Method for calculating stability of geotextile reinforced cushion embankment on soft soil foundation

Abstract

The invention discloses a method for calculating the stability of a geotextile reinforced cushion embankment on a soft soil foundation, which comprises the following steps: step 10, setting the area range and the radius range of the circle center of an arc-shaped potential slip surface, and vertically segmenting a corresponding potential slip mass; 20, taking the horizontal action direction of the design ultimate tension of the geotechnical cloth at the intersection of the geotechnical cloth and the potential sliding surface in the transverse direction of the roadbed, and determining the anti-sliding torque provided by the geotechnical cloth; step 30, based on a simplified Bishop method principle, introducing earthquake acting force, establishing a stability calculation control equation, and searching, calculating and determining the most dangerous sliding surface and the most dangerous sliding body; 40, a non-uniform distribution mode is adopted, and the transverse tension of the geotechnical cloth in the most dangerous slip mass along the roadbed is determined; and step 50, calculating and determining a corresponding stability coefficient of the most dangerous slip mass by adopting a soil mass shear strength parameter reduction mode, and the stability coefficient is the solved target stability coefficient. The method is clear in mechanical concept, simple in principle and more reasonable and accurate in calculation result.

Description

Technical Field

[0001] The present invention relates to the technical field of roadbed engineering, in particular to a method for calculating the stability of a geotextile reinforced cushion embankment on a soft soil foundation. Background Art

[0002] When constructing embankments on soft soil foundations, high-strength geotextiles are often laid in the sub-base to improve the embankment's overall stability. This ensures that the mechanical properties of the embankment meet engineering requirements while also mitigating the economic challenges associated with stronger foundation treatments. Due to frictional resistance between the high-strength geotextile and the sub-base soil, and its high design ultimate tensile strength, laying high-strength geotextiles in the sub-base can help improve the overall mechanical properties of embankments on soft soil foundations.

[0003] To scientifically determine the effectiveness of geotextile reinforcement on the overall stability of embankments on soft soil foundations, it is necessary to conduct a reasonable analysis and calculation of the stability of the soft soil foundation-geotextile reinforcement embankment system. Among these, the proper consideration of the anti-slip effect of geotextiles is a key consideration.

[0004] Previous studies of the role of geotextiles in the stability analysis of soft soil foundation-geotextile-reinforced cushion embankment systems have considered only the overall tensile force exerted by the geotextile on the potential sliding body at the sliding surface. The tensile force was calculated to be a value between the horizontal and the tangential direction of the sliding surface at that point. This approach to the anti-slip effect of geotextiles is both conceptually flawed and subject to uncertainty in the subjective direction of the value. In reality, in addition to its overall tensile effect, the more important role of geotextiles is their local frictional resistance to potential sliding bodies. Previous stability analysis methods based on simplified Bishop and Fellenius methods cannot fully reflect the local frictional resistance of geotextiles.

[0005] Generally speaking, numerical simulation methods are a viable approach for analyzing the stability of embankment systems with soft soil foundations and geotextile-reinforced cushions. However, due to the technical difficulty and time-consuming calculation process, this approach has been difficult to implement on a large scale in practical engineering design. In particular, the proper simulation of the interaction between the geotextile and the soil, and the difficulty in determining the relevant contact parameters, make this problem difficult to achieve. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a method for calculating the stability of embankments with geotextile reinforced cushions on soft soil foundations, which can reasonably reflect the anti-slip effect of geotextiles and has a simple concept and a solution process that is easy to operate by computer. The technical solution is as follows:

[0007] The stability calculation method of the embankment with geotextile reinforced cushion on soft soil foundation includes the following steps:

[0008] Step 10: In the upper area of the embankment, the center area and radius of the arc-shaped potential sliding surface are set, and the corresponding potential sliding body is vertically divided into a plurality of strips;

[0009] Step 20, taking the design ultimate tensile force of the geotextile in the transverse direction of the roadbed at the intersection with the potential sliding surface as the horizontal direction, and determining the anti-slip torque provided by the geotextile;

