Method for calculating normal foundation coefficient of slope foundation under strip foundation

Abstract

The invention discloses a method for calculating the normal foundation coefficient of a slope foundation under a strip-shaped foundation. The method comprises the steps that 100, a failure system of the ultimate bearing capacity of the slope foundation under the strip-shaped foundation is divided into a rigid active area, two transition areas and two rigid passive areas; 200, according to the plastic limit analysis upper limit theorem, the relation of the energy dissipation rate, the gravity power and the power made by the evenly-distributed pressure stress of the bottom face of the strip-shaped foundation of the whole damage system can be obtained, and the evenly-distributed pressure stress of the bottom face of the strip-shaped foundation is obtained; step 300, solving the minimum value of the uniformly distributed pressure stress of the bottom surface of the strip-shaped foundation in the limit state, namely the limit bearing capacity of the slope foundation; step 400, taking the inclination angle of the slope surface as zero, and calculating the ultimate bearing capacity of the horizontal foundation under the same condition; and 500, according to the fact that the ratio of the normal foundation coefficient of the slope foundation to the foundation coefficient of the horizontal foundation is equal to the corresponding ultimate bearing capacity ratio, the normal foundation coefficient of the slope foundation is obtained through solving. The concept is clear and simple, and calculation operation is easy.

Description

Technical Field

[0001] The present invention relates to the technical field of subgrade coefficients, and more particularly to a method for calculating the normal subgrade coefficient of a slope subgrade under a strip foundation. Background Art

[0002] Slope stability and deformation control are one of the key control links often involved in the construction of mountain railways, highways, water conservancy and other projects. For related high-slope projects, a prestressed anchor cable ground beam structure is often used to reinforce the slope. Among them, the ground beam (generally a reinforced concrete beam, which can be regarded as a strip foundation) is placed on the slope surface of the slope, and mutual interaction is generated between the ground beam and the slope body under the action of the anchor cable tension. In the related engineering design analysis, the Winkler elastic foundation beam method is usually used to analyze the stress and deformation of the ground beam. During this process, the subgrade coefficient under the beam body is a key design parameter. In the past, the subgrade coefficient was generally determined based on the plate load test on a horizontal subgrade. However, due to the existence of the slope, the bearing characteristics of the slope subgrade are different from (weaker than) those of the horizontal subgrade under the same conditions. Therefore, its subgrade coefficient (the actually meaningful one is the normal subgrade coefficient along the slope surface) should not be equal to that of the horizontal subgrade, and the subgrade coefficient of the slope subgrade should actually be less than that of the horizontal subgrade. Therefore, the practice of still adopting the subgrade coefficient of the horizontal subgrade for the slope subgrade in the past overestimates the resistance performance of the subgrade and does not conform to the actual situation. Therefore, it is necessary to establish a reasonable method for determining its normal subgrade coefficient according to the specific situation of the slope subgrade to fully reflect the influence of factors such as the slope rate of the slope and the characteristics of the subgrade soil on the subgrade coefficient.

[0003] At present, there is no reported method for calculating and determining the normal subgrade coefficient of a slope subgrade. Generally speaking, for the determination of the normal subgrade coefficient of a slope subgrade, a plate load test method similar to that for determining the subgrade coefficient of a horizontal subgrade can be adopted. However, since it is necessary to set up a load plate, a loading system and a reaction force balance system on the slope surface, the actual operation is difficult. Especially when the slope is relatively large, the difficulty of the test operation is extremely high. Therefore, there are few reported experimental determination methods for the normal subgrade coefficient of a slope subgrade. At the same time, there is no related theoretical calculation method with clear concepts, simplicity and easy calculation and operation. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for calculating the normal subgrade coefficient of a slope subgrade under a strip foundation with clear concepts, simplicity and easy calculation and operation. The technical solution is as follows:

[0005] A method for calculating the normal subgrade coefficient of a slope subgrade under a strip foundation includes the following steps:

[0006] Step 100: Divide the failure system of the ultimate bearing capacity of the sloping foundation under the strip foundation into a rigid active zone, two transition zones, and two rigid passive zones. Among them, the rigid active zone is located in the sloping foundation under the strip foundation, the two transition zones are respectively located on the downhill side and the uphill side of the rigid active zone, and the two rigid passive zones are respectively located outside the two transition zones.

