A method for evaluating the stability of CFG pile composite foundation under embankment

Abstract

The present invention discloses a method for evaluating the stability of CFG pile composite foundations under embankments. The embankment load shared by the CFG pile top is determined using the soil arching effect of the Hewlett & Randolph method. The CFG pile top cushion reinforcement constraint force and the embankment load shared by the CFG pile are considered to improve the pile's bending resistance. The critical horizontal net thrust of the CFG pile during pile bending failure is determined. The horizontal net thrust coefficient is used to characterize the asynchrony of the CFG pile's bending and tensile failure. The horizontal net thrust of the CFG pile that does not reach the ultimate bending strength is determined. A governing equation is established based on the static equilibrium conditions of the CFG pile's anti-sliding section. The anti-sliding moment of the pile is determined to be composed of the anti-sliding moment formed by the bending strength of the pile cross section, the vertical embankment load borne by the pile top, and the restraining force of the horizontal cushion reinforcement. The mechanical analysis model of the present invention objectively reflects the contributions of multiple factors to anti-sliding.

Description

Technical Field

[0001] The present invention belongs to the field of road and railway engineering, and in particular relates to a method for evaluating the stability of a CFG pile composite foundation under an embankment. Background Art

[0002] CFG piles are high-bonding piles formed by mixing cement, fly ash, crushed stone, and other materials with water. They significantly reduce foundation settlement and deformation, increase bearing capacity, and enhance foundation stability. They are widely used in my country's high-speed railway and highway subgrade projects. However, the lateral anti-sliding stability of CFG pile composite foundations is relatively poor, and instability accidents occur frequently. Furthermore, the evaluation method for their stability is still not perfect.

[0003] Regarding the stability evaluation methods for CFG pile composite foundations, relevant technical specifications at home and abroad have yet to reach a consensus. The composite shear strength method uses a composite equivalent of the pile-soil shear strength in the pile reinforcement area, while the BS8006 method uses the vertical ultimate bearing capacity of the pile below the sliding surface as the anti-slip force acting on the sliding surface to calculate the anti-slip moment. Both methods significantly overestimate the stability of composite foundations. The equivalent shear strength method uses the bending strength of the pile body to determine the anti-slip force provided by the pile length within the sliding surface for stability calculations. This method does not consider the anti-slip effects of the pile axial force and the reinforcement belt restraint force, and cannot accurately evaluate the stability of composite foundations. Therefore, it is urgent to establish a stability evaluation method for CFG pile composite foundations that comprehensively considers the anti-slip contribution of the pile body. Summary of the Invention

[0004] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for evaluating the stability of CFG pile composite foundation under an embankment, which solves the problem that the prior art method for evaluating the stability of CFG pile composite foundation fails to reflect the anti-slip contribution of CFG piles provided by multiple factors.

[0005] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: a method for evaluating the stability of CFG pile composite foundation under embankment, comprising the following steps:

[0006] S1. Obtain the parameters of the embankment and composite foundation, and obtain the embankment load shared by the CFG pile top;

[0007] S2. Assign the anti-sliding moment and the number of iterations of each CFG pile to zero, and obtain the initial potential sliding surface center, radius and stability safety factor when only the cushion reinforcement is set by the Swedish arc strip method;

[0008] S3. Based on the center and radius of the potential sliding surface, the distance from the intersection of the reinforcement strip and the potential sliding surface to the embankment toe, the length of the anti-sliding section of each CFG pile, and the distance from the CFG pile to the toe are obtained. Then, the anti-sliding moment of each CFG pile is calculated in combination with the embankment load shared by the CFG pile top.

[0009] S4. Based on the calculated anti-slip moment of each CFG pile, the center, radius and stability safety factor of the new potential slip surface are obtained by the Swedish arc strip method;

[0010] S5. Determine whether the difference between the stability safety factor under the new potential sliding surface and the stability safety factor under the initial potential sliding surface is less than a limit threshold. If so, proceed to S6; if not, increase the number of iterations by one and return to S3.

[0011] S6. Evaluate the stability of the CFG pile composite foundation under the embankment based on the stability safety factor under the new potential sliding surface.