[0010] Step 30: Based on the simplified Bishop method and by introducing earthquake forces in a pseudo-static manner, a stability calculation control equation is established, and the most dangerous sliding surface and the corresponding most dangerous sliding body are determined by search and calculation, as well as the length of each geotextile layer in the most dangerous sliding body along the transverse direction of the roadbed;

[0011] Step 40, adopting a non-uniform distribution mode that satisfies boundary conditions and static equilibrium conditions for the surface friction of the geotextile, and determining the lateral tension of the geotextile along the roadbed in the most dangerous sliding body from the static equilibrium relationship;

[0012] Step 50, for the determined most dangerous sliding body, based on the force balance equation of each block, according to the transfer coefficient method, using the soil shear strength parameter reduction method, calculate and determine the corresponding stability coefficient of the most dangerous sliding body. This stability coefficient is the target stability coefficient.

[0013] The outstanding advantages of the method for calculating the stability of the geotextile reinforced cushion embankment on the soft soil foundation of the present invention are: first, the method of the present invention reasonably considers the effect of the lateral friction resistance of the geotextile on the anti-sliding stability, and reasonably characterizes the contribution of the lateral friction resistance of the geotextile to the anti-sliding stability through the force of the relevant strips and blocks, thereby improving the defect of the previous analysis method that does not distinguish the different directions of the bottom surfaces of each strip and block; second, the method of the present invention adopts a non-uniform distribution pattern for the lateral friction resistance of the geotextile, which is more in line with its actual force characteristics, thereby improving the defect of the previous related uniform distribution; then, the method of the present invention is based on the overall arc sliding instability failure mode of the soft soil foundation-geotextile reinforced cushion embankment system, and introduces the contribution of the lateral friction resistance of the geotextile to the anti-sliding stability through the transfer coefficient method. The calculated target stability coefficient is more reasonable, and the nonlinear distribution effect characteristics of the lateral friction resistance of each layer of geotextile can be clearly defined.

[0014] In summary, the method of the present invention has clear mechanical concepts, concise principles, a relatively simple calculation process, easy computer operation, and more reasonable and accurate calculation results. It avoids the complex modeling and analysis steps and time-consuming calculation process of the numerical simulation method, and provides a convenient, effective and more conceptually reasonable method for the engineering design of geotextile reinforced cushion embankments on soft soil foundations, taking into account both technical significance and engineering practical value.

[0015] The present invention will be further described below with reference to 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 practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The drawings that constitute part of this invention are intended to assist in understanding the invention. The contents provided in the drawings and their related descriptions in the present invention may be used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0017] Figure 1 This is an analytical model diagram for calculating the stability of the geotextile reinforced cushion embankment on the soft soil foundation of the present invention.

[0018] Figure 2 This is a schematic structural diagram of a geotextile reinforced cushion embankment on a soft soil foundation according to an embodiment of the present invention.

[0019] Figure 3 Graph showing the calculation results of the most dangerous sliding surface and the most dangerous sliding body according to an embodiment of the present invention.

[0020] Figure 4 This is a comparison chart of the results of the most dangerous sliding surface obtained by the method of the present invention and numerical simulation in an embodiment of the present invention.

[0021] The relevant marks in the above drawings are:

[0022] 100-foundation, 200-cushion, 300-geotextile, 400-potential sliding surface, 500-shoulder, 600-area where the center of the potential sliding surface is located, 700-top surface of the embankment, 800-ground outside the embankment toe, 900-potential sliding body. DETAILED DESCRIPTION

[0023] The present invention is described clearly and completely below with reference to 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 with reference to the accompanying drawings, it should be noted that:

[0024] The technical solutions and technical features provided in each part of the present invention, including the following description, may be combined with each other unless there is any conflict.

[0025] In addition, the embodiments of the present invention described below are generally only part of the embodiments of the present invention, rather than all of the embodiments. Therefore, based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making any creative efforts should fall within the scope of protection of the present invention.