[0007] Step 200: According to the upper bound theorem of plastic limit analysis based on the equality of internal and external power in the system at the ultimate state, the relationship among the energy dissipation rate, the gravity power, and the power done by the uniform compressive stress on the bottom surface of the strip foundation in the entire failure system can be obtained, and then the calculation expression of the uniform compressive stress on the bottom surface of the strip foundation can be obtained.

[0008] Step 300: Solve the minimum value of the uniform compressive stress on the bottom surface of the strip foundation at the ultimate state according to the extreme value solution method, which is the ultimate bearing capacity of the sloping foundation.

[0009] Step 400: Take the slope angle of the slope surface as zero and calculate the ultimate bearing capacity of the horizontal foundation under the same conditions.

[0010] Step 500: According to the ratio of the normal foundation coefficient of the sloping foundation to the foundation coefficient of the horizontal foundation being equal to the ratio of the corresponding ultimate bearing capacities, solve to obtain the normal foundation coefficient of the sloping foundation.

[0011] The calculation method of the normal foundation coefficient of the sloping foundation under the strip foundation of the present invention has the following advantages: First, the present invention takes into account that the plate load test of the horizontal foundation is easy to operate and the corresponding foundation coefficient is easy to determine. Therefore, for the sloping foundation, the present invention determines the foundation coefficient of the sloping foundation through theoretical calculation methods based on the foundation coefficient determined by the test of the horizontal foundation under the same conditions. Second, the present invention is based on the ultimate bearing capacity analysis of the sloping foundation and the horizontal foundation under the same conditions, as well as the positive correlation between the foundation coefficient and the ultimate bearing capacity, and combines the foundation coefficient of the horizontal foundation to calculate and determine the normal foundation coefficient of the sloping foundation, which can fully reflect the slope gradient, the characteristics of the soil body of the sloping foundation, the bottom width of the strip foundation, and the friction characteristics between the bottom surface of the foundation and the sloping foundation. Further, the present invention determines the normal foundation coefficient of the sloping foundation under the strip foundation in a way with clear concepts, simple calculation expressions, and easy actual operation, establishes a theoretical calculation expression that is simplified and reasonable and has easy-to-determine parameters, can greatly improve the design calculation efficiency, overcomes the defects of the traditional test determination method, and does not require the extremely difficult and time-consuming on-site plate load test of the sloping foundation, providing a fast and effective technical means and algorithm basis for the design calculation operation of relevant practical projects, and has important technical significance and engineering application value.

[0012] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments. The 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 understood through the practice of the present invention. Description of the Drawings

[0013] The drawings forming a part of the present invention are used to assist in understanding the present invention. The content provided in the drawings and the related descriptions in the present invention can be used to explain the present invention, but do not constitute an improper limitation to the present invention. In the drawings:

[0014] Figure 1 It is a schematic diagram of the failure mode of the slope foundation ultimate bearing capacity analysis system of the present invention. Specific Embodiments

[0015] The present invention will be clearly and completely described below in conjunction with the accompanying drawings. Those of ordinary skill 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:

[0016] The technical solutions and technical features provided in each part including the following description in the present invention can be combined with each other without conflict.

[0017] In addition, the embodiments of the present invention involved in the following description are usually only a part of the embodiments of the present invention, rather than all the embodiments. Therefore, all other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts should fall within the scope of protection of the present invention.

[0018] Regarding the terms and units in the present invention. The terms "including", "having" and any variations thereof in the specification, claims and relevant parts of the present invention are intended to cover non-exclusive inclusion.

[0019] The specific embodiments of the method for calculating the normal foundation coefficient of the slope foundation under the strip foundation of the present invention include steps 100 - 500, specifically as follows:

[0020] Step 100, divide the failure system of the ultimate bearing capacity in the slope foundation under the strip foundation into a rigid active zone, two transition zones and two rigid passive zones. Among them, the rigid active zone is located in the slope foundation under the strip foundation, the two transition zones are respectively located on the downhill side and the uphill side of the rigid active zone, and the two rigid passive zones are respectively located outside the two transition zones;

[0021] Figure 1 It is a schematic diagram of the failure mode of the slope foundation ultimate bearing capacity analysis system of the present invention. As Figure 1As shown: ABC represents the rigid active zone, BCN represents the uphill-side transition zone, ACF represents the downhill-side transition zone, BNE represents the uphill-side rigid passive zone, and AFQ represents the downhill-side rigid passive zone.

