A method for calculating the stability of a constant shear strength slope

Abstract

The application provides a kind of equal shear strength side slope stability calculation method, comprising: dividing area step, composite foundation fill slope is divided into first area, second area and third area;Transformation model step, in first area, according to each pile body, it is divided into several repeated cross section square unit body, then the cross section of pile body is converted from circle into rectangle section with equivalent area, and the pile body is converted from cylindrical pile into rectangular pile;Re-modeling step, the fill of the second area of side slope is divided into different gravity areas, the equivalent gravity of the second area for modeling is obtained, and the model of the second area above the first area is re-established;Calculate the side slope stability coefficient step, obtain the height of the side slope in the second area, the length of the pile body to determine the third area range, establish the completed two-dimensional limit equilibrium method analysis model, and calculate the side slope stability coefficient in the second area.

Description

Technical Field

[0001] This invention relates to the field of soil and rock shear strength calculation, and in particular to a method for calculating the stability of slopes with equal shear strength. Background Technology

[0002] In slope engineering, the limit equilibrium method is typically used to calculate the stability of composite foundation fill slopes. Commercial software employing the two-dimensional limit equilibrium method (such as Lizheng Geotechnical and GEO5 Geotechnical software) is now available to assist in the calculation. However, when calculating the slope stability of composite foundation fill slopes, the composite shear strength parameters of the piles and soil are often obtained through the replacement rate, simplifying the reinforced piles and foundation soil into a composite material. This approach neglects the fact that the piles and foundation soil bear different loads under the influence of the pile-soil stress ratio, and that the two materials exhibit significant differences, which does not reflect the actual situation. Summary of the Invention

[0003] The purpose of this invention is to provide a method for calculating the stability of slopes with equal shear strength. The method uses the two-dimensional limit equilibrium method to model the composite foundation fill slope and fully considers the different loads borne by the piles and the foundation soil, so that the calculation results are as close as possible to the actual situation.

[0004] To address the aforementioned problems, this invention provides a method for calculating the stability of slopes with equal shear strength, comprising: a region division step, dividing the composite foundation fill slope into a first region, a second region, and a third region, wherein the first region is the pile driving region, the second region is the region formed above the pile driving region, and the third region is the remaining region of the composite foundation fill slope; a model transformation step, dividing the first region into several repeating square cross-section units based on each pile, each unit including one pile and foundation soil, and then transforming the piles in each unit from cylindrical piles to rectangular piles, with the cross-sectional area of ​​the rectangular piles being equal to that of the cylindrical piles; a remodeling step, dividing the slope fill in the second region into regions with different unit weights, obtaining the equivalent unit weight of the second region for modeling, and re-establishing the model of the second region above the first region; and a slope stability coefficient calculation step, obtaining the slope height and pile length in the second region to determine the range of the third region, establishing a complete two-dimensional limit equilibrium analysis model, and calculating the slope stability coefficient.

[0005] Furthermore, the transformation model step in the above-mentioned method for calculating the stability of slopes with equal shear strength also includes: a data measurement step: obtaining the pile diameter d and pile spacing s, as well as the unit weight γ of the pile. p Cohesion c p Internal friction angle φ of the pile p Obtain the unit weight γ of the foundation soil s Cohesion c s φ, the internal friction angle of the foundation soil sIn the transformation model step, the width b0 of the rectangular cross-section of the pile after the transformation is: Where s is the cross-sectional width of the unit cell.

[0006] Furthermore, in the remodeling step of the above-mentioned method for calculating the stability of slopes with equal shear strength, the equivalent unit weight γ′ of the second region corresponding to the rectangular pile in the element is... pi for: Where m is the replacement rate, n is the pile-soil stress ratio, and γ is the unit weight of the fill; in the remodeling step, the equivalent unit weight γ′ of the second region corresponding to the foundation soil in the unit cell is... si for: Where m is the replacement rate, n is the pile-soil stress ratio, and γ is the unit weight of the fill.

[0007] Furthermore, the formula for calculating the pile-soil stress ratio in the above-mentioned method for calculating the stability of slopes with equal shear strength is:

[0008] n = p pi / p si

[0009] Where, p pi p represents the stress shared by the pile. si The stress shared by the foundation soil;

[0010] Furthermore, in the above-mentioned method for calculating the stability of slopes with equal shear strength, the stress p shared by the piles... pi The calculation formula is:

[0011]

[0012] Stress p shared by the foundation soil si The calculation formula is:

[0013]

[0014] Among them, h i This refers to the fill height.

