Design limit displacement calculation method for slide-resistant pile reinforced slope

Abstract

The invention discloses a design limit displacement calculation method for a slide-resistant pile reinforced slope. The design limit displacement calculation method comprises the steps that 100, a slide mass is vertically divided into a plurality of blocks, and the blocks are sequentially numbered from back to front; 200, a corresponding static balance equation is established for each strip block, and the static balance equation of the strip block where the load-bearing section of the anti-slide pile is located needs to contain the internal force of the anti-slide pile on the potential sliding surface; step 300, forming a relational expression of a bending moment and an axial force by taking a shearing force as a variable and a relational expression of each internal force by taking a slope stability design safety coefficient as an independent variable; step 400, establishing a displacement expression of each block; step 500, expressing the shearing force of the bottom surface of the strip block along the potential sliding surface direction; step 600, determining an inter-strip tangential force and an inter-strip normal force of two adjacent strips; 700, solving to obtain the vertical design limit displacement of the top of the sliding body; and step 800, solving to obtain the horizontal design limit displacement of each block and the design limit displacement along the tangential direction of the potential sliding surface.

Description

Technical Field

[0001] The invention relates to the technical field of landslides and engineering slopes, and in particular to a method for calculating the design limit displacement of a slope reinforced with anti-slide piles. Background Art

[0002] The stability state of the slope (landslide) reinforced with anti-slide piles is closely related to the displacement of the slope. When the slope slides to the limit state, a certain displacement will inevitably occur. The displacement that the slope can produce when it reaches the limit state (including the design limit state) (here referred to as the limit displacement) is of great significance for fully understanding the potential displacement development of the slope. However, except for the numerical simulation method, most of the existing slope stability analysis methods do not link stability with displacement, nor do they achieve a reasonable analysis of the design limit displacement of the slope. Although there are a few stability analysis methods that link displacement in the past, the relevant analytical calculation methods are all for slopes that have not been reinforced, and do not involve the problem of slopes reinforced with anti-slide piles. The design limit displacement of slopes reinforced with anti-slide piles cannot be solved by analytical calculation methods. Generally, this problem can only be approximately analyzed through numerical simulation methods.

[0003] Although numerical simulation methods can be used to analyze the ultimate displacement of slopes, they actually use shear strength reduction technology to continuously reduce the shear strength of the slope sliding zone soil in the numerical simulation until the numerical model slope reaches the defined limit state. At this time, the slope displacement is considered to be its corresponding sliding ultimate displacement. However, the numerical simulation method has two defects:

[0004] First, it is necessary to establish a numerical model first, and the rationality of the numerical model depends on factors such as model parameters, grid accuracy, material constitutive model, boundary conditions, etc. Not only is the modeling process complicated, but there is also interference from human subjective operations, and it is difficult to have "inheritance" (different people need to start from modeling operations). The study of complex problems can still be used as a reference means, but it is not conducive to the rapid analysis and operation of actual engineering and technical personnel.

[0005] Second, during the strength reduction process, the deformation parameters of the slope should also be adaptively adjusted synchronously with the strength parameters, but there is currently a lack of reasonable synchronous adjustment strategies, so this method has conceptual flaws. Summary of the invention

[0006] The main purpose of the present invention is to provide a method for calculating the design limit displacement of an anti-slide pile reinforced slope, so as to solve the technical problem that the design limit displacement of an anti-slide pile reinforced slope cannot be reasonably calculated in the prior art.

[0007] In order to achieve the above object, the present invention provides a method for calculating the design limit displacement of a slope reinforced with anti-slide piles, and the technical solution is as follows:

[0008] The design limit displacement calculation method for the anti-slide pile reinforced slope includes the following steps:

[0009] Step 100: for the slope reinforced with anti-slide piles, based on the basic geometric and physical mechanical parameters of the slope, the pile design parameters, and the specified slope stability design safety factor, determine the position of the potential sliding surface of the slope and the length of the load-bearing section of the anti-slide piles, divide the sliding body vertically into a number of strips from the rear edge of the sliding body to the front, and number the strips from the back to the front, determine the bottom length, bottom inclination angle, and deadweight of each strip, wherein the load-bearing section of the anti-slide pile is included in a strip;

[0010] Step 200: Under the specified slope stability design safety factor condition, for each strip, according to the static equilibrium conditions of horizontal force, vertical force and moment, a corresponding static equilibrium equation is established, wherein, for the strip where the load section of the anti-sliding pile is located, the static equilibrium equation needs to include the internal force of the anti-sliding pile at the potential sliding surface, and the internal force includes shear force, bending moment and axial force;

[0011] Step 300: Establishing calculation expressions for various internal forces of the anti-slide pile at the potential sliding surface, forming relationship expressions of bending moment and axial force with shear force as a variable, and relationship expressions of various internal forces with slope stability design safety factor as an independent variable;