[0026] Regarding 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 the related parts are intended to cover non-exclusive inclusions.

[0027] The specific implementation of the method for calculating the stability of an embankment with a geotextile reinforced cushion on a soft soil foundation of the present invention includes steps 10-50, which are as follows:

[0028] Step 10: In the upper area of the embankment, the area range and radius range of the center of the arc-shaped potential sliding surface are set, and the corresponding potential sliding body is vertically divided into several strips.

[0029] Figure 1 This is an analytical model diagram for calculating the stability of the geotextile reinforced cushion embankment on the soft soil foundation of the present invention.

[0030] like Figure 1 As shown, for the embankment bearing system formed by placing geotextile 300 in the bottom cushion layer 200 of the embankment 100 (referred to as geotextile reinforced cushion embankment-foundation system), according to the symmetry of the embankment 100, one of the two toe points of the embankment 100 is used as the coordinate origin O, and a plane rectangular coordinate system is established with the horizontal inside of the embankment 100 as the positive direction of the x-axis and the vertical upward direction as the positive direction of the y-axis.

[0031] For the geotextile-reinforced cushion embankment-foundation system, outside the shoulder 500 near the coordinate origin O, an area 600 with a width of 2 to 5 times the embankment height h and a height of 1 to 4 times the embankment height h is defined as the location of the potential sliding surface center A (x0 on the horizontal axis and y0 on the vertical axis). The range of the potential sliding surface radius r0, which varies from 1 to 5 times the embankment height h, is used to determine the possible location of the arc-shaped potential sliding surface 400. The range of variation for the potential sliding surface center A and radius r0 is a sufficient and appropriate range provided by the applicant based on computational experience. From the perspective of practical engineering significance, exceeding this range generally does not affect the calculation results of the minimum stability coefficient and the corresponding most dangerous sliding surface.

[0032] For any potential sliding body 900 formed by the potential sliding surface 400, the embankment top surface 700, and the ground outside the embankment slope foot 800, it is vertically divided into n strips of equal width, generally n = 20 to 30, and the n strips are numbered sequentially starting from 1 from the rear side to the front side of the potential sliding body 900.

[0033] Step 20: The design ultimate tensile force of the geotextile at the intersection with the potential sliding surface along the transverse direction of the roadbed is taken in the horizontal direction to determine the anti-slip torque provided by the geotextile.

[0034] Relative to the center A(x0, y0) and radius r0 of any specified potential slip surface in the area, the design ultimate tension of the geotextile along the transverse direction of the roadbed at the intersection with the potential slip surface is taken in the horizontal direction, and the calculation expression of the general anti-slip moment provided by it is:

[0035]

[0036] Where M t is the anti-slip torque provided by the geotextile at the intersection with the potential slip surface; j is the number of each geotextile layer in the cushion layer from top to bottom, and the number increases from top to bottom, j = 1, 2, ..., m, where m is the total number of geotextile layers in the cushion layer; T d is the design ultimate tension of each layer of geotextile; y0 is the ordinate of the center of the potential sliding surface, y tj is the ordinate of the intersection of the jth layer of geotextile and the potential sliding surface, which can be obtained by jointly solving the arc equation of the potential sliding surface and the position equation of each geotextile in the cushion layer.

[0037] Step 30, based on the simplified Bishop method principle and introducing the earthquake force in a pseudo-static manner, establish the stability calculation control equation, search and calculate to determine the most dangerous sliding surface and the corresponding most dangerous sliding body, as well as the length of each layer of geotextile along the transverse direction of the roadbed in the most dangerous sliding body.

