High and steep slope roadbed reinforcement and gravity retaining wall combined supporting structure and design method

Abstract

The invention discloses a high and steep slope roadbed reinforcement and gravity type retaining wall combined supporting structure and a design method, the supporting structure comprises an embankment supporting structure and a drainage system, the embankment supporting structure comprises a gravity type retaining wall, the gravity type retaining wall is arranged on a moderately weathered slate of a slope toe, a reinforcement area is arranged above the gravity type retaining wall, and the drainage system is arranged on the gravity type retaining wall. The reinforcement area comprises a non-modified reinforcement area and a modified reinforcement area from inside to outside, and reinforcement materials are laid in the reinforcement area in a layered mode. A reinforced modified soil cushion layer is horizontally laid between the bottom of the reinforced area and the top of the gravity type retaining wall, and rib materials are laid in the reinforced modified soil cushion layer in a full-section mode. Identifying a damage mode of overall instability; and the rib material length and the retaining wall height are optimized according to different failure modes. Based on the cooperative supporting effect between the modified reinforcement and the gravity type retaining wall, the overall stability of the combined structure is improved, the length of the reinforcement and the height of the retaining wall are optimized, the construction cost is reduced, and the dual purposes of cost saving and engineering performance optimization are achieved.

Description

Technical Field

[0001] This invention belongs to the field of computer-aided roadbed design technology, and relates to a combined support structure and design method for steep slope roadbed reinforcement and gravity retaining wall. Background Technology

[0002] With the deepening of my country's national strategy to build a strong transportation network and the full implementation of the "National Comprehensive Three-Dimensional Transportation Network Planning Outline," the highway network is continuously extending into mountainous and hilly areas, forming a large number of steep embankment sections. Existing reinforcement technologies for treating steep embankment slopes face the dual challenges of stability and economy. The main reasons are: ① Traditional embankment filling and support techniques reinforce the embankment as a whole, failing to rationally utilize its stress characteristics, resulting in seriously unreasonable reinforcement lengths in the reinforced areas, leading to resource waste and increased project costs; ② Under steep embankment conditions, traditional gravity retaining walls rely excessively on their own weight to resist earth pressure, and the increase in wall height leads to a significant increase in material consumption and a decrease in economy; ③ Due to their large filling height and steep slope, steep embankments often face engineering challenges such as high earth pressure, and high risks of slippage and overturning. Therefore, it is necessary to develop a new type of support structure for steep sloping roadbeds that balances safety and economy.

[0003] The invention patent with publication number CN110258220A discloses a method for ecologically filling road embankments with high-strength steel wire mesh reinforcement. This invention patent strengthens the embankment as a whole by using high-strength steel wire mesh, which can improve the overall shear strength of the embankment slope. However, the embankment below the road is only subjected to the pressure of the upper load. Strengthening this part of the embankment will result in material waste and increase the project cost.

[0004] The invention patent with publication number CN118774169A discloses a gravity retaining wall for high embankment in complex and steep terrain and a construction method thereof. The invention patent adopts an integrated structure of pile foundation and cap, which solves the stability problem of gravity retaining wall foundation in complex and steep sections and improves its bearing capacity. However, it only considers the bearing capacity requirements of gravity retaining walls with a height of 5m-6m or less in steep slope embankment support, and does not fully consider the stability requirements.

[0005] In summary, existing methods for reinforcing steep and high slope roadbeds have the following problems:

[0006] (1) Existing methods for reinforcing high and steep embankments usually adopt an overall reinforcement strategy, without differentiated design based on the stress characteristics of different areas of the embankment, resulting in material waste and increased costs. The length of the reinforcement material is not optimized in conjunction with the local stability calculation results, resulting in redundancy or insufficiency.

[0007] (2) Under the condition of high and steep embankment, traditional gravity retaining walls rely too much on their own weight to resist earth pressure. The continuous increase in wall height leads to a significant increase in material consumption and a decrease in economic efficiency.

[0008] (3) Due to the large filling height and steep slope, high and steep embankments often face engineering problems such as high soil pressure, high risk of sliding and overturning. Summary of the Invention

[0009] To address the aforementioned issues, this invention provides a combined support structure of reinforced and gravity retaining walls for steep slope subgrades, comprising a gravity retaining wall, a reinforced zone, and a reinforced modified soil cushion layer. Based on the synergistic support effect between the modified reinforcement and the gravity retaining wall, the overall stability of the combined structure is improved, the project cost is reduced, and the dual goals of cost savings and optimized engineering performance are achieved.

[0010] Another objective of this invention is to provide a design method for a combined support structure of reinforced subgrade and gravity retaining wall on steep slopes, which optimizes the length of the reinforcing bars and the height of the retaining wall.

[0011] The technical solution adopted in this invention is a combined support structure of reinforced roadbed and gravity retaining wall for steep slopes, including an embankment support structure and a drainage system. The embankment support structure includes a gravity retaining wall, which is set on moderately weathered slate at the toe of the slope. A reinforcement zone is provided above the gravity retaining wall. The reinforcement zone includes a non-modified reinforcement zone and a modified reinforcement zone from the inside to the outside. Reinforcing materials are laid in layers in the reinforcement zone.

[0012] A reinforced modified soil cushion layer is laid horizontally between the bottom of the reinforced zone and the top of the gravity retaining wall, and the reinforced modified soil cushion layer is filled with reinforcement in a full-section manner.

[0013] Furthermore, a platform is provided at the top of the modified and reinforced area, and a backfill layer is laid on the outer side of the moderately weathered slate above the reinforced area; a stepped structure is provided at the moderately weathered slate behind the gravity retaining wall, and a backfill layer is laid in the area between the gravity retaining wall, the stepped structure of the moderately weathered slate, and the reinforced and modified soil cushion layer.