[0015] The present invention provides a method for establishing a slope model with equal shear strength in a two-dimensional limit equilibrium software. The analysis model in the two-dimensional limit equilibrium software is divided into three regions with different properties based on its characteristics. By eliminating the longitudinal shape differences between the pile and the foundation soil to conform to the plane strain assumption, the three-dimensional model of the circular pile composite foundation is transformed into a three-dimensional model of the rectangular pile composite foundation. Its two-dimensional cross-sectional view is then analyzed to establish a composite foundation region model. The fill slope on the composite foundation is considered as a load. Taking into account the influence of the pile-soil stress ratio, the fill slope on the upper part of the composite foundation is divided into regions with different unit weights to simulate the effect of the pile-soil stress ratio. The equivalent unit weight of the fill slope region on the composite foundation used for modeling is calculated, establishing a fill slope region model on the composite foundation. The range of other regions is determined based on the slope height and pile length, and original parameters are assigned to establish a complete two-dimensional limit equilibrium analysis model. This allows the software to automatically search for the most dangerous sliding surface, thereby calculating the slope stability coefficient. This invention, based on the principle of equivalent shear strength substitution and the principle of calculating the equivalent unit weight of slope fill when considering the pile-soil stress ratio, provides a more practical method for establishing an equal shear strength slope model in two-dimensional limit equilibrium software. Attached Figure Description

[0016] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0017] Figure 2 This is a schematic diagram of a three-dimensional model of an equivalent pre-composite foundation fill slope according to an embodiment of the present invention;

[0018] Figure 3 This is a plan view of the composite foundation area according to an embodiment of the present invention;

[0019] Figure 4 This is a schematic diagram of the equivalent front unit cross-section according to an embodiment of the present invention;

[0020] Figure 5 This is a schematic diagram of the equivalent cross-section of the unit body according to an embodiment of the present invention;

[0021] Figure 6 This is a schematic diagram of a three-dimensional model of an equivalent composite foundation fill slope according to an embodiment of the present invention;

[0022] Figure 7 This is an equivalent two-dimensional cross-sectional view of the slope according to an embodiment of the present invention;

[0023] Figure 8 This is a schematic diagram of the equivalent unit weight calculation of the fill slope area on the composite foundation according to an embodiment of the present invention;

[0024] Figure 9 This is another schematic diagram illustrating the equivalent unit weight of the fill slope area on the composite foundation according to an embodiment of the present invention;

[0025] Figure 10 This is a schematic diagram of a complete two-dimensional limit equilibrium method analysis model for composite foundation fill slope according to an embodiment of the present invention;

[0026] Figure 11 This is a schematic diagram of the computing software interface used according to an embodiment of the present invention;

[0027] Figure 12 This is a schematic diagram of another interface of the computing software used according to an embodiment of the present invention;

[0028] Figure 13 This is a schematic diagram of another interface of the computing software used according to an embodiment of the present invention;

[0029] Figure 14 This is a schematic diagram of another interface of the computing software used according to an embodiment of the present invention.

[0030] Figure label:

[0031] 1: First area;

[0032] 11: Pile body;

[0033] 11a: Rectangular pile;

[0034] 12: Unitary body;

[0035] 13 Foundation Soil

[0036] 2: Second area;

[0037] 21: Slope backfilling;

[0038] 22: The area of ​​soil filling on the slope above the pile;

[0039] 23: The area of ​​the fill soil on the upper slope of the foundation soil;

[0040] 3: Third area;

[0041] 4: Original ground surface. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments and the accompanying drawings. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0043] The embodiments of the present invention and their calculation principles will be described below with reference to the accompanying drawings.

[0044] refer to Figure 1The embodiments shown in this invention can be roughly divided into the following steps: dividing the area, transforming the model, remodeling, and calculating the slope stability coefficient.

[0045] refer to Figure 2 After the piling is completed, the area is divided into three zones. The piling area is the composite foundation area, i.e., the first zone. The slope filling area is formed on top of it, i.e., the second zone. The other areas are the third zone.

[0046] Next, the model is transformed. The first region can be divided into several sets of repeating square cross-section units based on each pile. Each set of units includes a pile and foundation soil. Due to the difference in shape between the pile and the foundation soil, the unit does not conform to the plane strain assumption in the longitudinal direction. Therefore, it is necessary to eliminate the shape difference between the pile and the foundation soil in the longitudinal direction to conform to the plane strain assumption.

[0047] Next, refer to Figure 3 The piles arranged in a square pattern in the plane are circular piles with a diameter of d and a spacing of s. The unit weight of the piles is γ, obtained from field tests. p The cohesion is c p The internal friction angle of the pile is The unit weight of the foundation soil is γ s The cohesion is c s The internal friction angle of the foundation soil is Take a single unit cell for analysis, such as Figure 4 As shown, the unit has a length and width of s, a pile diameter of d, and a pile area of ​​A. p A p =πd 2 / 4, in pile area A p Without changing the dimensions, the area of ​​the circle is equivalent to the area of ​​a rectangle with length s and width b0, that is, the cylindrical pile is transformed into a rectangular pile, while the cross-sectional area of ​​the cylindrical pile is equal to the cross-sectional area of ​​the rectangular pile, such as... Figure 5 As shown, the formula for calculating b0 is: The transformed model is as follows Figure 6 As shown.