[0012] Step 400: according to the sliding displacement compatibility conditions between the strips and blocks, the displacement expressions of the strips and blocks are established in sequence from the trailing edge of the sliding body to the front;

[0013] Step 500: In the static equilibrium equation of each bar, the shear force on the bottom surface of the bar along the potential sliding surface is expressed by using the shear stress-shear displacement relationship equation;

[0014] Step 600: Determine the relationship expression between the inter-strip tangential force and the inter-strip normal force of two adjacent blocks according to the inter-strip force assumption of Morgenstern-Price;

[0015] Step 700: Under the specified slope stability design safety factor condition, the static equilibrium equations and constraint conditions of all strips are combined to obtain the vertical design limit displacement of the top of the sliding body of the anti-slide pile reinforced slope;

[0016] Step 800: Substitute the vertical design limit displacement of the top of the sliding body into the displacement expression of each strip, and obtain the horizontal design limit displacement of each strip of the anti-slide pile reinforced slope and the tangential design limit displacement along the potential sliding surface under the specified slope stability design safety factor.

[0017] The outstanding advantages of the calculation method of the design limit displacement of the anti-slide pile reinforced slope of the present invention are: it fully considers the key control factors such as the stability design safety factor of the anti-slide pile reinforced slope, the internal force of the anti-slide pile, static balance, deformation coordination, shear constitutive structure, etc., the calculation principle is clear, the calculation process is simple and easy to operate, and the calculation results are relatively accurate. It avoids the complicated modeling and analysis steps and time-consuming calculation process of the numerical simulation method, can reasonably reflect the stability and deformation coordination relationship of the anti-slide pile reinforced slope, and has a simplified solution process, which provides a convenient and effective method for the design and analysis of the management of landslides or engineering slopes, taking into account both technical significance and engineering practical value.

[0018] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments. Additional aspects and advantages of the present invention will be partially given in the following description, partially become apparent from the following description, or be learned through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The drawings constituting a part of the present invention are used to assist in understanding the present invention. The contents provided in the drawings and their related descriptions in the present invention can be used to explain the present invention, but do not constitute improper limitations on the present invention. In the drawings:

[0020] Figure 1 Schematic diagram of the vertical division of the sliding body in the slope of the slope reinforced with anti-slide piles.

[0021] Figure 2 This is a schematic diagram of the force analysis of a strip containing the load-bearing section of anti-slide piles in the sliding body of a slope reinforced with anti-slide piles.

[0022] Figure 3 Schematic diagram of the force analysis of an arbitrary strip in the sliding body of a slope reinforced with anti-slide piles that does not contain anti-slide piles.

[0023] Figure 4 It is a schematic diagram of a slope reinforced with anti-slide piles in an embodiment.

[0024] Figure 5 Schematic diagram of the vertical division of the sliding body into strips in the embodiment.

[0025] Figure 6 It is a comparison diagram of the designed limit displacement of each point on the sliding body surface along the potential sliding surface obtained by numerical simulation in the embodiment and the calculation result of the present invention.

[0026] Figure 7 It is a comparison diagram of the horizontal design limit displacement of each point on the sliding body surface obtained by numerical simulation in the embodiment and the calculation result of the present invention. DETAILED DESCRIPTION

[0027] The present invention is described clearly and completely below in conjunction with the accompanying drawings. A person 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:

[0028] The technical solutions and technical features provided in each part of the present invention, including the following description, may be combined with each other if there is no conflict.

[0029] In addition, the embodiments of the present invention involved in the following description are generally only a part of the embodiments of the present invention, rather than all the embodiments. Therefore, based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0030] About the terms and units in the present invention: The terms "include", "have" and any variations thereof in the description and claims of the present invention and related parts are intended to cover non-exclusive inclusions.

[0031] The specific implementation of the design limit displacement calculation method for anti-slide pile reinforced slope of the present invention includes steps 100-800, which are as follows:

[0032] Step 100: For the slope reinforced with anti-slide piles, based on the basic geometric and physical mechanical parameters of the slope, the pile design parameters, and the specified slope stability design safety factor, determine the position of the potential sliding surface of the slope and the length of the load-bearing section of the anti-slide piles, divide the sliding body vertically into several strips from the rear edge of the sliding body to the front, and number each strip from the back to the front, determine the bottom length, bottom inclination and deadweight of each strip, wherein the load-bearing section of the anti-slide pile is included in a strip. The details are as follows:

[0033] The potential sliding surface of the slope reinforced by the anti-slide piles is determined by calculation under the specified slope stability design safety factor condition, and the load-bearing section of the anti-slide piles refers to the part of the anti-slide piles above the potential sliding surface. The calculation can be carried out by the limit equilibrium method or the numerical simulation method, the former such as the Morgenstern-Price method and the transfer coefficient method, and the latter such as the finite element strength reduction method.