[0038] Based on the simplified Bishop method for soil slope stability analysis and the introduction of seismic forces in a classic pseudo-static manner, the stability calculation control equation is established as follows:

[0039]

[0040] Where, F s is the reference stability coefficient; i is the number of the bar in the potential sliding body; W i , α i 、l i 、c i 、 are the deadweight of the strip corresponding to the i-th strip (calculated according to the soil weight), the inclination angle of the bottom surface of the strip, the length of the bottom surface of the strip, the cohesion and internal friction angle of the soil at the bottom of the strip; ξ j is the intermediate variable for calculating the i-th block; q i is the uniformly distributed strip load on the top surface of the i-th strip. For the relevant strip, it is taken as the uniformly distributed strip load q on the top surface of the embankment. For the strip not involved in the embankment top surface load, it is taken as zero. h and k v are the horizontal and vertical earthquake influence coefficients respectively; y ei is the vertical coordinate of the centroid of the i-th bar.

[0041] The center or radius of the potential slip surface is changed by a certain amount within a set range. An iterative calculation method is used to determine the corresponding stability coefficients of different potential slip surfaces. The potential slip surface corresponding to the minimum value is taken as the most dangerous slip surface. The iterative calculation specifically includes the following calculation steps:

[0042] Step I: Specify the center and radius of the initial potential sliding surface within the set range, and calculate the initial reference stability coefficient F according to the stability calculation control equation shown in formula (2): s0 ;

[0043] Step II: Continuously change the center and radius of the circle relative to the center and radius of the current potential sliding surface in a small increment within the set range. The small increment can be ±0.1m. According to formula (2), several corresponding reference stability coefficients F are calculated. sk , where k represents the kth iteration; if it is iterated N times, a total of N F sk ;

[0044] Step III :Get F s0 With all F sk The minimum value F in smin The corresponding potential sliding surface is the most dangerous sliding surface.

[0045] According to the geometric position of the most dangerous sliding surface and the geometric position of each layer of geotextile, the length of each layer of geotextile in the most dangerous sliding body along the transverse direction of the roadbed can be determined.

[0046] Step 40: adopt a non-uniform distribution mode that satisfies boundary conditions and static equilibrium conditions for the surface friction of the geotextile, and determine the lateral tension of the geotextile along the roadbed in the most dangerous sliding body according to the static equilibrium relationship.

[0047] For the friction resistance of the geotextile on one side, according to the general analysis of elastic theory (Xiao Shiguo, Zhao Linzhi. Approximate analytical algorithm for the side friction resistance of suspension bridge tunnel anchorage. Journal of Southwest Jiaotong University, 2018, 53(5): 974-981; Xiao Shiguo, Zhou Depei. A method for determining the length of the anchoring section of non-full-length bonded anchor cables. Chinese Journal of Rock Mechanics and Engineering, 2004, 23(9): 1530-1534.), the general expression of the friction resistance of the j-th layer of geotextile on one side can be constructed to meet the boundary condition that the shear stress at both ends of the geotextile in the most dangerous sliding body is zero:

[0048]

[0049] Where, τ j (x) is the unilateral surface friction of the jth layer of geotextile in the most dangerous sliding body; x is the abscissa of any point on the geotextile along the transverse direction of the roadbed in the most dangerous sliding body; ajis the abscissa of the endpoint of the jth layer of geotextile in the most dangerous sliding mass, which is close to the embankment slope. λ is the curve shape correction coefficient, which is determined based on numerical simulation and test results, and is generally 1.0 to 2.0, and can often be taken as 1.5. aj is the length of the jth layer of geotextile along the transverse direction of the roadbed in the most dangerous sliding body; τ 0j is the basic friction resistance of the jth layer of geotextile in the most dangerous sliding body. The ultimate tensile force T of the geotextile at the most dangerous sliding surface can be designed based on the d Determine, according to the static equilibrium condition, T d The calculation expression is:

[0050]

[0051] Substituting equation (4) into equation (5) can determine the basic friction resistance τ 0j The calculation expression is:

[0052]

[0053] According to the static equilibrium relationship, the tensile force T on any cross section of the j-th layer of geotextile in the most dangerous sliding body is j The calculation expression of (x) is:

[0054]

[0055] Step 50, for the determined most dangerous sliding body, based on the force balance equation of each block, according to the transfer coefficient method, using the soil shear strength parameter reduction method, calculate and determine the corresponding stability coefficient of the most dangerous sliding body. This stability coefficient is the target stability coefficient.

