents the horizontal component of the resultant earth pressure acting on the entire wall. aH E mH E bH These are the horizontal components of the resultant earth pressure on the upper wall back, platform, and lower wall back, respectively; M b M is the resultant moment of earth pressure and the self-weight of the wall; rO M GO These are the earth pressure on the back of the wall and the torque exerted by the wall's own weight on the centroid of the wall's base, respectively.

[0082] The beneficial effects of the present invention will be illustrated below through specific embodiments.

[0083] Example 1

[0084] Figure 3 This is a schematic diagram of the counterweight retaining wall supporting the backfill in this embodiment.

[0085] like Figure 3 As shown, in this embodiment, the top surface of the backfill behind the wall is a single plane without load (q=0), and the relevant calculation parameters are: γ s =20 kN / m 3 φ=34°, c=c w =0、γ w =22 kN / m 3 , q=0, δ CD =φ / 8、δ BC =φ / 12、δ AB =φ / 4 (Q and B do not coincide) or φ / 2 (Q and B coincide), the ultimate bearing capacity of the foundation at the base of the wall is σ. u =350kPa, other basic parameters are shown in Table 1.

[0086] Following steps 10 to 40, the active earth pressures acting on the counterweight retaining wall under the two modes of rotation around the wall toe and rotation around the wall heel are calculated and shown in Table 1.

[0087] Table 1

[0088]

[0089] Example 2

[0090] Figure 4 This is a schematic diagram of the counterweight retaining wall supporting the backfill in this embodiment.

[0091] like Figure 4 As shown, in this embodiment, the top surface of the backfill behind the wall is a two-segment broken line, with a strip load q = 30 kPa acting on the latter segment. The relevant calculation parameters are: γ s =19 kN / m 3 φ=32°, c= c w =0、γ w =22 kN / m 3 δ CD =φ / 8、δ BC =φ / 12、δ AB =φ / 4 (Q and B do not coincide) or φ / 2 (Q and B coincide), the ultimate bearing capacity of the foundation at the base of the wall is σ. u =250kPa, other basic parameters are shown in Table 2.

[0092] Following steps 10-40, the active earth pressures acting on the counterweight retaining wall under the two modes of rotation around the wall toe and rotation around the wall heel are calculated and shown in Table 2.

[0093] Table 2

[0094]

[0095] Result verification:

[0096] For Examples 1 and 2, the results obtained by finite element limit analysis and the method of the present invention are compared in Tables 3 and 4, respectively. It can be seen that the deviations of the calculation results obtained by the method of the present invention from those obtained by finite element limit analysis are (-13.89~5.81)% and (-14.63~12.18)%, respectively, both within the acceptable error range in engineering, indicating that the method of the present invention is reasonable.

[0097] Table 3

[0098]

[0099] Table 4

[0100]

[0101] The foregoing has described the relevant content of the present invention. Those skilled in the art will be able to implement the present invention based on these descriptions. All other embodiments obtained by those skilled in the art based on the above description of the present invention without inventive effort should fall within the scope of protection of the present invention.

Claims

1. A method for calculating the active earth pressure of a counterweight retaining wall under rotation mode around the wall base, wherein the contact surface between the counterweight retaining wall and the backfill soil includes the lower wall back, the platform, and the upper wall back; characterized in that: The calculation method includes the following steps: Step 10: Along the slope direction, within the slope cross section, project the lower wall back, platform, and upper wall back as segments AB, BC, and CD respectively; project the bottom surface of the wall as segment AK; project the top surface of the backfill behind the wall as a straight line or two broken line segments DYJ composed of segments DY and YJ; project the action surface of segment YJ and strip load as segment ZI; project the overall slip surface as two broken line segments AQF composed of segments AQ and QF; and project the local slip surface as a straight line segment XBQ composed of segments XB and BQ. Step 20: Using segments AQF and XBQ, the potential sliding soil wedge ABCDXYFQ behind the wall under two rotation modes, rotating around the wall toe K point and rotating around the wall heel A point, is divided into three zones: the rear side zone XYFQ, the upper wall zone DXBC, and the lower wall zone ABQ. Step 30: Establish equations for each zone according to the mechanical equilibrium conditions to determine the earth pressure acting on segments AB, BC and CD. Step 40: Taking the wall as a condition for rotating around the wall toe point K or the wall heel point A and making the backfill behind the wall reach an active limit equilibrium state, the optimization solution method is used to calculate the overall slip surface inclination angle, the local slip surface inclination angle, and the active earth pressure acting on the upper back wall, platform, lower back wall, and the entire wall under the two rotation modes.