[0048] refer to Figure 7 After the conversion, only the cross-sectional shape of the pile changes, from circular to rectangular, but the volume of the pile remains unchanged. The original cylindrical pile is transformed into a rectangular pile. Therefore, the unit weight and shear strength parameters of the pile and the foundation soil in the first region remain unchanged and conform to the plane strain assumption. At this point, the relevant parameters of the composite foundation region can be assigned to the model in the two-dimensional limit equilibrium method calculation software, i.e., the unit weight of the pile in the first region is γ. p The cohesion is c p The internal friction angle of the pile is The unit weight of the foundation soil is γ sThe cohesion is c s The internal friction angle of the foundation soil is

[0049] refer to Figure 8 The fill slope in the second region can be regarded as a load. Considering the influence of the pile-soil stress ratio, the fill slope in the upper part of the first region is divided into regions with different unit weights to simulate the effect of the pile-soil stress ratio. The equivalent unit weight of the fill slope region on the composite foundation used for modeling is calculated, and the fill slope region model on the first region is established.

[0050] When a certain load is applied to the first region, due to the influence of the pile-soil stress ratio, the actual load shared by the pile and the foundation soil is not the same. Figure 7 The two-dimensional profile of the composite foundation fill slope shown is used to analyze one unit i and the slope fill above it. The slope fill above unit i is regarded as the load acting on the composite foundation unit i.

[0051] like Figure 8 As shown, the upper slope fill area corresponding to unit i has a fill unit weight of γ, a cohesion of c, and a third internal friction angle of γ. The fill height is h. i Then the soil stress p acting on unit i i for:

[0052] p i =γh i (1)

[0053] Due to the influence of the pile-soil stress ratio, the stress shared by the pile body is p. pi The stress shared by the foundation soil is p. si The substitution rate is m. According to the principle of substitution rate, we know that:

[0054] p i =mp pi +(1-m)p si (2)

[0055] The pile-soil stress ratio is: n = p pi / p si According to formulas (1) and (2), the corresponding stress p shared by the pile can be obtained. pi for:

[0056]

[0057] The corresponding stress p shared by the foundation soil si for:

[0058]

[0059] Therefore, if the original unit weight of the slope fill is used for calculation, the effect of the pile-soil stress ratio cannot be reflected. To make the calculation results more consistent with the actual situation, the unit weight of the slope fill needs to be equivalent, so that the total weight of the fill above the pile and the foundation soil is consistent with the actual load shared by the pile and the foundation soil. In this way, the equivalent unit weight parameter required for the second region on the first region can be calculated.

[0060] Maintain the slope fill height h i Without changing the load, the equivalent unit weight γ′ of the upper slope fill area corresponding to the pile in element i is obtained by performing an equivalent conversion. pi for:

[0061]

[0062] Substituting formula (3) into formula (5) yields:

[0063]

[0064] The equivalent unit weight γ′ of the upper slope fill area corresponding to the foundation soil in unit i si for:

[0065]

[0066] Substituting formula (4) into formula (7) yields:

[0067]

[0068] Based on this method, the equivalent unit weight of the slope fill area above each block is calculated and assigned to the model.

[0069] Next, based on the slope height and pile length, the range of other areas in the third region is determined, and the original parameters are assigned to establish a complete two-dimensional limit equilibrium method analysis model. The two-dimensional limit equilibrium method software (such as Lizheng Rock & Soil) is used to automatically search for the most dangerous sliding surface, thereby calculating the slope stability coefficient.

[0070] refer to Figure 10 For a composite foundation fill slope with a slope height of h and a pile length of l, the complete model can be extended outwards by one slope height from both the top and bottom of the slope, and the thickness of the foundation soil can be taken as twice the pile length below the original ground surface. At this point, a complete composite foundation fill slope model can be created using AutoCAD software.

[0071] refer to Figure 11 In the Lizheng Geotechnical Software, select the slope stability analysis module, import the CAD model of the composite foundation fill slope into the module, set the basic information, and refer to... Figure 12The standard adopted is the "Technical Specification for Building Slope Engineering". For the circular arc stability calculation, the target is automatically searched for the most dangerous slip surface, and the simplified Bishop method recommended in the specification is selected for the circular arc stability analysis. Based on the parameters of each area of ​​the composite foundation fill slope obtained from the above steps, the settings are configured in the software as follows: Figure 13 As shown. The unit weight of the pile in area one is γ. p The cohesion is c p The internal friction angle is The unit weight of the foundation soil is γ s The cohesion is c s The internal friction angle is The equivalent unit weight of the upper slope fill area corresponding to the central pile in Zone 2 is γ′. pi The cohesion is c, and the internal friction angle is... The equivalent unit weight of the upper slope fill area corresponding to the foundation soil in the strip is γ′ si The cohesion is c, and the internal friction angle is... In Region 3, the original foundation soil parameters are used, and the unit weight of the foundation soil is γ. s The cohesion is cs and the internal friction angle is... The original slope fill parameters are used for the slope fill: unit weight γ, cohesion c, and internal friction angle θ.