[0014] Furthermore, the unmodified reinforced area is filled with plain soil in layers; the modified reinforced area is filled with modified soil in layers. The modified soil in the reinforced modified soil cushion layer has the same composition as the modified soil in the modified reinforced area, which is a mixture of cement and plain soil in a mass ratio of 2:25 to 1:10.

[0015] Furthermore, the drainage system includes longitudinal drainage ditches on the embankment slope, a continuous drainage layer, and drainage holes in front of the wall. The longitudinal drainage ditches are located on the surface of the embankment slope on the other side, and are set at fixed intervals along the longitudinal direction of the embankment slope, extending from the top of the slope to the bottom of the slope.

[0016] The continuous drainage layer is located between the backfill layer and the gravity retaining wall, and is constructed using permeable materials.

[0017] The drainage hole in front of the wall is a row of PVC pipes with a diameter of 50~100mm, which are set at a fixed distance above the embankment base. The outer end is inclined downward and the inner end is embedded with a continuous drainage layer. The pipe body is wrapped with reverse filter geotextile.

[0018] A design method for a combined support structure of reinforced subgrade and gravity retaining wall on steep slopes includes the following steps:

[0019] S1 identifies the failure modes of overall instability;

[0020] S2, for Mode 1: the sliding surface shears the unmodified and modified reinforced areas, and the reinforcement is pulled out of the slope; the most dangerous sliding surface is searched using Slide software, and the soil above the most dangerous sliding surface and located inside the reinforced area is divided into multiple vertical soil strips. The unbalanced thrust method is used to calculate the unbalanced thrust transmitted by the soil strips close to the reinforced area, thereby determining the length of reinforcement inside the reinforced area required to resist the unbalanced thrust.

[0021] S3, for Mode 2: Soil slides out from the top of the gravity retaining wall; calculate the remaining sliding force under different combinations of reinforced modified soil cushion thickness and gravity retaining wall height, and then determine the optimal combination of reinforced modified soil cushion thickness and gravity retaining wall height.

[0022] S4, for Mode 3: Overturning or sliding of gravity retaining wall; considering the earth pressure behind the wall, the weight of the soil wedge, and the tensile force of the reinforcement material on the gravity retaining wall transmitted through the reinforced modified soil cushion layer, establish static equilibrium equations in the X and Y directions, and verify the anti-sliding and anti-overturning stability of the gravity retaining wall.

[0023] Furthermore, in S2, the method for calculating the length of the reinforcing bar is as follows:

[0024] S21, the intersection point Q of the most dangerous sliding surface and the reinforced zone is cut vertically. The outer side of the cutting line is the soil strip block of the reinforced zone, and the inner side of the cutting line is cut vertically with equal width to obtain multiple soil strip blocks.

[0025] S22, the anti-sliding force of the reinforced soil strip. Calculate using the following formula:

[0026]

[0027] In the formula, The area of ​​the soil strip in the reinforced zone; The unit weight of the soil in the reinforced area; The angle between the lower part of the reinforced soil strip and the horizontal direction; The internal friction angle of the soil strip in the reinforced zone; The cohesion of the sliding surface of the soil strip in the reinforced zone; The length of the soil strip in the reinforced zone;

[0028] The pull-out resistance of the reinforcing bars in the reinforced zone is calculated based on the pull-out resistance generated by the upper and lower surfaces of the reinforcing bars using the following formula:

[0029]

[0030] In the formula, This refers to the pull-out resistance of the reinforcing steel. This refers to the vertical earth pressure above the reinforcing steel. Width of the reinforcing bar; This refers to the length of the reinforcing bar. The coefficient of friction;

[0031] To balance the landslide thrust transmitted from adjacent reinforced soil blocks to the reinforced soil blocks, the required anti-sliding force of the reinforced soil blocks is... Calculate using the following formula:

[0032]

[0033] In the formula, The safety factor for sliding down the most dangerous sliding surface; The landslide thrust transmitted from adjacent reinforced soil blocks to the reinforced soil blocks is calculated using the unbalanced thrust method.

[0034] The length of the reinforcing bar is obtained by simultaneous calculation. .

[0035] Furthermore, the calculation of the landslide thrust transmitted from the adjacent reinforced soil block to the reinforced soil block using the unbalanced thrust method specifically involves:

[0036]

[0037] In the formula, Indicates the first The first block of earth is sent to the second... The thrust of the first soil strip is parallel to the first... The bottom surface of each soil block; The landslide safety factor; For the first The weight of a single soil block; Indicates the first The angle between the lower part of the soil strip and the horizontal direction; Indicates the first The length of each soil strip; Indicates the first The internal friction angle of a soil block; Indicates the first Cohesion of the sliding surface of the soil strip; Indicates the first The first block of earth is sent to the second... The thrust of each soil block; Indicates the thrust from the first The first block of earth is sent to the second... The transfer coefficient of each soil block;

[0038] Transmission coefficient Calculated using the following formula:

[0039]

[0040] In the formula, Indicates the first -1 Angle between the lower part of the soil strip and the horizontal direction.

[0041] Furthermore, in S3, the method for calculating the residual sliding force of the reinforced modified soil cushion layer and gravity retaining wall composite structure is as follows:

[0042] S31, the pull-out resistance of the reinforcing material. and tensile strength The smaller value represents the anti-slip force generated by the reinforcing material. ;

[0043] S32, when the most dangerous sliding surface passes through the reinforced modified soil cushion layer, considering the contribution of the reinforcement layer, the resulting anti-sliding force is calculated using the following formula:

[0044]

[0045] This represents the resistive force of the i-th soil block; For the first The self-weight of each soil block; Indicates the first The angle between the lower part of the soil strip and the horizontal direction; Indicates the first The internal friction angle of a soil block; Indicates the first Cohesion of the sliding surface of the soil strip; Indicates the first The length of each soil strip;

[0046] S33, the remaining sliding force on the reverse slope section is calculated using the following formula:

[0047]

[0048] Indicates the first The first block of earth is sent to the second... The thrust of a single soil block, Indicates the first The first block of earth is sent to the second... The thrust of each soil block Indicates the thrust from the first The first block of earth is sent to the second... The transfer coefficient of a soil strip, For the first The downward force of each soil block.