[0022] Step 200: According to the upper bound theorem of plastic limit analysis where the power inside and outside the system is equal at the limit state, the relationship among the energy dissipation rate, gravitational power, and the power done by the uniform compressive stress on the bottom surface of the strip foundation of the entire failure system can be obtained. Furthermore, the calculation expression for the uniform compressive stress on the bottom surface of the strip foundation can be obtained.

[0023] For the entire failure system of the slope foundation, according to the upper bound theorem of plastic limit analysis, when the limit state is reached, the power inside and outside the system is equal, and we can get:

[0024] D all = G all + W q (1)

[0025] In the formula, D is the energy dissipation rate, G is the gravitational power, all represents the entire failure system; W q is the power done by the uniform compressive stress on the bottom surface of the strip foundation.

[0026] D all 、G all 、W q The calculation expressions are respectively:

[0027] D all = D AB + D AC + D BC + D CN + D CF + D FQ + D NE + D BCN + D ACF (2)

[0028] G all = G ABC + G BNE + G AFQ + G BCN + G ACF (3)

[0029] W q = q·b·v (4)

[0030] In the formula, AB represents the contact surface between the strip foundation and the slope surface; AC and BC respectively represent the downhill side boundary surface and the uphill side boundary surface of the rigid active zone; CN and CF respectively represent the logarithmic spiral surfaces of the uphill side transition zone and the downhill side transition zone; FQ and NE respectively represent the bottom surfaces of the downhill side rigid passive zone and the uphill side rigid passive zone; q is the uniform compressive stress on the bottom surface of the strip foundation; b is the width of the bottom surface of the strip foundation; v is the moving speed of the strip foundation pressing against the slope body along the normal direction of the slope surface, which can be taken as the unit speed;

[0031] The calculation expressions of the energy dissipation rates on the surfaces AB, AC, BC, CF, CN, FQ and NE are respectively:

[0032] D AB = q·b·f·v x cosπ (5)

[0033] D AC = c·|AC|·(v y sinα1 - v x cosα1) (6)

[0034] D BC = c·|BC|·(v y sinα2 + v x cosα2) (7)

[0035]

[0036]

[0037]

[0038]

[0039] The calculation expressions of the energy dissipation rates of the transition zones BCN and ACF are respectively:

[0040]

[0041]

[0042] The calculation expressions of the gravitational powers of the rigid active zone ABC, the rigid passive zones BNE and AFQ are respectively:

[0043]

[0044]

[0045]

[0046] The calculation expressions of the gravitational powers of the transition zones BCN and ACF are respectively:

[0047]

[0048]

[0049] Wherein, f is the friction coefficient between the bottom surface of the strip foundation and the foundation soil; v x is the tangential component of the movement velocity of the rigid active zone along the slope surface; v y is the normal component of the movement velocity of the rigid active zone along the slope surface, which can be taken as the unit velocity; c is the cohesion of the slope foundation soil; is the internal friction angle of the slope foundation soil; γ is the unit weight of the slope foundation soil; e is the natural constant; π is the circumference ratio; | | represents the geometric length; α1 is the angle between the downhill side boundary surface of the rigid active zone and the slope surface; α2 is the angle between the uphill side boundary surface of the rigid active zone and the slope surface; θ1 is the apex angle of the downhill side transition zone; θ2 is the apex angle of the uphill side transition zone; V C1 and V C2 are the velocities moving downward and upward at the intersection point C of the downhill side boundary surface and the uphill side boundary surface of the rigid active zone respectively; v N is the velocity at the intersection point N of the downhill side boundary surface and the uphill side boundary surface of the uphill side transition zone; v F is the velocity at the intersection point F of the downhill side boundary surface and the uphill side boundary surface of the downhill side transition zone; β is the slope angle of the slope; η1 is the apex angle variable corresponding to any position in the downhill side transition zone starting from the slope surface; η2 are the apex angle variables corresponding to any position in the uphill side transition zone starting from the slope surface respectively.