[0056] For the most dangerous sliding body identified, based on the force balance equation of each block, the recursive expression for calculating the stability coefficient can be obtained according to the classical transfer coefficient method:

[0057] E i =E i-1 ×ψ i-1 +Q i -R i / K s (8)

[0058] in:

[0059]

[0060] Q i =(1+k v )W i sinα i +k h W i cosα i -Ti cosα i (10)

[0061]

[0062] Where, E i is the residual thrust transmitted forward by the i-th block in the most dangerous sliding body; ψ i is the transfer coefficient of the i-th block in the most dangerous sliding body, and ψ0=0; Q i 、R i are the sliding force and anti-sliding force of the i-th block in the most dangerous sliding body; K s is the target stability coefficient; T i is the total net tension provided by the geotextile in each strip in the most dangerous sliding body. For the strip involving the geotextile, its value is determined according to formula (12), and for the other strips, its value is taken as zero.

[0063] Therefore, according to formula (8), in order to satisfy the residual thrust transmitted forward by the nth block (the last block) is equal to zero (E n =0) as a condition, the target stability coefficient K can be calculated s .

[0064] The beneficial effects of the present invention are described below through specific examples.

[0065] Figure 2 This is a schematic structural diagram of a geotextile reinforced cushion embankment on a soft soil foundation according to an embodiment of the present invention.

[0066] like Figure 2 As shown, the embankment has a slope of 1:2.0, an embankment height h of 6m, and a top width of 7.5m. A strip load with a distribution width of 3.7m acts on the top of the embankment, and the net distance between the load and the shoulders on both sides is 1.9m. The internal friction angle of the foundation soil is 10°, the cohesion is 12kPa, and the specific gravity is 17.0kN / m 3 The internal friction angle of the embankment fill is 35°, the cohesion is 0kPa, and the density is 20kN / m 3 The thickness of the cushion layer is 60cm, and the total number of layers is 2. Two layers of geotextiles are arranged with a vertical spacing of 30cm. The distance from the upper and lower surfaces of the cushion layer is 15cm respectively. The x of the upper and lower geotextiles is 2. aj The other relevant calculation parameters are summarized in Table 1.

[0067] Table 1

[0068] parameter symbol Value Strip load on top of embankment q 70kPa Design ultimate tensile strength of geotextile <![CDATA[T d ]]> 100kN / m Horizontal seismic influence coefficient <![CDATA[k h ]]> 0.1 Vertical seismic influence coefficient <![CDATA[k v ]]> 0.065 Curve shape correction factor λ 1.5

[0069] Step 10

[0070] by Figure 2 The toe point on the left side of the embankment shown is the coordinate origin O, and a plane rectangular coordinate system is established with the horizontal inner side of the embankment as the positive direction of the x-axis and the vertical upward direction as the positive direction of the y-axis.

[0071] On the outer side of the shoulder, the potential sliding surface center is defined as an area with a width of four times the embankment height h (24m) and a height of three times the embankment height h (18m). The potential sliding surface radius ranges from 1 to 5 times the embankment height h (6 to 30m). The potential sliding mass is vertically divided into 24 equal-width strips, i.e., n = 24.

[0072] Step 20

[0073] According to formula (1), we can get:

[0074]

[0075] Step 30

[0076] According to formula (2) and (3), we can get:

[0077]

[0078] Take the initial potential sliding surface as the center (3m, 10m) and the radius as 12m, and continuously change the center and radius of the current sliding surface in increments of ±0.1m. With the calculation accuracy controlled at 0.01, perform iterative calculations according to steps I to III until the calculation control requirements are met. At this time, the corresponding F smin is 1.149, and the corresponding potential sliding surface is the most dangerous sliding surface. The coordinates of its center A are (5.682m, 8.648m) and the radius is 14.070m. Figure 3 The calculation results of the most dangerous sliding surface and the most dangerous sliding body are shown.