[0049] Furthermore, the method for determining the reverse slope section is as follows:

[0050] Starting from the vertex N of the gravity retaining wall edge, draw an initial ray that forms a fixed angle downwards with the horizontal direction. The initial ray intersects the arc of the most dangerous sliding surface at point N. The reverse extension lines intersect the lower surface of the reinforced modified soil cushion layer at points. It intersects the slope surface at point ;

[0051] Using N as the base point, the initial ray is rotated clockwise at fixed angles to generate a series of new rays, which intersect the arc of the most dangerous sliding surface at points a, b, c, d, and e, respectively. The extended rays in the opposite direction intersect the reinforced modified soil cushion at point [missing information]. , , , and The slope surface intersects at point , , , and ;

[0052] Connect the intersection points of the most dangerous sliding surface and the slope surface to form a line segment. , , , and That is, the reverse slope section.

[0053] Furthermore, the pull-out force of the reinforcing bar is calculated. When the length of the reinforcing bar is the length of the reinforcing bar anchorage section after the most dangerous sliding surface passes through the reinforcing bar.

[0054] The beneficial effects of this invention are:

[0055] (1) Based on the stress magnitude and failure mode of different locations inside the embankment, the present invention adopts different structures and materials for targeted design, dividing the embankment structure into three areas: the reinforced area resists the sliding force, the cushion layer transmits and diffuses stress, and the gravity retaining wall provides rigid support, providing anti-slip and anti-overturning capabilities. Based on the synergistic support effect between the modified reinforcement and the gravity retaining wall, the overall stability of the combined structure is improved.

[0056] (2) This invention uses the unbalanced thrust method to calculate stability, optimizes the length of the reinforcing material, and solves the problems of material waste and local instability in the existing reinforcement of high and steep embankments.

[0057] (3) This invention utilizes the relationship between the height of the reinforced modified soil cushion layer and the height of the retaining wall to determine the optimal height of the gravity retaining wall that matches the fixed thickness of the reinforced modified soil cushion layer by suppressing the possibility of soil sliding out from the top of the gravity retaining wall, thus ensuring the overall stability of the structure. Compared with traditional methods, this invention reduces the height of the gravity retaining wall and effectively solves the problem of excessively large cross-sectional dimensions and material waste in traditional gravity retaining walls in high and steep embankment scenarios. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0059] Figure 1 This is a zoning diagram of a high-fill embankment according to an embodiment of the present invention.

[0060] Figure 2 This is a cross-sectional view of a high-fill embankment according to an embodiment of the present invention.

[0061] Figure 3 This is a diagram showing the arrangement of reinforcing bars in the reinforced area according to an embodiment of the present invention.

[0062] Figure 4 This is a simplified diagram of the calculation of the residual sliding force in the calculation model of this invention embodiment.

[0063] Figure 5 This is a simplified diagram of the calculation of the remaining sliding force in the reverse slope section in the calculation model of the embodiment of the present invention.

[0064] Figure 6 This is a simplified diagram illustrating the trial calculation of wall height in the calculation model of this invention embodiment.

[0065] Figure 7 This is a simplified diagram of the forces acting on the soil wedge in the calculation model of this invention embodiment.

[0066] Figure 8 This is a simplified diagram of the stress on the retaining wall section in the calculation model of this invention embodiment.

[0067] In the diagram, 1. Fill layer; 2. Moderately weathered slate; 3. Unmodified reinforced area; 4. Modified reinforced area; 5. Reinforced modified soil cushion layer; 6. Gravity retaining wall; 7. Most dangerous sliding surface. Detailed Implementation

[0068] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0069] Example 1,

[0070] A combined support structure of reinforced embankment and gravity retaining wall for steep slopes includes an embankment support structure and a drainage system; such as Figure 1 As shown, the embankment, from top to bottom, consists of a gentle slope section (1:20, 1.2m high), a steep slope section (1:1.5, 8m high), a 2m wide platform, a reinforced area (1:1, 9.5m high), and a gravity retaining wall 6. In this embodiment of the invention, the total height of the high and steep embankment reaches 31 meters, with an angle of 30° from the bottom of the slope to the edge of the road, making it higher and steeper than typical steep slope embankments.

[0071] The embankment support structure includes a reinforced zone, a reinforced modified soil cushion layer 5, and a gravity retaining wall 6 made of rubble concrete. The gravity retaining wall 6 is located on the moderately weathered slate 2 at the toe of the slope. A reinforced zone is located above the gravity retaining wall 6, which is divided into a non-modified reinforced zone 3 and a modified reinforced zone 4. The outer side of the reinforced embankment is the modified reinforced zone 4, and the inner side is the non-modified reinforced zone 3. The reinforced embankment is constructed using layered filling, with each layer compacted and leveled. Subsequently, a layer of reinforcing material (geogrid) is laid on the top surface of each layer of fill, and U-shaped nails are used to anchor it to the lower layer of fill along its length and edges. The non-modified reinforced zone 3 is constructed using layered plain soil. The plain soil is silty clay with the following parameters: unit weight 18 kN / m³, internal friction angle 8°, and cohesion 12 kPa. Modified reinforcement zone 4 is constructed using layered modified soil. The modified soil is a mixture of cement and plain soil at a mass ratio of 2:25 to 1:10. In this example, the parameters of the modified soil are: unit weight of 20 kN / m³, internal friction angle of 24°, and cohesion of 40 kPa. Modified reinforcement zone 4 is used to protect the surface layer of the embankment. Its internal friction angle is greater than that of the inner soil, reducing landslides and controlling the length of the reinforcement material in the reinforcement zone.