[0012] Further: In S1, the embankment load N shared by the CFG pile top is calculated i The specific expression is:

[0013] N i =γ e h pi s 2 v i

[0014] Where, γ e is the weight of embankment fill, h pi is the height of the embankment soil column at the top of the CFG pile, s is the square spacing of the CFG piles, v i The proportion of CFG piles sharing the embankment fill load.

[0015] Furthermore, the proportion of the CFG piles sharing the embankment fill load is calculated by the Hewlett & Randolph method.

[0016] Further: in said S3, the anti-slip torque of each CFG pile includes the anti-slip torque of the CFG pile within the potential slip surface and the anti-slip torque of the CFG pile outside the potential slip surface;

[0017] Calculation of the anti-sliding moment M of the CFG pile within the potential sliding surface RPim The specific expression is:

[0018]

[0019] Where, W is the flexural modulus of the CFG pile section, l Cm is the distance from the intersection of the potential sliding surface to the toe of the embankment, m is the number of iterations, l maxm is the anti-sliding section length of the key CFG pile, l him 、l Nim 、l Tm F him 、N i , ΔT m The force arm to the center of the potential sliding surface, ΔT m is the reinforcement restraint force of the CFG pile top cushion layer, Fhim is the horizontal net thrust of the CFG pile, β im is the horizontal net thrust coefficient of CFG pile bearing, f tk is the tensile strength of CFG pile, N km is the embankment load shared by the top of the key CFG pile, A is the cross-sectional area of the CFG pile, a is the side length of the CFG pile cap, T C is the tensile force per unit width of the reinforcement in the cushion layer at the potential sliding surface;

[0020] Calculation of the anti-sliding moment M of the CFG pile outside the potential sliding surface RPim The specific expression of ′ is:

[0021] M RPim ′=l Nim N i .

[0022] Furthermore: the horizontal net thrust coefficient β of the CFG pile bearing im The specific expression is

[0023]

[0024] Where, l im is the length of the anti-sliding section of the CFG pile, x im is the distance from the CFG pile to the slope foot, x km The distance from the key CFG pile to the slope foot is r m is the radius;

[0025] The tensile force per unit width of the reinforcement of the cushion layer at the potential sliding surface is T C The specific expression is:

[0026] T C =0.4T max

[0027] Where, T max It is the ultimate tensile strength of the cushion reinforcement.

[0028] Further: in S5, the limit threshold is 0.01.

[0029] Further: S6 specifically includes:

[0030] Determine whether the new potential sliding surface stability safety factor is less than the foundation stability safety factor control limit. If so, the foundation stability is good; if not, the foundation stability is insufficient.

[0031] The beneficial effects of the present invention are:

[0032] (1) The present invention provides a method for evaluating the stability of CFG pile composite foundations under embankments. The embankment load shared by the CFG pile top is obtained through the soil arch effect of the Hewlett & Randolph method. The role of the CFG pile top pad reinforcement constraint force and the embankment load shared by the CFG pile in improving the bending resistance of the pile body is comprehensively considered to obtain the key CFG pile bearing horizontal net thrust when the pile body is bent and damaged. The pile bearing horizontal net thrust coefficient is used to characterize the asynchrony of the CFG pile body bending and tensile failure. The CFG pile bearing horizontal net thrust that has not reached the bending strength limit is obtained. The control equation is established based on the static equilibrium condition of the CFG pile anti-sliding section. The pile anti-sliding moment is composed of the anti-sliding moment formed by the bending strength of the pile body section, the vertical embankment load borne by the pile top, and the horizontal pad reinforcement constraint force. The mechanical analysis model of the present invention can objectively reflect the anti-sliding contribution of multiple factors.

[0033] (2) The present invention performs stability analysis of the CFG pile composite foundation under the embankment based on the arc strip method until the difference in the potential sliding surface stability safety factor of two adjacent iterations is within the limit threshold range. The calculated stability safety factor has good applicability, is simple to operate, and is convenient for engineering application. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 This is a flow chart of a method for evaluating the stability of a CFG pile composite foundation under an embankment according to the present invention.