[0050] Among them, from the velocity compatibility condition permitted by the movement, the calculation expressions of V C1 , V C2 , v N and v F are respectively as follows:

[0051]

[0052]

[0053]

[0054]

[0055] Meanwhile, from the geometric relationship of the entire failure system, the calculation expressions of the geometric lengths of the velocity discontinuity surfaces AC, BC, NE, FQ and the interfaces BE, AQ, BN, AF are respectively as follows:

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063]

[0064] Thus, by combining equations (1) to (30), the calculation expression for the uniform compressive stress q at the bottom of the strip foundation can be obtained as follows:

[0065]

[0066] Step 300: Solve for the minimum value of the uniform compressive stress q at the bottom of the strip foundation in the limit state according to the extreme value solution method, which is the ultimate bearing capacity qu of the slope foundation uβ ;

[0067] In the limit state, the minimum value of the uniform compressive stress q at the bottom of the strip foundation is the ultimate bearing capacity of the foundation. Among them, both v and v y can be taken as the unit speed. There are 5 independent variables related to the uniform compressive stress q at the bottom of the strip foundation, namely: α1, α2, θ1, θ2, and v x . Thus, according to the extreme value solution method in mathematics, the condition for the uniform compressive stress q at the bottom of the strip foundation to obtain the minimum value is:

[0068]

[0069] Among them, the corresponding constraint conditions are:

[0070]

[0071] Thus, the value of the uniform compressive stress q at the bottom of the strip foundation solved by satisfying equations (31), (32), and (33) is the ultimate bearing capacity qu of the slope foundation uβ .

[0072] Step 400: Take the slope angle β = 0, keep the other parameters unchanged, and the ultimate bearing capacity calculated according to equations (31), (32), and (33) is the ultimate bearing capacity qu of the horizontal foundation under the same conditions u0 .

[0073] Step 500: Solve for the normal subgrade coefficient of the slope subgrade according to the ratio of the normal subgrade coefficient of the slope subgrade to the subgrade coefficient of the horizontal subgrade being equal to the ratio of the corresponding ultimate bearing capacities.

[0074] Since the magnitude of the subgrade coefficient is generally positively correlated with the magnitude of its ultimate bearing capacity, therefore, take the ratio of the normal subgrade coefficient of the slope subgrade to the subgrade coefficient of the horizontal subgrade to be equal to the ratio of the corresponding ultimate bearing capacities, and its expression is:

[0075]

[0076] Furthermore, through mathematical transformation, the calculation expression for the normal subgrade coefficient of the slope subgrade can be obtained as:

[0077]

[0078] In the formula, m β is the ratio of the normal subgrade coefficient of the slope subgrade to the subgrade coefficient of the horizontal subgrade; k β is the normal subgrade coefficient of the slope subgrade; k0 is the subgrade coefficient of the horizontal subgrade; q uβ is the ultimate bearing capacity of the slope subgrade under the strip foundation; q u0 is the ultimate bearing capacity of the horizontal subgrade under the strip foundation.

[0079] The beneficial effects of the present invention will be illustrated below through embodiments.

[0080] Embodiment 1

[0081] A certain slope subgrade is cohesive soil, and the relevant calculation parameters are shown in Table 1.

[0082] Table 1

[0083]

[0084] Take the slope angles β = 0°, 10°, 20°, 30° as the 4 typical cases to be calculated.

[0085] Substitute the relevant parameters into formulas (31), (32), (33), and solve for the ultimate bearing capacity q of the slope subgrade when the slope angles β = 0°, 10°, 20°, 30°. uβ The results are shown in Table 2. At the same time, to verify the rationality of the calculation results of the method of the present invention, the FLAC3D numerical simulation method is used to calculate the ultimate bearing capacity values of the corresponding slope subgrades, which are also listed in Table 2.

[0086] As can be seen from Table 2, when the slope inclination angle β = 0°, 10°, 20°, 30°, the relative errors (the absolute value of the difference between the two divided by the numerical simulation result) between the method of the present invention and the numerical simulation results are 10.7%, 9.8%, 8.1%, 5.0% respectively, all within the acceptable error range in actual engineering, indicating the rationality of the method of the present invention.

[0087] Table 2

[0088]

[0089] According to the calculation results of the method of the present invention in Table 2, the normal foundation coefficient k of the slope foundation with slope inclination angles β = 10°, 20°, 30° can be calculated according to Equation (35). β The calculation results and the ratio m of the foundation coefficient k0 of the horizontal foundation β are shown in Table 3, that is, the normal foundation coefficients k of the slope foundations corresponding to slope inclination angles β = 10°, 20°, 30° β are 38.12 MPa / m, 35.94 MPa / m, and 33.54 MPa / m respectively.