[0072] A reinforced modified soil cushion layer 5 is horizontally laid between the bottom of the reinforced zone and the top of the gravity retaining wall 6. The reinforced modified soil cushion layer 5 is a layered structure horizontally positioned between the reinforced zone and the gravity retaining wall 6. The vertical spacing of the reinforcement (geogrid) within the reinforced modified soil cushion layer 5 is 0.5m. The reinforced modified soil cushion layer 5 is used to control the height of the gravity retaining wall 6. This cushion layer is composed of modified soil and reinforcement. The reinforcement is laid in a full-section manner, meaning the length of the reinforcement is consistent with the length of the cushion layer (reinforced modified soil cushion layer 5), ensuring uniform distribution of reinforcement. The thickness of the cushion layer is determined based on calculations. The reinforcement within the reinforced modified soil cushion layer 5 is anchored within the gravity retaining wall 6. The gravity retaining wall 6, the reinforced zone, and the reinforced modified soil cushion layer 5 form an integrated support structure, enhancing the support structure's resistance to sliding and overturning.

[0073] The top of the modified and reinforced zone 4 is provided with a 2m wide platform. The outer side of the moderately weathered slate 2 in the gentle and steep sections above the reinforced zone is covered with a soil fill layer 1. The area between the gravity retaining wall 6, the moderately weathered slate 2 and the reinforced and modified soil cushion layer 5 is the soil fill layer 1. The connection between the soil fill layer 1 and the moderately weathered slate 2 is provided with a stepped structure.

[0074] The drainage system consists of longitudinal drainage ditches on the embankment slope, a continuous drainage layer, and drainage holes in front of the wall. One side of the embankment has a support structure (free face), and the other side of the roadbed has longitudinal drainage ditches on the slope surface. These longitudinal drainage ditches are installed every 4 meters along the longitudinal direction of the embankment slope, extending from the top to the bottom of the slope. The longitudinal drainage ditches on the embankment slope are 10 meters wide and 0.2 to 0.4 meters deep.

[0075] The continuous drainage layer is located at the backfill layer 1 behind the wall. It is filled with permeable material (sand, gravel or crushed stone) to form a continuous drainage layer with a thickness of 0.4m to drain the water in the backfill material. The top and bottom of the drainage layer are sealed with 0.4m thick mortar (or other impermeable material) to prevent water from seeping down.

[0076] The drainage holes in front of the wall use PVC pipes with a diameter of 50~100mm. A row of holes is set at a height of 30cm above the embankment base, with a hole spacing of 2m~3m. The outer end is slightly inclined downward with a slope of 5%, and the inner end is embedded with a continuous drainage layer. The pipe body is wrapped with reverse filter geotextile to prevent clogging.

[0077] Example 2,

[0078] The design method of the combined support structure of reinforced roadbed and gravity retaining wall on steep slope described in Example 1 proposes three failure modes based on this embankment structure, namely the three failure modes of overall instability of the embankment slope, and provides a detailed analysis and calculation for each failure mode.

[0079] The first failure mode for the overall instability of the embankment slope is as follows: the soil within a certain range below the embankment slope shears through the fill and modified soil along the sliding surface, while the reinforcement is pulled out of the slope. The second failure mode is as follows: the soil within a certain range below the embankment slope slides out from the top of the retaining wall along the sliding surface. The third failure mode is as follows: the gravity retaining wall overturns or slides. Based on the first failure mode, the length of the reinforcement in the reinforced zone of the structure can be optimized. Based on the second failure mode, the relationship between the thickness of the cushion layer and the height of the retaining wall can be obtained, and the optimal height of the retaining wall can be designed. Based on the third failure mode, the overall stability of the composite structure can be ensured.

[0080] We will analyze and calculate a high and steep embankment example, with the following specific parameters:

[0081] S1: Semi-rigid composite support structure for high and steep embankments, with a total height of 22.25m (from the bottom of gravity retaining wall 6 to the top of the reinforced area).

[0082] S2: The height of each layer of fill and modified soil in the reinforced zone is 0.5m, and the width of the modified soil is 2m (i.e. the width of the modified reinforced zone 4).

[0083] S3: The reinforcing bars located between the soil layers in the reinforced zone are named sequentially from top to bottom as: Reinforcing Bar 1, Reinforcing Bar 2, ..., Reinforcing Bar 18, such as... Figure 2 As shown.

[0084] S4: Based on the most dangerous sliding surface 7, determine the fracture surface of the reinforced zone, optimize the length of the reinforcement material using the target pull-out stability coefficient, and ensure that the reinforced zone has sufficient pull-out capacity. The total width of the reinforced zone is determined by the total length of the reinforcement material (i.e., the width of the reinforced zone of each layer is equal to the length of the reinforcement material of that layer).

[0085] S5: Based on the failure mode of soil sliding out from the top of gravity retaining wall 6, the structural stability of different combinations of reinforced modified soil cushion layer 5 thickness and gravity retaining wall 6 height is systematically verified. Combining the target stability coefficient and structural optimization target, the optimal match between cushion layer thickness and retaining wall height is achieved.

[0086] S6: Based on the overturning or sliding failure mode of the gravity retaining wall 6, the overall stability of the semi-rigid composite support structure of the high and steep embankment is verified.