[0035] Figure 2 This is a diagram of the stability analysis model of the CFG pile composite foundation under the embankment of the present invention. DETAILED DESCRIPTION

[0036] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0037] Example 1:

[0038] like Figure 1 As shown, in one embodiment of the present invention, a method for evaluating the stability of a CFG pile composite foundation under an embankment includes the following steps:

[0039] S1. Obtain the parameters of the embankment and composite foundation, and obtain the embankment load shared by the CFG pile top;

[0040] S2. Assign the anti-sliding moment and the number of iterations of each CFG pile to zero, and obtain the initial potential sliding surface center, radius and stability safety factor when only the cushion reinforcement is set by the Swedish arc strip method;

[0041] S3. Based on the center and radius of the potential sliding surface, the distance from the intersection of the reinforcement strip and the potential sliding surface to the embankment toe, the length of the anti-sliding section of each CFG pile, and the distance from the CFG pile to the toe are obtained. Then, the anti-sliding moment of each CFG pile is calculated in combination with the embankment load shared by the CFG pile top.

[0042] S4. Based on the calculated anti-slip moment of each CFG pile, the new potential sliding surface center, radius and stability safety factor are obtained by the Swedish arc strip method;

[0043] S5. Determine whether the difference between the stability safety factor under the new potential sliding surface and the stability safety factor under the initial potential sliding surface is less than a limit threshold. If so, proceed to S6; if not, increase the number of iterations by one and return to S3.

[0044] S6. Evaluate the stability of the CFG pile composite foundation under the embankment based on the stability safety factor under the new potential sliding surface.

[0045] In S1, calculate the embankment load N shared by the CFG pile top i The specific expression is:

[0046] N i =γ e h pi s 2 v i

[0047] Where, γ e is the weight of embankment fill, h pi is the height of the embankment soil column at the top of the CFG pile, s is the square spacing of the CFG piles, v i The proportion of CFG piles sharing the embankment fill load.

[0048] In this embodiment, the embankment and composite foundation parameters include the geometric dimensions of the embankment and the ground, the physical and mechanical indicators of the roadbed filler and the foundation soil, the CFG pile body and material and arrangement parameters, and the strength of the cushion reinforcement;

[0049] The proportion of the CFG piles sharing the embankment fill load is calculated by the Hewlett & Randolph method.

[0050] When CFG piles are arranged in an equilateral triangle, the effective area of a single pile is equivalent, and the expression for the spacing s of CFG piles in a square arrangement is:

[0051]

[0052] Where s e The spacing of CFG piles arranged in an equilateral triangle.

[0053] In said S3, the anti-slip torque of each CFG pile includes the anti-slip torque of the CFG pile within the potential slip surface and the anti-slip torque of the CFG pile outside the potential slip surface;

[0054] Calculation of the anti-sliding moment M of the CFG pile within the potential sliding surface RPim The specific expression is:

[0055]

[0056] Where, W is the flexural modulus of the CFG pile section, l Cm is the distance from the intersection of the potential sliding surface to the toe of the embankment, m is the number of iterations, l maxm is the anti-sliding section length of the key CFG pile, l him 、l Nim 、l Tm F him 、N i , ΔT m The force arm to the center of the potential sliding surface, ΔT m is the reinforcement restraint force of the CFG pile top cushion layer, F him is the horizontal net thrust of the CFG pile, β im is the horizontal net thrust coefficient of CFG pile bearing, f tk is the tensile strength of CFG pile, N km is the embankment load shared by the top of the key CFG pile, A is the cross-sectional area of the CFG pile, a is the side length of the CFG pile cap, T C is the tensile force per unit width of the reinforcement in the cushion layer at the potential sliding surface;

[0057] Calculation of the anti-sliding moment M of the CFG pile outside the potential sliding surface RPim The specific expression of ′ is:

[0058] M RPim ′=l Nim N i .

[0059] In this embodiment, when the CFG pile has a pile cap, the side length of the CFG pile cap is a. When the CFG pile has no pile cap, the side length of the CFG pile cap is the side length of the top section of the CFG pile. The area of a circular cross-section pile or a circular pile cap is equivalent to a=(πd 2 / 4) 1 / 2 , d is the diameter of a circular cross-section pile or a circular pile cap.