2. The calculation method as described in claim 1, characterized in that: In step 30: the resultant normal earth pressure E acting on segment CD a1 The resultant normal earth pressure E acting on segment BC a2 The resultant normal earth pressure E acting on segment AB b1 The resultant force T of the tangential earth pressure acting on segment CD a1 The resultant force T of the tangential earth pressure acting on segment BC a2 The resultant force T of the tangential earth pressure acting on segment AB b1 The system of simultaneous equations is as follows: ； ； ； ； Among them, E a and T a These are the normal earth pressure and tangential earth pressure acting on segment XB, respectively; E b φ is the normal earth pressure acting on section BQ; φ is the internal friction angle of the backfill behind the wall; c is the cohesion of the backfill behind the wall; c w For wall-soil interface cohesion; δ CD δ BC δ AB These are the interface friction angles for segments CD, BC, and AB, respectively; l BX l CD l BC l AB These are the lengths of segments BX, CD, BC, and AB, respectively.

3. The calculation method as described in claim 2, characterized in that: In step 40, the normal earth pressure E acting on segment XB a Normal earth pressure E acting on segment BQ b The resultant normal earth pressure E acting on segment CD a1 The resultant normal earth pressure E acting on segment BC a2 The resultant normal earth pressure E acting on segment AB b1 The calculation expressions are as follows: ； ； ； ； Where θ1 is the horizontal inclination angle of segment QF; θ2 is the vertical inclination angle of point B, the endpoint of platform segment BC; θ3 is the horizontal inclination angle of segment AQ; γ s The unit weight of the backfill soil behind the wall; β a β b These are the vertical inclination angles of the upper and lower wall backs, respectively; γ w The wall weight is denoted by W; Gs1 and Gs2 are the soil self-weights of the rear side zone XYFQ, the upper wall zone DXBC, and the lower wall zone ABQ, respectively; QF l ZF l BQ l AQ α1 and α2 are the lengths of segments QF, ZF, BQ, and AQ, respectively; q is the strip load acting vertically on segment YJ; and α1 and α2 are the horizontal inclination angles of segments DY and YJ, respectively.

4. The calculation method as described in claim 3, characterized in that: The governing equations for the active limit equilibrium state of the wall as it rotates about point K at its toe are: ; The governing equations for the active limit equilibrium state of the wall as it rotates around point A on its heel are: ; Among them, F s t M is the stability coefficient of the wall rotating about point K at the wall toe; r t With M d t These are the anti-tilting moment and overturning moment of the wall rotating about point K at the wall toe, respectively; F s h Let σ be the rotational stability coefficient of the wall about point A on its heel. u and σ max These are the ultimate bearing capacity of the foundation and the maximum compressive stress at the base of the wall, respectively.

5. The calculation method as described in claim 4, characterized in that: The anti-tilting moment M of the wall rotating about point K at the wall toe r t and overturning moment M d t The calculation expressions are as follows: ； ； Among them, b t b p b b These are the top width, platform width, and bottom width of the retaining wall, respectively; H a H b These are the height of the upper wall back, the height of the lower wall back, and the total height of the retaining wall; M GK This is the torque exerted by the wall's own weight on point K at the wall's toe.

6. The calculation method as described in claim 4, characterized in that: Maximum compressive stress σ of the base max The calculation expression is: ； Where N is the normal pressure on the bottom surface of the wall. E V G is the vertical component of the resultant earth pressure acting on the entire wall. W For the weight of the wall itself.

7. The calculation method as described in claim 4, characterized in that: The optimization solution method is as follows: based on the minimum stability coefficient of the overall rotational stability of the wall when the backfill reaches the active limit equilibrium state, the optimized solution values ​​of the corresponding four independent variables are obtained; the four independent variables are the horizontal inclination angle θ1 of segment QF, the vertical inclination angle θ2 of point B at the end of platform segment BC, the horizontal inclination angle θ3 of segment AQ, and the normal earth pressure E acting on segment XB. a ; The constraints satisfied by the four independent variables are as follows: ； Where η is the inclination angle of line segment DB; K a c It is the Coulomb active earth pressure coefficient.

8. The calculation method as described in claim 4, characterized in that: The formula for calculating the resultant active earth pressure E acting on the entire wall is: ; Among them, E V This refers to the vertical component of the resultant earth pressure acting on the entire wall. E aV E mV E bV These are the vertical components of the resultant earth pressure on the upper wall back, platform, and lower wall back, respectively; E H This refers to the horizontal component of the resultant earth pressure acting on the entire wall. E aH E mH E bH These are the horizontal components of the resultant earth pressure on the upper back wall, platform, and lower back wall, respectively. ； 。

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