[0087] Calculation example:

[0088] like Figure 1 As shown, the reinforced embankment is 9.5 meters high with a slope of 45°. The embankment is divided into a non-reinforced zone 3 and a modified reinforced zone 4. The modified reinforced zone 4 is located 2 meters from the embankment slope surface to the interior of the embankment; the remaining area is the non-reinforced zone 3. The unit weight of the fill in the non-reinforced zone 3 is... internal friction angle Cohesion The density of modified soil in the modified reinforced zone 4 internal friction angle The cohesion is The safety factor for the embankment slope is 1.35.

[0089] like Figure 2 As shown, the embankment reinforcement area is constructed using layered filling. The non-modified reinforcement area 3 and the modified reinforcement area 4 are filled in layers from bottom to top with a layer height of 0.5m, for a total of 19 layers, and each layer is compacted and leveled. Subsequently, a layer of reinforcement is laid on the top surface of each layer of fill, and U-shaped nails are used to anchor it to the lower layer of fill along its length and edges.

[0090] For the first failure mode of this embankment slope instability, the most dangerous sliding surface 7 of the embankment was first automatically searched using slide software, that is, the most dangerous sliding surface 7 that slides horizontally out from each layer of modified soil was determined. For example... Figure 3 As shown, the most dangerous sliding surface 7 is cut into 10 soil strips from top to bottom, of which the first 9 soil strips ( The 10th soil strip (the reinforced zone soil strip) is obtained by vertically cutting the most dangerous sliding surface 7 with equal width. The 10th soil strip is obtained by vertically cutting the boundary Q between the most dangerous sliding surface 7 and the reinforced zone. Each soil strip is simplified as follows: Figure 4 As shown, the thrust is calculated using the unbalanced thrust method, and the derived formula is obtained:

[0091] (1)

[0092] In equation (1), Indicates the first The first block of earth is sent to the second... The thrust of the first soil strip is parallel to the first... The bottom surface of each soil block; For the landslide safety factor, take ; For the first The weight of a single soil block; Indicates the first The angle between the lower part of the soil strip and the horizontal direction; Indicates the first The length of each soil strip; , Each soil layer represents the first soil layer. Cohesion and internal friction angle of the side surface (sliding surface) of the soil strip; Indicates the first The first block of earth is sent to the second... The thrust of the first soil strip is parallel to the first... The bottom surface of each soil block; Indicates the thrust from the first The first block of earth is sent to the second... The transfer coefficient of each soil block.

[0093] Transmission coefficient Calculated using equation (2):

[0094] (2)

[0095] Indicates the first -1 Angle between the lower part of the soil strip and the horizontal direction.

[0096] The calculation steps are consistent for each layer. Taking layer 19 as an example, the calculation process is shown. The landslide thrust of soil blocks 1 to 9, which are the most dangerous sliding surfaces of the reinforced soil from layer 19 (the bottom layer), is calculated. See Table 1.

[0097] Table 1. Landslide thrust of soil blocks 1-9 on the most dangerous sliding surface when the reinforced soil from the 19th layer slides out of the slope.

[0098]

[0099] Table 1 For the first The sliding force of each soil block This is the positive pressure; the slider number in Table 1 is the soil strip number.

[0100] For the first failure mode of slope instability, the anti-sliding force provided by the No. 10 soil block is utilized. and the pull-out strength of the reinforcing bars This is to balance the unbalanced thrust transmitted by the 9th soil block.

[0101] The anti-sliding force of soil block No. 10 Calculate according to formula (3):

[0102] (3)

[0103] In equation (3), This represents the area of ​​the 10th soil strip. The weight of soil; The angle between the lower part of the 10th soil block and the horizontal direction; The internal friction angle of the 10th soil strip; The cohesion of the sliding surface of the 10th soil block; This is the length of the 10th soil strip.

[0104] The pull-out resistance of the reinforcing bar should be calculated based on the pull-out resistance generated on both the top and bottom surfaces of the reinforcing bar using the following formula:

[0105] (4)

[0106] In equation (4): as reinforcement Pull-out resistance; as reinforcement Vertical earth pressure above, ; The weight of soil; From the top surface of the embankment to the reinforcement Height; For the width of the reinforcing bar, this is set. ; The total length of the reinforcing material in the soil; The coefficient of friction, In formula (4), the reinforcing material The first one in the above formula (1) In each soil block, 'i' indicates that the objects are different.

[0107] In order to balance the landslide thrust transmitted from soil block No. 9 to soil block No. 10 The required anti-sliding force for soil block No. 10 Calculate using the following formula:

[0108] (5)

[0109] In equation (5), The safety factor for the soil sliding along the circular arc sliding surface (the most dangerous sliding surface 7) is 1.35 here; The thrust transferred from the 9th soil block to the 10th soil block (2147.177 kN).

[0110] By combining the sliding resistance of soil block No. 10 (including the sliding resistance of the reinforced fill and modified soil) with the pull-out resistance of the reinforcement, the unbalanced thrust transmitted from soil block No. 9 is balanced, and the length of the reinforcement is then calculated by inversion. Specifically, by combining (3), (4), and (5), we obtain the length. The calculation formula is as follows:

[0111] (6)

[0112] The calculated lengths of the reinforcing bars in each layer are shown in Table 2.

[0113] Table 2 Length of reinforcement material in each layer of the reinforced zone

[0114]

[0115] Substituting the parameters of the plain soil into equation (3), the sliding resistance of the fill in the unmodified reinforced zone 3 is calculated. The area is the area of ​​the non-modified reinforced zone 3 in the 10th soil block; the sliding resistance of the fill in the modified reinforced zone 4 is calculated by substituting the parameters of the modified soil (a mixture of cement and plain soil) into equation (3). The area is the area of ​​modified reinforced zone 4 in soil block No. 10. In Mode 1, the calculated length of the reinforcement is... It is the length of the internal reinforcement material in the reinforced zone (non-modified reinforced zone 3 and modified reinforced zone 4).