[0060] The horizontal net thrust coefficient of the CFG pile bearing β im The specific expression is

[0061]

[0062] Where, l im is the length of the anti-sliding section of the CFG pile, x imis the distance from the CFG pile to the slope foot, x km The distance from the key CFG pile to the slope foot is r m is the radius, l i is the anti-sliding section length of the CFG pile;

[0063] The tensile force per unit width of the reinforcement of the cushion layer at the potential sliding surface is T C The specific expression is:

[0064] T C =0.4T max

[0065] Where, T max It is the ultimate tensile strength of the cushion reinforcement.

[0066] In S5, the limit threshold is 0.01.

[0067] The S6 is specifically:

[0068] Determine whether the new potential sliding surface stability safety factor is less than the foundation stability safety factor control limit. If so, the foundation stability is good; if not, the foundation stability is insufficient.

[0069] like Figure 2 As shown, in this embodiment, the mechanical principles of the present invention are specifically as follows:

[0070] (1) Static balance of the anti-sliding section of the pile:

[0071] The CFG piles under the embankment have a certain anti-slip effect on the composite foundation. In the potential arc sliding surface, the anti-slip section of the CFG pile satisfies the static equilibrium equation, and the tangential force P at the pile sliding surface i , normal force Q i and bending moment M i Horizontal net thrust F borne by pile hi , the reinforcement restraint force ΔT of the pile top cushion and the embankment load N shared by the pile top i Impact, such as Figure 2 As shown. Pile anti-slip moment M RPi The tangential force P of the pile i and bending moment M i Together, M RPi =P i rM i .

[0072] The static equilibrium equation of the CFG pile above the sliding surface is:

[0073]

[0074] Where, α i is the horizontal inclination angle of the tangent line at the pile sliding surface, and M RPi =Pi rM i , obtain the pile anti-slip moment M RPi =F hi l hi +N i l Ni -ΔTl T .

[0075] (2) CFG pile bending failure:

[0076] Under the action of embankment load, since the compressive strength of CFG pile material is much greater than its tensile strength, the tensile side of CFG pile reaches its limit under normal conditions. hk The pile bending moment M is generated by the reinforcement restraint force ΔT of the pile top cushion layer k =F hk l max / 3-ΔTl max When the key CFG pile is bent and damaged, the pile cross section appears to be caused by the pile body bending moment M k and axial force N k Bending tensile stress σ caused by combination t , and reach the pile tensile strength f tk .

[0077] When CFG piles are bent and damaged:

[0078]

[0079] Take σ t =f tk , obtain the ultimate bending moment M of the pile body u =W(f tk +N k / A) and the key CFG pile bearing horizontal net thrust F hk =3W(f tk +N k / A) / l max +3ΔT.

[0080] (3) The CFG pile body deforms in synergistic sliding with the composite foundation. The horizontal restraint force of the cushion reinforcement on the pile (cap) top is the tension difference within the range of the pile (cap) side length. The restraint force of the pile top reinforcement belt ΔT = T C a 2 / l C .

[0081] (4) The non-uniformity of the bearing and deformation of the foundation under the embankment will lead to the asynchrony of the bending failure of the CFG pile. The key CFG pile with the deepest sliding surface near the center of the circle is subjected to a greater side sliding effect. The maximum bending and tensile stress of the pile section at the position tangent to the sliding surface reaches the ultimate strength first, and bending and tensile failure occurs. The pile bearing horizontal net thrust coefficient β is usedi Characterizes the asynchronous nature of CFG pile bending and tensile failure, and the horizontal net thrust F of CFG piles at other positions that have not reached the bending strength limit hi =β i F hk =3β i W(f tk +N k / A) / l max +3β i ΔT.

[0082] (5) The CFG pile bears the horizontal net thrust F hi Substituting the constraint force ΔT of the pile top reinforcement into the anti-slip moment of the CFG pile in principle a, the following formula is obtained:

[0083]

[0084] Example 2:

[0085] This embodiment is directed to a specific experiment on a method for evaluating the stability of a CFG pile composite foundation under an embankment.