[0090] Table 3

[0091] Slope angle β (°) <![CDATA[Ratio m β > <![CDATA[Normal subgrade coefficient k of sloping foundation β (MPa / m)]]> 10 0.9514 38.12 20 0.8971 35.94 30 0.8371 33.54

[0092] Example 2

[0093] In a field test example of a slope foundation under a strip foundation (Yang Jiahao. Improvement research on the calculation method of the foundation bed coefficient of slope foundation and slope anchor frame. Master's thesis of Fuzhou University, 2024), the width of the foundation bottom surface is 0.5 m, and the foundation soil is gravelly silty clay. The relevant basic parameters are shown in Table 4. According to the plate load tests carried out on the slope foundation and the corresponding horizontal foundation on site, the foundation coefficient of the horizontal foundation is measured as k0 = 53.5 MPa / m, and the normal foundation coefficient k of the slope foundation β is 39.1 MPa / m.

[0094] Table 4

[0095]

[0096] Substituting the relevant parameters into Equations (31), (32), and (33), the ultimate bearing capacities of the horizontal foundation and the slope foundation with slope inclination angles β = 0° and 39° are solved as q u0 = 274.89 kPa and q uβ = 239.44 kPa respectively.

[0097] Calculated according to Equation (35), m β = 0.8710, and the normal foundation coefficient of the slope foundation is k β= 46.6 MPa / m.

[0098] Therefore, the relative error (the absolute value of the difference between the two divided by the field measured value) between the calculated value and the field measured value of the normal subgrade coefficient of the ramp subgrade of the method of the present invention is about 19%, not exceeding 20%, which is an acceptable error range in general practical engineering, further indicating the rationality of the method of the present invention.

[0099] The above has described the relevant content of the present invention. Those of ordinary skill in the art will be able to implement the present invention based on these descriptions. Based on the above content of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of the present invention.

Claims

1. The method for calculating the normal foundation coefficient of the slope foundation under the strip foundation is characterized by: The following steps are involved: Step 100, dividing the failure system of the ultimate bearing capacity of the slope foundation under the strip foundation into a rigid active zone, two transition zones and two rigid passive zones, wherein the rigid active zone is located in the slope foundation under the strip foundation, the two transition zones are respectively located on the downslope side and the upslope side of the rigid active zone, and the two rigid passive zones are respectively located outside the two transition zones; Step 200, according to the upper limit theorem of plastic limit analysis that the power inside and outside the system is equal when the limit state is reached, the relationship between the energy dissipation rate of the entire failure system, the gravity power, and the power produced by the uniformly distributed compressive stress on the bottom surface of the strip foundation can be obtained, and then the calculation expression of the uniformly distributed compressive stress on the bottom surface of the strip foundation can be obtained; Step 300, solving the minimum value of the uniformly distributed compressive stress on the bottom surface of the strip foundation under the limit state according to the extreme value solving method, which is the ultimate bearing capacity of the slope foundation; Step 400, taking the slope angle as zero, and calculating the ultimate bearing capacity of the horizontal foundation under the same conditions; Step 500, according to which the ratio of the normal foundation coefficient of the slope foundation to the foundation coefficient of the horizontal foundation is equal to the ratio of the corresponding ultimate bearing capacities, the normal foundation coefficient of the slope foundation is solved.

2. The method for calculating the normal foundation coefficient of the slope foundation under the strip foundation as claimed in claim 1, characterized in that: In step 200: The relationship between the energy dissipation rate, gravity power, and the power produced by the uniformly distributed compressive stress on the bottom of the strip foundation is expressed as follows: D all =G all +W q ; The calculation expression of the uniformly distributed compressive stress on the bottom surface of the strip foundation is: Where D is the energy dissipation rate, G is the gravity power, all represents the entire failure system, AB represents the contact surface between the strip foundation and the slope; W q is the power produced by the uniformly distributed compressive stress on the bottom of the strip foundation; q is the uniformly distributed compressive stress on the bottom of the strip foundation; b is the width of the bottom of the strip foundation; v is the speed of the strip foundation moving along the normal direction of the slope toward the slope, which can be taken as unit speed; f is the friction coefficient between the bottom of the strip foundation and the foundation soil; v x is the tangential component of the velocity of the rigid active zone along the slope.