[0116] For the second failure mode of embankment slope instability, namely the sliding of soil within a certain range below the embankment slope from the top of the retaining wall along the sliding surface, the thickness of the reinforced modified soil cushion layer 5 is a key parameter affecting the location, shape, and overall safety factor of the most dangerous sliding surface 7. Therefore, to ensure design safety, it is necessary to determine the optimal retaining wall height that matches the thickness of the reinforced modified soil cushion layer 5 through stability analysis.

[0117] Taking a case where the thickness of the reinforced modified soil cushion layer 5 is 1.5m and the height of the gravity retaining wall 6 is 12m as an example. First, the most dangerous sliding surface 7 is automatically searched and determined using slide software, such as... Figure 6 As shown, the most dangerous sliding surface was cut into 14 soil strips (see...). Figure 6 In Among them, the soil strip 11 located in the reinforced modified soil cushion layer 5 is divided separately due to its different parameters, while the remaining soil strips are obtained by vertical cutting of equal width. The residual sliding force at the intersection of the sliding surface and the reverse slope section is calculated using equation (1). (i.e., landslide thrust) The specific results are shown in Table 3:

[0118] Table 3. Residual sliding force values ​​at the intersection of the sliding surface and the reverse slope section

[0119]

[0120] like Figure 6 As shown, multiple reverse slope sections are determined through geometric construction, and the residual sliding force of these reverse slope sections is calculated using the unbalanced thrust method. First, starting from the vertex N of the retaining wall edge, a line is drawn that makes an angle of θ with the horizontal direction. (here) The initial ray, which represents the internal friction angle of the fill soil and slopes downwards, intersects the arc of the sliding surface (referring to the most dangerous sliding surface 7) at point [missing information]. The reverse extension lines intersect the lower surface of the reinforced modified soil cushion layer 5 at points. It intersects the slope surface at point Next, using N as the base point, the initial ray is rotated clockwise every 5° to generate a series of new rays, which intersect the sliding surface arc at points a, b, c, d, and e, respectively, and their backward extensions intersect the cushion layer at point [missing information]. , , , , The slope surface intersects at point , , , , Finally, connect the corresponding intersections of the sliding surface and the slope surface to form a line segment. , , , , This refers to the reverse slope section. A and B are the symbols representing the soil strips where the most dangerous sliding surface intersects with the reverse slope section.

[0121] Since the sliding surface passes through the reinforced modified soil cushion layer 5, the reinforcement will generate pull-out and tensile forces during the sliding process, which directly affects the magnitude of the anti-sliding force. The variation in the thickness of the reinforced modified soil cushion layer 5 further modulates the strength of the anti-sliding force, thereby affecting the residual sliding force at a given retaining wall height.

[0122] When performing stability analysis, the contribution of the reinforcement layer must be considered simultaneously; therefore, the pull-out force of the reinforcement is introduced. and tensile strength The smaller value is used for calculation. In the calculation of the reverse slope section, the sliding direction of the sliding surface is always taken as the positive direction. At this time, the component of gravity along the sliding surface is negative, that is, the anti-slip force. Therefore, when calculating the remaining sliding force of the reverse slope section, there is no need to multiply by the safety factor.

[0123] The anti-sliding force generated by the reinforcement (here referring only to the reinforcement materials in the reinforced modified soil cushion layer 5, emphasizing the relationship between the cushion layer thickness and the retaining wall height) Calculate using the following formula:

[0124] (7)

[0125] In the formula, This indicates the total number of reinforcement (reinforcing material) layers in the reinforced modified soil cushion layer 5; Indicates the first The layer of reinforcement corresponds to the pull-out resistance of the smooth surface; Indicates the first Allowable tensile force for layered reinforcement.

[0126] The pull-out resistance of the reinforcing bars is horizontal to the left, and its main function is to prevent the grid from being pulled out. It is calculated using the following formula:

[0127] (8)

[0128] In equation (8) This refers to the effective length of the reinforcing steel. The total length of the reinforcing steel in the soil refers to the total geometric length of a single layer of reinforcing steel laid in the embankment. The effective anchorage length refers to the portion of the reinforcing steel within the anchorage zone that can generate sufficient pull-out resistance through friction and interlocking. The sliding surface divides the soil into an anchorage zone and a non-anchorage zone; the area outside the sliding surface is the non-anchorage zone, and the area inside the sliding surface is the anchorage zone. The sliding surface passes through the reinforcing steel twice, dividing it into three segments, namely the left anchorage segment. Non-anchored section and the right anchorage section ,like Figure 6 As shown, the effective length of the reinforcing bar calculated by equation (8) refers to the left anchorage section. and the right anchorage section When the sliding surface passes through the reinforcement, in the force analysis of the soil block, the corresponding anchorage length is used when calculating the pull-out force of the reinforcement: the effective length of the reinforcement used in the data in Table 3 is the left anchorage section. The effective length of the reinforcing steel used in the data in Table 4 is the right anchorage section. .

[0129] The tensile strength of the reinforcing steel is in the opposite direction to the soil sliding direction. Its main function is to limit soil sliding, and it is calculated using the following formula:

[0130] (9)

[0131] In the formula, Indicates the allowable tensile strength of the reinforcing steel; Indicates the width of the reinforcing bar, here .

[0132] The reinforcing bars are made with ultimate tensile strength. For reinforcing bars with a strength of 275 kN / m, the allowable tensile strength is... for:

[0133] (10)

[0134] In the formula, This represents the strength reduction factor, which takes into account factors such as mechanical damage, material creep, chemical and biological damage during laying. It should be determined based on practical experience, and 2.5 to 5.0 can be used when there is no experience.