[0086] In this example, the foundation is a clay layer, the embankment width B = 30m, the embankment height h = 8m, and the slope ratio 1:n = 1:1.5. The foundation is reinforced with CFG piles with a diameter of d = 0.5m, a pile length L = 12m, a square pile spacing s = 2.0m, a pile cap side length a = 1.2m, and a pile ultimate tensile strength f tk =1.27MPa; the crushed stone cushion layer is 0.6m thick, with a layer of ultimate tensile strength T in the middle max =80kN / m geogrid. The roadbed profile is as follows Figure 2 shown.

[0087] Table 1 Roadbed material parameters

[0088]

[0089] The CFG pile top load N shared by the embankment is determined by Hewlett & Randolph method. i As shown in Table 2, the slope foot of the left side of the embankment is taken as the coordinate origin (0, 0), and the anti-sliding moment M of each CFG pile is assigned. RPi0 = 0, the number of iterations m = 0, the Swedish arc strip method is used to calculate the stability of the CFG pile composite foundation, and the potential arc sliding surface center O1 (4.65m, 8.52m), radius r1 = 14.49m and stability safety factor K1 = 1.015 are obtained. For the potential arc sliding surface O1, according to the formula Determine the anti-sliding moment M of the CFG pile body within the arc sliding surface O1 RPi1 ; Then by formula M RPim =lNi N i , determine the anti-sliding moment M of the CFG pile outside the arc sliding surface O1 RPi1 .

[0090] Table 2 Anti-sliding moment of CFG pile under potential arc sliding surface

[0091]

[0092] The anti-sliding moment M of the CFG pile under the potential arc sliding surface O1 is obtained RPi1 The Swedish arc strip method was used to calculate the stability of the CFG pile reinforced cushion composite foundation. The second iteration yielded the potential arc sliding surface center O2 (1.74, 9.03), radius r2 = 12.22 m, and stability safety factor K2 = 1.337. By comparing |K2 - K1| > ε, where ε is the iterative calculation threshold of 0.01, the above iterative process was repeated to obtain the stability safety factor K3 = 1.552 for the CFG pile composite foundation in the third iteration. By comparing |K3 - K2| > ε, the stability safety factor K4 = 1.547 for the CFG pile reinforced cushion composite foundation in the fourth iteration was obtained using the same method. By comparing |K4 - K3| ≤ ε, the stability safety factor K = K4 = 1.547 for the CFG pile composite foundation was output. By comparing K ≥ [K], the foundation stability is good, and [K] is the control limit of the foundation stability safety factor of 1.25.

[0093] The beneficial effects of the present invention are as follows: the present invention provides a method for evaluating the stability of a CFG pile composite foundation under an embankment, obtains the embankment load shared by the CFG pile top through the soil arch effect of the Hewlett & Randolph method, comprehensively considers the role of the CFG pile top cushion reinforcement constraint force and the embankment load shared by the CFG pile in improving the bending resistance of the pile body, obtains the key CFG pile bearing horizontal net thrust when the pile body is bent and damaged, uses the pile bearing horizontal net thrust coefficient to characterize the asynchrony of the CFG pile body bending and tensile damage, obtains the CFG pile bearing horizontal net thrust that has not reached the bending strength limit, establishes a control equation based on the static equilibrium condition of the CFG pile anti-sliding section, and obtains that the pile body anti-sliding moment is composed of the anti-sliding strength of the pile body section, the vertical embankment load borne by the pile top, and the anti-sliding moment formed by the horizontal cushion reinforcement constraint force. . The mechanical analysis model of the present invention can objectively reflect the anti-sliding contribution of multiple factors.

[0094] The present invention adopts the arc strip method to perform stability analysis of CFG pile composite foundation until the difference between the potential sliding surface stability safety factors of two adjacent iterations is within a limit threshold range. The calculated stability safety factor has good applicability, simple operation, and is convenient for engineering application.

[0095] In the description of the present invention, it should be understood that the terms "center", "thickness", "upper", "lower", "horizontal", "top", "bottom", "inner", "outer", "radial", etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and "third" are used for descriptive purposes only and cannot be understood as indicating or implying the relative importance or the number of technical features implicitly specified. Therefore, the features defined by "first", "second", and "third" may explicitly or implicitly include one or more of such features.