[0034] Figure 1 Schematic diagram of the vertical division of the sliding body in the slope of the slope reinforced with anti-slide piles.

[0035] like Figure 1As shown, 10 is an anti-sliding pile, 20 is a sliding body, 30 is a potential sliding surface, 40 is a sliding body surface, and 50 is the first strip at the rear edge of the sliding body. The total number of vertical strips n of the sliding body 20 should be large enough, preferably n ≥ 15, and the strips are numbered from 1 to n from the rear edge to the front edge of the sliding body 20.

[0036] Step 200: Under the specified slope stability design safety factor conditions, for each strip, according to the static equilibrium conditions of horizontal force, vertical force and moment, establish the corresponding static equilibrium equation, wherein, for the strip where the load section of the anti-slide pile is located, the static equilibrium equation must include the internal force of the anti-slide pile at the potential sliding surface, and the internal force includes shear force, bending moment and axial force. The details are as follows:

[0037] Figure 2 Figure 1 is a schematic diagram of the force analysis of a strip j containing an anti-sliding pile load section in the sliding body. Figure 2 As shown, for the force analysis of strip j, according to the static equilibrium conditions of horizontal force, vertical force and moment, three static equilibrium equations can be obtained:

[0038]

[0039] Where W j is the deadweight of bar j; N j is the normal force acting on the bottom surface of bar j; T j is the tangential force acting on the bottom surface of bar j; H j is the inter-strip tangential force acting on the vertical strip interface in front of strip j; P j is the inter-strip normal force acting on the vertical strip interface in front of strip j; q j is the full load on the top surface of strip j; z j is the inter-strip normal force P j The distance from the bottom surface of strip j along the vertical strip interface direction; b j is the width of bar j; N p 、M p and Q p are the axial force, bending moment and shear force of the anti-sliding pile (the pile section at the bottom of the load-bearing section) at the potential sliding surface; α j is the inclination angle of the bottom surface of bar j.

[0040] Figure 3 It is a schematic diagram of the force analysis of any strip i in the sliding body without the anti-sliding pile load section. Figure 3 As shown in the figure, for the force analysis of strip i, according to the static equilibrium conditions of horizontal force, vertical force and moment, three static equilibrium equations can be obtained:

[0041]

[0042] Where i is the number of the strip without the anti-sliding pile load section, 1≤i≤n, and i≠j, and n is the total number of strips; W i is the deadweight of block i; N i is the normal force acting on the bottom surface of bar i; T i is the tangential force acting on the bottom surface of bar i; H i is the inter-strip tangential force acting on the vertical strip interface in front of strip i; P i is the inter-strip normal force acting on the vertical strip interface in front of strip i; q i is the full load on the top surface of strip i; z i is the inter-strip normal force P i The distance from the bottom surface of strip i along the vertical strip interface direction; b i is the width of bar i; α i is the inclination angle of the bottom surface of bar i.

[0043] Step 300: Establish the calculation expressions of the internal forces of the anti-slide piles at the potential sliding surface, form the relationship expressions of the bending moment and axial force with the shear force as the variable, and the relationship expressions of the internal forces with the slope stability design safety factor as the independent variable. The details are as follows:

[0044] According to the plastic deformation model of soil on the pile side proposed by Japanese scholars Ito et al. (Ito T, Matsui T. Methods to estimate lateral force acting on stability piles [J]. Soils and Foundations, 1975, 15 (4): 43–59.), the stability design safety factor F s Under the condition, the simplified expression of the design thrust p(y) (linear distribution force along the height) of the pile on the soil is:

[0045]

[0046] Where D is the pile diameter or the length of the cross section of the pile, y is the depth from the pile top, γ is the soil weight; η1, η2, η3, is a dimensionless coefficient; c0 and They are the calculated cohesion and the calculated internal friction angle of the potential sliding surface soil considering the stability design safety factor;

[0047] η1, η2, η3, The calculation expressions are:

[0048]

[0049] c0, The calculation expressions are:

[0050]

[0051] In the formula, c and are the actual average cohesion and average internal friction angle of the potential sliding surface soil respectively; F s Design in a safety factor for stability.

[0052] Therefore, the design shear force Q of the pile body at the potential sliding surface can be obtained from the horizontal to static equilibrium relationship in the load section of the anti-sliding pile. p The expression is:

[0053]

[0054] Therefore, substituting equation (3) into equation (4) yields the shear force Q of the anti-slide pile at the potential sliding surface: p The relational expression with the slope stability design safety factor as the independent variable.