[0135] When the sliding surface (referring to the most dangerous sliding surface 7) passes through the reinforced modified soil cushion layer 5, considering the resistance of the reinforcement, the resulting anti-slip force is calculated using the following formula:

[0136] (11)

[0137] This represents the resistance force of the i-th soil block.

[0138] like Figure 5 As shown, the remaining sliding force on the reverse slope section is calculated using the following formula:

[0139] (12)

[0140] Indicates the first The first block of earth is sent to the second... The thrust of each soil block Indicates the first The first block of earth is sent to the second... The thrust of each soil block Indicates the thrust from the first The first block of earth is sent to the second... The transfer coefficient of a soil strip, For the first The component of the sliding force of each soil block refers to the component of gravity along the direction of the most dangerous sliding surface 7:

[0141]

[0142] Under the condition that the thickness of the subgrade is 1.5m and the height of the retaining wall is 12m, the remaining sliding force of each reverse slope section can be calculated, as shown in Table 4.

[0143] Table 4 Residual sliding force values ​​on the reverse slope section

[0144]

[0145] The peak residual sliding force of the reverse slope section under different retaining wall heights was calculated when the cushion layer thickness was 1.5m, as shown in Table 5.

[0146] Table 5. Peak Residual Sliding Force at Various Retaining Wall Heights

[0147]

[0148] In the stability analysis of the reverse slope section, when the calculated peak value of the residual sliding force is positive, it indicates that the retaining wall provides insufficient anti-sliding force, and the wall height needs to be increased. Conversely, if the peak value is excessively negative (a shift from positive to negative is considered insignificant, but a shift from negative to even larger negative values ​​indicates excessive negativity), it indicates that the retaining wall structure is too conservative and there is room for optimization, suggesting that the wall height can be appropriately reduced. By comparing the low peak values ​​of the negative residual sliding force under the same cushion layer thickness and different retaining wall heights, the optimal height of the retaining wall under that cushion layer thickness can be determined, thus achieving an economical and reasonable design while satisfying stability requirements. Based on this method, the optimal retaining wall height under different cushion layer thicknesses can be calculated, as shown in Table 6.

[0149] Table 6 Optimal Retaining Wall Height for Various Subbase Thicknesses

[0150]

[0151] It can be concluded that, from the perspective of preventing soil from sliding off the top of the wall, the height of the retaining wall can be gradually reduced as the thickness of the cushion layer increases. It is known that when the residual sliding force is at a low negative value, it indicates that the structure is in a stable state under the combination of cushion layer thickness and retaining wall height. The corresponding retaining wall height at this point is the optimal retaining wall height under that cushion layer thickness, thus determining the optimal combination of the thickness of the reinforced modified soil cushion layer 5 and the height of the gravity retaining wall 6.

[0152] To address the stress characteristics of different areas of steep embankments, this embodiment of the invention employs zoned reinforcement in unmodified reinforcement zone 3 and modified reinforcement zone 4, avoiding material waste caused by overall reinforcement and improving economic efficiency. Through the synergistic effect of the reinforced modified soil cushion layer 5 and the gravity retaining wall 6, the height of the retaining wall can be effectively reduced, material usage can be decreased, and project costs can be lowered.

[0153] For the third failure mode, the parameters in the calculation model are as follows:

[0154] Height of retaining wall (gravity retaining wall 6) ,width The height of the soil at the front end of the retaining wall is The angle between the front end and the horizontal line is The heavy-duty retaining wall =24kN / m 3 Cohesion =1200kPa, internal friction angle =33.5°, the soil behind the wall is heterogeneous soil, and from top to bottom the soil consists of modified soil, unmodified soil and moderately weathered slate 2, with a soil height of 2. The depths are 0.75m, 8.25m, and 3m, respectively. Among them, the unit weight of moderately weathered slate is... =20kN / m 3 Soil cohesion =100kPa, internal friction angle =38°, wall back is vertical, backfill is horizontal, wall is rigid, wall back is rough, and the friction angle between wall and soil is... , Values Combined internal friction angle Therefore Take 8°.

[0155] Based on the fundamental assumptions of Coulomb's earth pressure theory, the force exerted by a reinforced gravity retaining wall on a soil wedge is established from the limit equilibrium state of the sliding soil wedge. The calculation formula will consider the forces acting on a gravity retaining wall with reinforcing steel. The calculation formula is entered into an Excel spreadsheet, and the maximum value of the force is solved using Excel's built-in solver. This refers to the active earth pressure value of a gravity retaining wall considering the effect of reinforcement, and also yields the angle between the fracture surface of the backfill and the vertical plane. .

[0156] like Figure 7 As shown, based on the geometric relationship of the soil wedge, the area of ​​each soil layer in the soil wedge is obtained:

[0157] (13)

[0158] (14)

[0159] In the formula, The area of ​​the unmodified soil; The area of ​​modified soil and moderately weathered slate.

[0160] Gravity is:

[0161] (15)

[0162] In the formula, The unit weight of unmodified soil (fill soil within the soil wedge) is taken as 18 kN / m³. The unit weight of the modified soil (value is 20 kN / m³). This represents the weight of the soil wedge.

[0163] The reinforcement acting on the soil wedge is as follows:

[0164] (16)

[0165] Based on the static equilibrium conditions of the soil wedge, equilibrium equations in the X and Y directions are established.

[0166] From the equilibrium condition in the X direction, we get:

[0167] (17)

[0168] (18)

[0169] The equilibrium equations here all take into account the effect of the reinforcing steel. In the equations, It is the soil reaction force; Indicates the internal friction angle between the wall and the soil; Indicates the overall tensile force of the reinforcing steel; Indicates the combined internal friction angle. This indicates the angle between the fracture surface and the vertical direction.