Claims

1. A method for evaluating the stability of CFG pile composite foundation under embankment, characterized in that: The following steps are involved: S1. Obtain the parameters of the embankment and composite foundation, and obtain the embankment load shared by the CFG pile top; S2. Assign the anti-sliding moment and the number of iterations of each CFG pile to zero, and obtain the initial potential sliding surface center, radius and stability safety factor when only the cushion reinforcement is set by the Swedish arc strip method; S3. Based on the center and radius of the potential sliding surface, the distance from the intersection of the reinforcement strip and the potential sliding surface to the embankment toe, the length of the anti-sliding section of each CFG pile, and the distance from the CFG pile to the toe are obtained. Then, the anti-sliding moment of each CFG pile is calculated in combination with the embankment load shared by the CFG pile top. S4. Based on the calculated anti-slip moment of each CFG pile, the center, radius and stability safety factor of the new potential slip surface are obtained by the Swedish arc strip method; S5. Determine whether the difference between the stability safety factor under the new potential sliding surface and the stability safety factor under the initial potential sliding surface is less than a limit threshold. If so, proceed to S6; if not, increase the number of iterations by one and return to S3. S6. Evaluate the stability of the CFG pile composite foundation under the embankment based on the stability safety factor under the new potential sliding surface; In said S3, the anti-slip torque of each CFG pile includes the anti-slip torque of the CFG pile within the potential slip surface and the anti-slip torque of the CFG pile outside the potential slip surface; Calculation of the anti-slip moment of CFG piles within the potential slip surface The specific expression is: Where, W is the flexural modulus of the CFG pile section, is the distance from the intersection of the potential sliding surface to the toe of the embankment, m is the number of iterations, is the anti-sliding section length of the key CFG pile, l him 、 l Nim 、 l Tm They are F him 、 N i 、 ΔT m The force arm to the center of the potential sliding surface, ΔT m is the reinforcement restraint force of the CFG pile top cushion layer, F him is the horizontal net thrust of the CFG pile, is the horizontal net thrust coefficient of CFG pile bearing, f tk is the tensile strength of CFG pile, N km The embankment load shared by the key CFG pile tops, A is the cross-sectional area of the CFG pile, a is the side length of the CFG pile cap, T C is the tensile force per unit width of the reinforcement in the cushion layer at the potential sliding surface; Calculation of the anti-slip moment of CFG piles outside the potential sliding surface The specific expression is: ； is the embankment load.

2. The method for evaluating the stability of CFG pile composite foundation under embankment according to claim 1, characterized in that: In S1, the embankment load shared by the CFG pile top is calculated The specific expression is: Where, γ e The embankment is heavily filled. is the height of the embankment soil column at the top of the CFG pile, is the square spacing of CFG piles, The proportion of CFG piles sharing the embankment fill load.

3. The method for evaluating the stability of CFG pile composite foundation under embankment according to claim 2, characterized in that: The proportion of the CFG piles sharing the embankment fill load is calculated by the Hewlett & Randolph method.

4. The method for evaluating the stability of CFG pile composite foundation under embankment according to claim 1, characterized in that: The horizontal net thrust coefficient of the CFG pile bearing The specific expression is Where, l im is the length of the anti-sliding section of the CFG pile, x im is the distance from the CFG pile to the slope foot, x km is the distance from the key CFG pile to the slope foot, r m is the radius; Tensile force per unit width of the reinforcement of the cushion layer at the potential sliding surface T C The specific expression is: T C =0.4 T max Where, T max It is the ultimate tensile strength of the cushion reinforcement.

5. The method for evaluating the stability of CFG pile composite foundation under embankment according to claim 1, characterized in that: In S5, the limit threshold is 0.

01.

6. The method for evaluating the stability of CFG pile composite foundation under embankment according to claim 1, characterized in that: The S6 is specifically: Determine whether the new potential sliding surface stability safety factor is less than the foundation stability safety factor control limit. If so, the foundation stability is good; if not, the foundation stability is insufficient.

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