[0079] According to the geometric position of the most dangerous sliding surface and the geometric position of each layer of geotextile, it can be determined that the lengths of the first and second layers of geotextile along the transverse direction of the roadbed in the most dangerous sliding body are 16.24m and 16.62m respectively.

[0080] Step 40

[0081] According to formulas (4) and (6), the frictional resistance of the first and second layers of geotextile on one side from top to bottom is:

[0082]

[0083] According to formula (7), the tensile forces of the first and second layers of geotextiles from top to bottom along the embankment are:

[0084]

[0085] Step 50

[0086] According to formula (12), when i = 1 to 3 and 21 to 24, the strips and blocks do not involve geotextiles, T i =0, T of the remaining bars i Calculate according to the above formula in formula (12).

[0087] Then, according to equations (8) to (11) and condition E n =0, starting from i=1, through recursive calculation, the target stability coefficient K can be obtained s =1.085.

[0088] Results test:

[0089] Calculated according to the traditional simplified Bishop method, when no geotextile is laid in the cushion layer, the target stability coefficient of the foundation-embankment system is 0.989, which is smaller than the target stability coefficient of 1.085 calculated by the method of the present invention when geotextile is laid in the cushion layer. This is consistent with the fact that the stability should be improved when geotextile is laid in the cushion layer, which to a certain extent illustrates the rationality of the method of the present invention.

[0090] On the other hand, the stability coefficient calculated by the FLAC3D numerical simulation method is 1.112, and the absolute value of the relative error between the method of the present invention and it is about 2.4%; the comparison of the most dangerous sliding surface calculation results of the two is shown in Figure 4 ,It can be seen that the most dangerous sliding surfaces of the method of the present invention and the FLAC3D numerical simulation method are generally consistent.

[0091] Therefore, the comparison of these results shows that the method of the present invention is reasonable.

[0092] The above describes the relevant contents of the present invention. Based on this description, a person skilled in the art will be able to implement the present invention. Based on the above contents of the present invention, all other embodiments obtained by a person skilled in the art without making any creative efforts should fall within the scope of protection of the present invention.

Claims

1. Calculation method for embankment stability with geotextile reinforced cushion on soft soil foundation, characterized by: The following steps are involved: Step 10: In the upper area of the embankment, the center area and radius of the arc-shaped potential sliding surface are set, and the corresponding potential sliding body is vertically divided into a plurality of strips; Step 20, taking the design ultimate tensile force of the geotextile in the transverse direction of the roadbed at the intersection with the potential sliding surface as the horizontal direction, and determining the anti-slip torque provided by the geotextile; Step 30: Based on the simplified Bishop method and by introducing earthquake forces in a pseudo-static manner, a stability calculation control equation is established, and the most dangerous sliding surface and the corresponding most dangerous sliding body are determined by search and calculation, as well as the length of each geotextile layer in the most dangerous sliding body along the transverse direction of the roadbed; Step 40, adopting a non-uniform distribution mode that satisfies boundary conditions and static equilibrium conditions for the surface friction of the geotextile, and determining the lateral tension of the geotextile along the roadbed in the most dangerous sliding body from the static equilibrium relationship; Step 50, for the determined most dangerous sliding body, based on the force balance equation of each block, according to the transfer coefficient method, using the soil shear strength parameter reduction method, calculate and determine the corresponding stability coefficient of the most dangerous sliding body. This stability coefficient is the target stability coefficient.

2. The method for calculating the stability of an embankment with a geotextile reinforced cushion on a soft soil foundation according to claim 1, wherein: In step 10: Take one of the two toe points of the embankment as the coordinate origin O, and establish a plane rectangular coordinate system with the horizontal inner side of the embankment as the positive direction of the x-axis and the vertical upward as the positive direction of the y-axis; The rectangular area with a width of 2 to 5 times the embankment height and a height of 1 to 4 times the embankment height is taken as the area where the center of the potential sliding surface is located, and the range of the radius of the potential sliding surface is 1 to 5 times the embankment height. For any potential sliding body formed by the potential sliding surface, the top surface of the embankment, and the ground outside the embankment slope foot, it is vertically divided into n strips of equal width, and the n strips are numbered starting from 1 from the rear side to the front side of the sliding body.