[0055] According to the static equilibrium condition of the anti-sliding pile load section, the axial force N of the anti-sliding pile at the potential sliding surface can be obtained: p and bending moment M p and shear force Q p There are the following relationship expressions:

[0056]

[0057] M p =κ p HkDJ p (6)

[0058] In the formula, γ p , A p and S p They represent the weight, cross-sectional area and pile spacing of the anti-sliding pile respectively; μ represents the pile-soil friction coefficient; κ p It is the coefficient of net thrust on the side of the anti-sliding pile in the loaded section, which is related to the net thrust distribution pattern on the pile side. Its value range is between 1 / 3 and 1 / 2, and it can generally be taken as 0.35. h0 represents the length of the loaded section of the anti-sliding pile.

[0059] Therefore, substituting equation (4) into equations (5) and (6) yields the axial force N of the anti-slide pile at the potential sliding surface: p and bending moment M p The relational expression with the slope stability design safety factor as the independent variable.

[0060] Step 400: Based on the sliding displacement compatibility conditions between the strips and blocks, the displacement expressions of the strips and blocks are established sequentially from the trailing edge of the sliding body to the front. The details are as follows:

[0061] Considering each strip as a rigid body, when the slope produces sliding displacement, the sliding displacement ω of the kth strip can be deduced from the displacement coordination between the strips. k The relationship between the vertical displacement of the first strip at the trailing edge of the sliding body or the vertical displacement v0 of the top of the sliding body is:

[0062]

[0063] Where k is the number of each block from the trailing edge to the leading edge of the sliding body starting from 1, 1≤k≤n; ψ k is the dilatancy angle of the potential sliding surface soil at the bottom of strip k, taken as

[0064] From the shear dilatancy of the sliding zone soil, the tangential (shear) displacement δ of the strip k along the potential sliding surface can be further derived: k , horizontal displacement u k The relationship between the vertical displacement v0 of the first strip is expressed as:

[0065]

[0066] Step 500: In the static equilibrium equation of each bar, the shear force on the bottom surface of the bar along the potential sliding surface is expressed by the shear stress-shear displacement relationship equation. Specifically, it is as follows:

[0067] According to the soil shear test results, the soil shear stress τ k and shear displacement δ k The relationship equation expression is:

[0068] τ k =G k δ k (1+δ k ε / s k ) ρ (10)

[0069] In the formula, τ k G is the tangential stress of the soil at the bottom of block k along the potential sliding surface; k It represents the linear shear modulus or shear stiffness of the soil at the bottom of strip k along the potential sliding surface; ε and ρ are the strain softening coefficient and strain softening index, respectively, which are the fitting parameters of the test curve. Both are dimensionless coefficients and can be obtained by fitting the shear test data. Among them, ε is generally taken as 2, and ρ is generally taken as between -0.5 and -1.0; s k is the derived quantity related to the normal stress at the bottom of strip k, and the peak strength is characterized by Coulomb's strength theorem, which states that the shear strength of the soil is equal to the cohesion c k and normal stress Nk / l k Multiply by the tangent of the internal friction angle The sum of s k The calculation expression is:

[0070]

[0071] Among them, c k , l k are the cohesion, internal friction angle and length of the potential sliding surface at the bottom of strip k, respectively, and l k =b k / cosα k .

[0072] Step 600: According to the Morgenstern-Price inter-strip force assumption, determine the relationship expression between the inter-strip tangential force and the inter-strip normal force of two adjacent blocks. Specifically, it is as follows:

[0073] According to the Morgenstern-Price interstripe force H k Assumptions:

[0074] H k =λf k P k (12)

[0075] In the formula, λ is a constant to be determined; f k is a function that characterizes the inter-strip force coefficient and is a sinusoidal function related to the position of the strip k. k The expression is:

[0076]

[0077] Among them, L x is the projection length of the entire potential sliding surface in the horizontal direction, and its value can be obtained from the potential sliding surface position determined in step 100; k is the horizontal distance between the front inter-strip interface of strip k and the starting point of the potential sliding surface of the trailing edge of the sliding body, and its expression is:

[0078]

[0079] Where m is the number of the stripe from the 1st stripe to the kth stripe; l m is the bottom length of the mth block.

[0080] Step 700: Under the specified slope stability design safety factor condition, the static equilibrium equations and constraint conditions of all strips are combined to solve the vertical design limit displacement v of the top of the sliding body of the anti-slide pile reinforced slope. 0u The details are as follows:

[0081] For bar k, the tangential force along its bottom surface is:

[0082] T k =τ k l k (14)

[0083] Combining equations (1), (2), (8), (10), (12), and (14), we can obtain the control equations as follows:

[0084]

[0085] In the formula, is a symbolic function that is easy to express, x p It indicates the horizontal distance between the center axis of the anti-slide pile and the slope foot point O;

[0086] Intermediate variable χ k The expression is:

[0087]

[0088] Intermediate variable ξ k The expression is:

[0089]

[0090] Intermediate variable A k , B k , R k , U k The expressions are:

[0091]

[0092] T k = x k [(W k +q k )sinα k -N p sinα k -Q p cosα k ] (18)

[0093]

[0094] In addition, the residual thrust of the last strip at the leading edge of the sliding body is set to zero as a constraint condition. Further deduction from equations (15) to (19) shows that the calculation expression for the vertical displacement v0 at the top of the sliding body is:

[0095]

[0096] Where r is the bar number between the kth bar and the nth bar.