3. The method for calculating the normal foundation coefficient of the slope foundation under the strip foundation as claimed in claim 2, characterized in that: The energy dissipation rate of the entire destruction system D all The calculation expression is: D all =D AB +D AC +D BC +D CN +D CF +D FQ +D NE +D BCN +D ACF ; D AB =q·b·f·v x cosπ; D AC =c·|AC|·(v y sinα1-v x cosα1); D BC =c·|BC|·(v y sinα2+v x cosα2); Where AC and BC represent the downslope boundary surface and upslope boundary surface of the rigid active zone, respectively; CN and CF represent the logarithmic spiral surfaces of the upslope transition zone and the downslope transition zone, respectively; FQ and NE represent the bottom surfaces of the downslope rigid passive zone and the upslope rigid passive zone, respectively; BCN represents the upslope transition zone; ACF represents the downslope transition zone; v y is the normal component of the velocity of the rigid active zone along the slope surface, which can be taken as unit velocity; c is the cohesion of the slope foundation soil; is the internal friction angle of the slope foundation soil; γ is the weight of the slope foundation soil; e is a natural constant; π is the circumference of a circle; | | represents the geometric length; α1 is the angle between the downslope boundary surface of the rigid active zone and the slope surface; α2 is the angle between the upslope boundary surface of the rigid active zone and the slope surface; θ1 is the vertex angle of the downslope transition zone; θ2 is the vertex angle of the upslope transition zone; V C1 and V C2 are the velocities of the downhill and uphill sides at the intersection C of the downhill boundary surface and the uphill boundary surface of the rigid active zone, respectively; v N v is the velocity at the intersection point N of the downhill side boundary surface and the uphill side boundary surface of the uphill side transition zone; F It is the velocity at the intersection F of the downhill side boundary surface and the uphill side boundary surface of the downhill side transition zone.

4. The method for calculating the normal foundation coefficient of the slope foundation under the strip foundation as claimed in claim 3, characterized in that: The gravitational power of the entire destruction system G all The calculation expression is: G all =G ABC +G BNE +G AFQ +G BCN +G ACF ; Where ABC represents the rigid active area; BNE represents the rigid passive area on the uphill side; AFQ represents the rigid passive area on the downhill side; β is the slope inclination angle of the slope; η1 is the vertex angle variable corresponding to any position in the downhill transition zone from the slope surface; η2 is the vertex angle variable corresponding to any position in the uphill transition zone from the slope surface.

5. The method for calculating the normal foundation coefficient of the slope foundation under the strip foundation as claimed in claim 4, characterized in that: The calculation expression of the geometric length of each boundary surface is:

6. The method for calculating the normal foundation coefficient of the slope foundation under the strip foundation as claimed in claim 2, characterized in that: The power W produced by the uniformly distributed compressive stress on the bottom of the strip foundation q The calculation expression is: W q =q·b·v Where q is the uniformly distributed compressive stress on the bottom of the strip foundation; b is the width of the bottom of the strip foundation; and v is the velocity of the strip foundation moving toward the slope along the normal direction of the slope.

7. The method for calculating the normal foundation coefficient of the slope foundation under the strip foundation as claimed in claim 2, characterized in that: In step 300, the expression for obtaining the minimum value of the uniformly distributed compressive stress on the bottom surface of the strip foundation according to the mathematical extreme value solution method is: Where α1 is the angle between the downslope boundary surface of the rigid active zone and the slope surface; α2 is the angle between the upslope boundary surface of the rigid active zone and the slope surface; θ1 is the vertex angle of the downslope transition zone; θ2 is the vertex angle of the upslope transition zone.

8. The method for calculating the normal foundation coefficient of the slope foundation under the strip foundation as claimed in claim 7, characterized in that: The constraints in step 300 are: Where: is the internal friction angle of the slope foundation soil; v y is the normal component of the velocity of the rigid active zone along the slope; π is the pi.

9. The method for calculating the normal foundation coefficient of a slope foundation under a strip foundation as claimed in claim 1, characterized in that: In step 500, the calculation expression of the normal foundation coefficient of the slope foundation is: In the formula, k β is the normal foundation coefficient of the slope foundation; k0 is the foundation coefficient of the horizontal foundation; q uβ is the ultimate bearing capacity of the slope foundation under the strip foundation; q u0 is the ultimate bearing capacity of the horizontal foundation under the strip foundation.

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