[0072] After the parameters are set, the sliding safety factor of the composite foundation fill slope can be calculated, such as... Figure 14 As shown.

[0073] The method for calculating the stability of slopes with equal shear strength provided in the Lizheng Geotechnical Software of this invention establishes an analysis model in the Lizheng Geotechnical Software by dividing it into three regions with different properties based on its characteristics. By eliminating the longitudinal shape differences between the pile and the foundation soil to conform to the plane strain assumption, the three-dimensional model of the circular pile composite foundation is transformed into a three-dimensional model of the rectangular pile composite foundation, and its two-dimensional cross-sectional view is analyzed to establish a composite foundation region model. The fill slope on the composite foundation is regarded as a load, and considering the influence of the pile-soil stress ratio, the fill slope on the upper part of the composite foundation is divided into regions with different unit weights to simulate the effect of the pile-soil stress ratio. The equivalent unit weight of the fill slope region on the composite foundation used for modeling is calculated to establish a fill slope region model on the composite foundation. The range of other regions is determined according to the slope height and pile length, and original parameters are assigned to establish a complete two-dimensional limit equilibrium method analysis model, so that the software can automatically search for the most dangerous sliding surface and calculate the slope sliding safety factor. This invention, based on the principle of equivalent shear strength substitution and the principle of calculating the equivalent unit weight of slope fill when considering the pile-soil stress ratio, provides a more practical method for establishing and calculating the stability of slope models with equal shear strength in the Lizheng Geotechnical Software.

[0074] It should be understood that the specific embodiments described above are merely illustrative or explanatory of the principles of the invention and do not constitute a limitation thereof. Therefore, any modifications, equivalent substitutions, improvements, etc., made without departing from the spirit and scope of the invention should be included within the protection scope of the invention. Furthermore, the appended claims are intended to cover all variations and modifications falling within the scope and boundaries of the appended claims, or equivalent forms of such scope and boundaries.

Claims

1. A method of calculating the stability of a slope of equal shear strength, characterized by, Comprise: The step of dividing the area, the composite foundation slope is divided into first area, second area and third area, wherein the first area is the piling area, the second area is the area formed above the piling area, and the third area is the remaining area of the composite foundation slope; The conversion model step, the first area is divided into several repeated square cross-section unit bodies according to each pile body, each unit body includes a pile body and foundation soil, the pile body in each unit body is converted from a cylindrical pile to a rectangular pile, the cross-sectional area of the rectangular pile is equal to that of the cylindrical pile, and the width of the rectangular pile is equal to that of the unit body; The conversion model step also includes: Data measurement step: obtaining the pile diameter of the pile body and the pile spacing , and the unit weight of the pile body , the cohesion , the internal friction angle of the pile body , obtaining the unit weight of the foundation soil , the cohesion , the internal friction angle of the foundation soil ; In the conversion model step, the width of the rectangular cross section of the pile body after the completion of the conversion is: W = 2.5 mm ， wherein, is the cross-sectional width of the unit body; The step of re-modeling, the slope fill of the second area is divided into areas with different specific gravities to obtain the equivalent specific gravity of the second area for modeling, and the model of the second area above the first area is re-established; In the step of remodeling, the second area corresponding to the rectangular pile in the unit body is equivalent to the second area corresponding to the rectangular pile in the unit body is: ， wherein, is the replacement rate, is the pile-soil stress ratio, is the fill density; In the step of remodeling, the second area equivalent weight of the foundation soil in the unit body is: ， wherein, is the replacement rate ， is the pile-soil stress ratio, is the fill density; calculating the slope stability coefficient step, obtaining the height of the slope in the second area, the length of the pile body to determine the range of the third area, establishing the completed two-dimensional limit equilibrium method analysis model, and calculating the slope stability coefficient.

2. The equal shear strength slope stability calculation method according to claim 1, wherein: The pile-soil stress ratio calculation formula is: ， wherein, is the stress shared by the pile, is the stress shared by the ground soil.

3. The equal shear strength slope stability calculation method according to claim 2, wherein: The stress shared by the pile The calculation formula is: ， the stress shared by the subsoil The calculation formula is: ， wherein, H is the height of the fill.

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