[0097] Under the specified slope stability design safety factor, substituting it into equation (20) and solving it, we can obtain the vertical design limit displacement value v of the sliding body top corresponding to the slope stability design safety factor: 0u .

[0098] Step 800: Set the vertical design limit displacement v of the top of the sliding body 0u Substituting into the displacement expression of each strip, the horizontal design limit displacement u of each strip of the slope reinforced with anti-slide piles under the specified slope stability design safety factor can be obtained: ku and the tangential design limit displacement δ along the potential sliding surface ku The details are as follows:

[0099] The vertical design limit displacement value v of the top of the sliding body is 0u Substituting into equations (8) and (9), we can obtain the tangential design limit displacement and horizontal design limit displacement (positive toward the leading edge of the sliding body 20) of each block along the potential sliding surface under the specified slope stability design safety factor. The calculation expressions are:

[0100]

[0101] In the formula, δ ku 、u ku are the tangential design limit displacement and horizontal design limit displacement of strip k along the potential sliding surface respectively.

[0102] The beneficial effects of the calculation method of the present invention are illustrated below by examples.

[0103] Figure 4 Schematic diagram of a soil slope reinforced by anti-slide piles in an embodiment. Figure 4 As shown in Figure 1, the slope geometric parameters include: slope height of 10m, slope surface horizontal inclination of 30°, slope top surface horizontal, soil is homogeneous material (i.e., the physical and mechanical parameters of each strip are the same), and its basic physical and mechanical parameters include: soil weight γ, average cohesion c and average internal friction angle 20kN / m respectively 3 , 16 kPa and 12°, dilatancy angle ψ k is the average internal friction angle 1 / 3 of ψ k =4°; the shear stiffness G, strain softening coefficient ε and strain softening index ρ of the soil are taken as 10kPa / mm, 2 and -0.7 respectively, and the top surface load of the sliding body q = 0kPa. The safety factor F of slope stability design s =1.25.

[0104] A single row of anti-sliding piles with a side length of 1.5 m is set at 10 m from the slope foot, that is, the horizontal distance x between the center axis of the anti-sliding pile and point O at the slope foot is p =10m, the length of the pile cross section D = 1.5m, the cross-sectional area of ​​the pile A p =2.25m 2 , the friction coefficient between the pile side and the soil μ=0.3, the pile spacing S p =6.8m, the weight of the pile is γ p =25kN / m 3 , net thrust coefficient of the pile side at the loaded section κ p =0.35.

[0105] The following is the calculation process of the embodiment:

[0106] Step 100: Based on the basic geometric and physical mechanical parameters of the slope, the pile design parameters, and the specified slope stability design safety factor, the position of the potential sliding surface of the slope and the length of the load-bearing section of the anti-slide pile are first calculated according to the Morgenstern-Price method. Then the sliding body is segmented.

[0107] Figure 5 Schematic diagram of the vertical segmentation of the sliding body in the embodiment. Figure 5 As shown, the sliding body 20 is divided into 20 strips with equal width, that is, n = 20. The inclination angle of the bottom surface of each strip, the length of the bottom surface, and the deadweight of the strip are listed in Table 1. Among them, the load-bearing section of the anti-sliding pile 10 is included in the 11th strip, that is, j = 11, and the length of the load-bearing section of the anti-sliding pile h0 = 5.45m is obtained from the geometric relationship in the figure.

[0108] Table 1

[0109] Block number k Bottom length (m) Inclination angle of bottom surface (°) Block deadweight (kN / m) k=i=1 2.321 <![CDATA[64.330(α1)]]> 21.04 k=i=2 1.856 57.191 57.76 k=i=3 1.607 51.273 85.94 k=i=4 1.449 46.051 101.74 k=i=5 1.338 41.289 109.44 k=i=6 1.257 36.856 114.22 k=i=7 1.194 32.668 116.60 k=i=8 1.146 28.669 116.94 k=i=9 1.108 24.819 115.47 k=i=10 1.078 21.085 112.37 k=j=11 1.054 17.443 107.77 k=i=12 1.036 13.873 101.77 k=i=13 1.022 10.358 94.44 k=i=14 1.013 6.881 85.83 k=i=15 1.007 3.430 75.98 k=i=16 1.006 -0.009 64.91 k=i=17 1.007 -3.447 52.62 k=i=18 1.013 -6.899 39.12 k=i=19 1.022 -10.375 24.37 k=i=20 1.036 -13.891 8.34