3. The method for calculating the stability of an embankment with a geotextile reinforced cushion on a soft soil foundation according to claim 2, wherein: In step 20, the calculation expression of the anti-slip torque is: Where M t is the anti-slip torque provided by the geotextile at the intersection with the potential slip surface; j is the number of each layer of geotextile in the cushion layer from top to bottom, and the number increases from top to bottom, j = 1, 2, ..., m, m is the total number of geotextile layers in the cushion layer; T d is the design ultimate tension of each layer of geotextile; y0 is the ordinate of the center of the potential sliding surface; y tj is the ordinate of the intersection of the jth layer of geotextile and the potential sliding surface.

4. The method for calculating the stability of an embankment with a geotextile reinforced cushion on a soft soil foundation according to claim 3, wherein: In step 30, the stability calculation control equation is: Where, F s is the reference stability coefficient; i is the number of the bar in the potential sliding body; W i , α i 、l i 、c i 、 are the deadweight of the strip corresponding to the i-th strip, the inclination angle of the bottom surface of the strip, the length of the bottom surface of the strip, the cohesion of the soil at the bottom of the strip, and the internal friction angle; ξ j is the intermediate variable for calculating the i-th block, r0 is the radius of the potential sliding surface; q i is the uniformly distributed strip load on the top surface of the i-th strip; k h and k v are the horizontal and vertical earthquake influence coefficients respectively; y ei is the vertical coordinate of the centroid of the i-th bar.

5. The method for calculating the stability of an embankment with a geotextile reinforced cushion on a soft soil foundation according to claim 4, wherein: In step 30, the center or radius of the potential sliding surface is changed by a certain amount within a set range, and an iterative calculation method is used to calculate and determine the corresponding stability coefficients of different potential sliding surfaces. The potential sliding surface corresponding to the minimum value is taken as the most dangerous sliding surface.

6. The method for calculating the stability of an embankment with a geotextile reinforced cushion on a soft soil foundation according to claim 5, wherein: In step 40, the calculation expression for the tension of the geotextile along the lateral direction of the roadbed in the most dangerous sliding body is: Where, T j (x) is the tension of the jth layer of geotextile in the most dangerous sliding mass on any transverse section of the roadbed; τ j (x) is the unilateral surface friction of the jth layer of geotextile in the most dangerous sliding body; x is the abscissa of any point on the geotextile along the transverse direction of the roadbed in the most dangerous sliding body; aj is the horizontal coordinate of the end point of the j-th layer of geotextile in the most dangerous sliding body close to the embankment slope.

7. The method for calculating the stability of an embankment with a geotextile reinforced cushion on a soft soil foundation according to claim 6, wherein: In step 40, the unilateral surface friction resistance τ of the jth layer of geotextile in the most dangerous sliding body j The calculation expression of (x) is: Where λ is the curve shape correction coefficient; l aj is the length of the jth layer of geotextile along the transverse direction of the roadbed in the most dangerous sliding body; τ 0j is the basic friction resistance of the jth layer of geotextile in the most dangerous sliding body.

8. The method for calculating the stability of an embankment with a geotextile reinforced cushion on a soft soil foundation according to claim 6, wherein: In step 50, the recursive expression for calculating the stability coefficient corresponding to the most dangerous sliding body is: E i =E i-1 ×ψ i-1 +Q i -R i / K s ; in: Q i =(1+k v )W i sinα i +k h W i cosα i -T i cosα i ; Where, E i is the residual thrust transmitted forward by the i-th block in the most dangerous sliding body, and E n =0;ψ i is the transfer coefficient of the i-th block in the most dangerous sliding body, and ψ0=0; Q i 、R i are the sliding force and anti-sliding force of the i-th block in the most dangerous sliding body; K s is the target stability coefficient; T i is the total net tension provided by the geotextile in the i-th strip in the most dangerous sliding body.

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