[0110] Step 200: According to equations (1) and (2), we can obtain:

[0111] For the strip where the anti-sliding pile is located, that is, taking j = 11, we have:

[0112]

[0113] For strips without anti-sliding piles, i.e. i≠11, we have:

[0114]

[0115] Step 300: From formula (3e), we can get:

[0116] c0=16 / F s

[0117]

[0118] Therefore, according to equations (3a) to (3d) and equations (3) and (4), we can obtain: the shear force Q of the anti-sliding pile at the potential sliding surface p and slope stability design safety factor F s The relationship between the anti-sliding pile and the potential sliding surface can be obtained by equations (5) and (6). p and bending moment M p and slope stability design safety factor F s The relationship between.

[0119] Step 400: According to equations (7), (8), and (9), we can obtain:

[0120]

[0121] Step 500: According to equations (10) and (11), we can obtain:

[0122] τ k =10Δ k (1+Δ k 2 / s k ) -0.7 (kPa)

[0123]

[0124] Step 600: According to Table 1, L x =20.111m, then from formula (13) we can get f k The expression is:

[0125]

[0126] Step 700: Put F s =1.25, D = 1.5m, A p =2.25m 2 ,μ=0.3,S p =6.8m,γ p =25kN / m 3 , κ p =0.35,ψ k =4° and other related parameters into formula (20), and solve formula (20) to obtain the corresponding slope stability design safety factor F s The vertical design limit displacement value v of the sliding body top 0u =20.61mm.

[0127] Step 800: According to equations (21) and (22), the expressions for the tangential design limit displacement and horizontal design limit displacement of each strip along the potential sliding surface are:

[0128]

[0129] Thus, the tangential design limit displacement and horizontal design limit displacement of each block along the potential sliding surface can be obtained, see Table 2.

[0130] Table 2

[0131] Block number k <![CDATA[u ku (mm)]]> <![CDATA[δ ku (mm)]]> Block number k <![CDATA[u ku (mm)]]> <![CDATA[δ ku (mm)]]> k=i=1 11.74 23.66 k=j=11 12.97 13.30 k=i=2 12.06 20.07 k=i=12 13.02 13.19 k=i=3 12.25 18.02 k=i=13 13.08 13.13 k=i=4 12.40 16.66 k=i=14 13.14 13.12 k=i=5 12.52 15.69 k=i=15 13.19 13.16 k=i=6 12.61 14.98 k=i=16 13.25 13.25 k=i=7 12.70 14.44 k=i=17 13.30 13.38 k=i=8 12.77 14.02 k=i=18 13.36 13.57 k=i=9 12.84 13.70 k=i=19 13.42 13.82 k=i=10 12.91 13.47 k=i=20 13.49 14.14

[0132] Comparison verification:

[0133] The three-dimensional numerical simulation method of FLAC3D commercial software for geotechnical mechanics analysis was used to carry out numerical simulation analysis on the above example, and the displacement of the slope when it reached the design limit state was determined by the strength reduction method. The design limit state mentioned here is the limit state corresponding to the stability design safety factor.

[0134] Figure 6 It is a comparison diagram of the designed limit displacement of each point on the sliding body surface along the potential sliding surface obtained by numerical simulation and the calculation result of the present invention. Figure 7 The figure is a comparison chart of the horizontal design limit displacement of each point on the sliding body surface obtained by numerical simulation and the calculation result of the present invention. Figure 6 , Figure 7 As shown, the distribution curves of the two are relatively close and have basically the same change characteristics.

[0135] The numerical simulation result of the vertical design limit displacement of the top of the slope sliding body is 24.32mm, and the calculation result of the present invention is 20.61mm. The absolute deviation between the two is 3.71mm, and the absolute value of the deviation of the algorithm of the present invention relative to the numerical simulation result is 15.3%. It should be noted that the difference in the stress state of the numerical simulation is one of the main reasons for the deviation between the two.

[0136] It can be seen that the calculation method of the present invention includes the stability design safety factor of the anti-sliding pile reinforced slope, the internal force of the anti-sliding pile, and the shear force of the anti-sliding pile at the potential sliding surface is calculated according to the plastic deformation mode of the soil on the pile side. Through the relationship between the axial force and the bending moment and the shear force, the three internal forces of the anti-sliding pile are specifically expressed in the form of shear force. On this basis, three basic equations are established for the sliding body, including the static equilibrium equation, the shear constitutive equation of the potential sliding surface soil, and the displacement compatibility equation between the strips and blocks. Combined with the boundary condition that the residual thrust of the leading edge of the sliding body is zero, the vertical design limit displacement value of the top of the sliding body corresponding to the slope stability design safety factor is calculated, and then the vertical design limit displacement of the top of the sliding body is substituted into the displacement expression of each strip, and the horizontal design limit displacement of each strip of the anti-sliding pile reinforced slope and the tangential design limit displacement along the potential sliding surface are obtained under the specified slope stability design safety factor. This calculation method is reasonable and has the following advantages:

[0137] (1) The calculation method of the present invention has clear mechanical concepts and concise principles. It comprehensively considers the internal forces of the anti-sliding piles and expresses the three internal forces as quantities closely related to the shear force of the pile body. The three internal forces of the anti-sliding piles are reasonably incorporated into the slope stability control equation of the connected displacement, thus forming a group of stability control equations of the connected displacement of the anti-sliding pile reinforced slope.

[0138] (2) The calculation method of the present invention determines the shear force of the pile body at the potential sliding surface by calculating the plastic deformation thrust of the soil on the side of the pile. The slope stability design safety factor is introduced during the calculation, and the pile body design shear force corresponding to the design safety factor can be obtained. As a result, the stability control equation group of the connection displacement of the anti-sliding pile reinforced slope contains the slope stability design safety factor, and the design limit displacement of the anti-sliding pile reinforced slope under the condition of the specified design safety factor can be solved.

[0139] (3) The calculation method of the present invention can calculate and determine the design limit displacement of the anti-slide pile reinforced slope under different stability design safety factor conditions, thereby realizing a one-to-one correspondence between the design limit displacement of the anti-slide pile reinforced slope and the stability design safety factor.

[0140] (4) The calculation method of the present invention uses a simple computer program to quickly calculate the design limit displacement of the anti-sliding pile reinforced slope. The calculation process is simple, the calculation time is short, and the result is relatively accurate. It avoids the complex modeling and analysis steps and time-consuming calculation process of the numerical simulation method, and provides a convenient and effective means for the analysis and judgment of the design limit displacement of the anti-sliding pile reinforced slope and related engineering design.

[0141] The above is a description of the relevant contents of the present invention. A person skilled in the art will be able to implement the present invention based on these descriptions. Based on the above contents of the present invention, all other embodiments obtained by a person skilled in the art without creative work shall fall within the scope of protection of the present invention.

Claims

1. The design limit displacement calculation method for anti-slide pile reinforced slope is characterized by: Includes steps: Step 100: for the slope reinforced with anti-slide piles, based on the basic geometric and physical mechanical parameters of the slope, the pile design parameters, and the specified slope stability design safety factor, determine the position of the potential sliding surface of the slope and the length of the load-bearing section of the anti-slide piles, divide the sliding body vertically into a number of strips from the rear edge of the sliding body to the front, and number the strips from the back to the front, determine the bottom length, bottom inclination angle, and deadweight of each strip, wherein the load-bearing section of the anti-slide pile is included in a strip; Step 200: Under the specified slope stability design safety factor condition, for each strip, according to the static equilibrium conditions of horizontal force, vertical force and moment, a corresponding static equilibrium equation is established, wherein, for the strip where the load section of the anti-sliding pile is located, the static equilibrium equation needs to include the internal force of the anti-sliding pile at the potential sliding surface, and the internal force includes shear force, bending moment and axial force; Step 300: Establishing calculation expressions for various internal forces of the anti-slide pile at the potential sliding surface, forming relationship expressions of bending moment and axial force with shear force as a variable, and relationship expressions of various internal forces with slope stability design safety factor as an independent variable; Step 400: According to the sliding displacement compatibility conditions between the strips and blocks, the displacement expressions of the strips and blocks are established in sequence from the trailing edge of the sliding body to the front; Step 500: In the static equilibrium equation of each bar, the shear force on the bottom surface of the bar along the potential sliding surface is expressed by using the shear stress-shear displacement relationship equation; Step 600: Determine the relationship expression between the inter-strip tangential force and the inter-strip normal force of two adjacent blocks according to the inter-strip force assumption of Morgenstern-Price; Step 700: Under the specified slope stability design safety factor condition, the static equilibrium equations and constraint conditions of all strips are combined to obtain the vertical design limit displacement of the top of the sliding body of the anti-slide pile reinforced slope; Step 800: Substitute the vertical design limit displacement of the top of the sliding body into the displacement expression of each strip, and obtain the horizontal design limit displacement of each strip of the anti-slide pile reinforced slope and the tangential design limit displacement along the potential sliding surface under the specified slope stability design safety factor.

2. The method for calculating the design limit displacement of the anti-slide pile reinforced slope according to claim 1, characterized in that: In step 100: the potential sliding surface of the slope is calculated and determined by using the limit equilibrium method or the numerical simulation method; the total number of strips formed by segmenting the sliding body is ≥ 15, and they are numbered in sequence from the trailing edge to the leading edge of the sliding body.

3. The method for calculating the design limit displacement of the anti-slide pile reinforced slope according to claim 2, characterized in that: In step 200: The static equilibrium equation of the strip containing the anti-sliding pile load section is: Where j is the bar number of the load-bearing section containing the anti-sliding pile; W j is the deadweight of block j; N j is the normal force acting on the bottom surface of bar j; T j is the tangential force acting on the bottom surface of bar j; H j is the inter-strip tangential force acting on the vertical strip interface in front of strip j; P j is the inter-strip normal force acting on the vertical strip interface in front of strip j; q j is the full load on the top surface of strip j; z j is the inter-strip normal force P j The distance from the bottom surface of strip j along the vertical strip interface direction; b j is the width of bar j; N p 、M p and Q p are the axial force, bending moment and shear force of the anti-slide pile at the potential sliding surface; α j is the inclination angle of the bottom surface of strip j; The static equilibrium equation of the strip without the anti-sliding pile load section is: Where i is the number of the strip without the anti-sliding pile load section, 1≤i≤n, and i≠j, and n is the total number of strips; W i is the deadweight of block i; N i is the normal force acting on the bottom surface of bar i; T i is the tangential force acting on the bottom surface of bar i; H i is the inter-strip tangential force acting on the vertical strip interface in front of strip i; P i is the inter-strip normal force acting on the vertical strip interface in front of strip i; q i is the full load on the top surface of strip i; z i is the inter-strip normal force P i The distance from the bottom surface of strip i along the vertical strip interface direction; b i is the width of bar i; α i is the inclination angle of the bottom surface of bar i.

4. The method for calculating the design limit displacement of the anti-slide pile reinforced slope according to claim 3, characterized in that: In step 300, the relationship between the axial force, bending moment and shear force of the anti-sliding pile at the potential sliding surface is expressed as: In the formula, γ p , A p and S p They represent the weight, cross-sectional area and pile spacing of the anti-sliding pile respectively; μ represents the pile-soil friction coefficient; κ p It is the coefficient of net thrust on the side of the anti-sliding pile in the loaded section, and its value range is between 1 / 3 and 1 / 2; h0 represents the length of the anti-sliding pile in the loaded section.

5. The method for calculating the design limit displacement of the anti-slide pile reinforced slope according to claim 4, characterized in that: The relationship between the shear force and the slope stability design safety factor in step 300 is expressed as: Where y represents the depth from the pile top; p(y) is the design thrust of the pile body on the soil side; The calculation expression of p(y) is: Where D is the pile diameter or the length of the pile cross section; γ represents the soil weight; η1, η2, η3, is a dimensionless coefficient; c0 and They are the calculated cohesion and the calculated internal friction angle of the potential sliding surface soil considering the stability design safety factor; η1, η2, η3, The calculation expressions are: c0, The calculation expressions are: c0=c / F s In the formula, c and are the actual average cohesion and average internal friction angle of the potential sliding surface soil respectively; F s Design in a safety factor for stability.

6. The method for calculating the design limit displacement of the anti-slide pile reinforced slope according to claim 5, characterized in that: In step 700, the calculation expression for the vertical displacement of the top of the sliding body of the anti-slide pile reinforced slope is: Where k is the number of the blocks from the trailing edge to the leading edge of the sliding body, starting from 1, 1≤k≤n; r is the number of the blocks between the kth block and the nth block; the intermediate variable A k , B k , R k , U k , χ k , k The expressions are: T k =χ k [(W k +q k )sinα k -N p sinα k -Q p cosα k ] Where v0 is the vertical displacement of the top of the sliding mass of the slope reinforced with anti-slide piles; λ is a constant to be determined; f k is a sine function related to the position of the bar k that characterizes the inter-bar force coefficient. L x is the horizontal projection length of the entire potential sliding surface; x k is the horizontal distance between the front inter-strip interface of strip k and the starting point of the potential sliding surface at the trailing edge of the sliding body, m is the number of the blocks from the 1st block to the kth block, l m is the length of the bottom edge of the mth block; ψ k is the dilatancy angle of the potential sliding surface soil at the bottom of strip k, taken as ρ is the strain softening index, ranging from -0.5 to -1.0; s k is a derived quantity related to the normal stress on the bottom surface of bar k.

7. The method for calculating the design limit displacement of the anti-slide pile reinforced slope according to claim 6, characterized in that: In step 800, the horizontal design limit displacement of each block of the anti-slide pile reinforced slope and the tangential design limit displacement along the potential sliding surface are: In the formula, v 0u is the vertical design limit displacement value of the top of the sliding body; δ ku 、u ku are the tangential design limit displacement and horizontal design limit displacement of strip k along the potential sliding surface respectively.

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