[0170] From the equilibrium condition in the Y direction, we get:

[0171] (19)

[0172] This represents the weight of the soil wedge.

[0173] Substituting (18) into (19), we get:

[0174] (20)

[0175] Substituting (16) into (20), we obtain the active earth pressure of the retaining wall under the synergistic effect of reinforcement:

[0176] (twenty one)

[0177] The forces acting on a gravity retaining wall considering the reinforcement will be considered. The calculation formulas are entered into an Excel spreadsheet, and the forces are set in Excel Solver. To solve for the objective, whose objective value is the maximum value, the angle between the fracture surface of the backfill soil and the vertical plane. Set to change variable cells, The value of the constraint range is and give A greater than The initial value can be obtained by solving the nonlinear GRG problem to obtain the force. maximum value This refers to the active earth pressure value of the gravity retaining wall 6 considering the reinforcement effect, and also obtains the angle between the fracture surface of the backfill behind the wall and the vertical plane. .

[0178] (twenty two)

[0179] The landslide thrust is the maximum residual sliding force on the most dangerous sliding surface. Active earth pressure The active earth pressure and the landslide thrust are compared, and the larger one is taken. Therefore, the stability of the retaining wall is verified by landslide thrust.

[0180] Gravity of retaining wall :

[0181] (twenty three)

[0182] This indicates the area of ​​the retaining wall. The unit weight of the retaining wall is 24 kN / m³.

[0183] This represents the vertical distance from the weight of the retaining wall to the toe of the retaining wall. This represents the area of ​​different blocks (the object of division is a retaining wall, and the division is based on the fact that the retaining wall is an irregular shape, divided into rectangles and triangles for easy calculation of the geometric center). This indicates the vertical distance from the center of gravity of different blocks to the toe of the retaining wall.

[0184] Weight of overlying soil:

[0185] (twenty four)

[0186] Equations (24) and (23) are essentially the same. Indicates the weight of the overlying soil. It represents the vertical distance from the weight of the overlying soil to the toe of the retaining wall.

[0187] Passive earth pressure in front of the retaining wall:

[0188] (25)

[0189] (26)

[0190] (27)

[0191] This is the passive earth pressure coefficient; This refers to the passive earth pressure in front of the wall; The internal friction angle of the soil in front of the wall. The unit weight of the soil in front of the wall is 20 kN / m³. The height of the soil in front of the wall; The cohesion of the soil in front of the wall. This is the horizontal component of the passive earth pressure in front of the wall.

[0192] like Figure 8 As shown in Table 7, the parameters of the retaining wall cross-section are as follows:

[0193] Table 7 Retaining Wall Cross-Sectional Parameters

[0194]

[0195] Anti-slip stability coefficient :

[0196] (28)

[0197] In the formula, Let be the coefficient of friction, and take . .

[0198] The vertical component of the resultant force acting on the base; The horizontal component of the resultant force acting on the base; This is the vertical component of the landslide thrust; This is the vertical component of the passive earth pressure in front of the wall; This is the horizontal component of the landslide thrust.

[0199] Anti-overturning stability coefficient :

[0200] (29)

[0201] To resist overturning moment; For overturning moment, The vertical distance from the vertical component of the landslide thrust to the toe of the retaining wall; The vertical distance from the horizontal component of the passive earth pressure in front of the wall to the toe of the retaining wall; The vertical distance from the vertical component of the passive earth pressure in front of the wall to the toe of the retaining wall; Let be the vertical distance from the horizontal component of the landslide thrust to the toe of the retaining wall. The calculation results show that, under the synergistic effect of the reinforcement, the retaining wall meets the requirements for both sliding stability and overturning stability.

[0202] To address the third failure mode of embankment slope instability, this invention verifies the overall stability of the support structure, focusing on evaluating its resistance to sliding and overturning. Because the support structure designed in this invention exhibits better overall stability under the synergistic effect of the reinforced modified soil cushion layer 5 and the reinforced zone.

[0203] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A combined support structure of reinforced embankment and gravity retaining wall for steep slope roadbeds, comprising an embankment support structure and a drainage system, characterized in that, The embankment support structure includes a gravity retaining wall (6), which is located on the moderately weathered slate (2) at the toe of the slope. A reinforced area is provided above the gravity retaining wall (6). The reinforced area includes a non-modified reinforced area (3) and a modified reinforced area (4) from the inside to the outside. Reinforcing materials are laid in layers in the reinforced area. A reinforced modified soil cushion layer (5) is laid horizontally between the bottom of the reinforced area and the top of the gravity retaining wall (6). Reinforcing materials are laid in the reinforced modified soil cushion layer (5) in a full-section manner, and the reinforcing materials in the reinforced modified soil cushion layer (5) are anchored in the gravity retaining wall (6).

2. The combined support structure of reinforced subgrade and gravity retaining wall for steep slopes according to claim 1, characterized in that, The modified and reinforced area (4) is provided with a platform at the top, and a backfill layer (1) is laid on the outside of the moderately weathered slate (2) above the reinforced area; a stepped structure is provided at the moderately weathered slate (2) behind the gravity retaining wall (6), and a backfill layer (1) is laid in the area between the gravity retaining wall (6), the stepped structure of the moderately weathered slate (2) and the reinforced and modified soil cushion layer (5).

3. The combined support structure of reinforced subgrade and gravity retaining wall for steep slopes according to claim 1, characterized in that, The unmodified reinforced area (3) is filled with plain soil in layers; the modified reinforced area (4) is filled with modified soil in layers. The modified soil of the reinforced modified soil cushion layer (5) has the same composition as the modified soil of the modified reinforced area (4), which is a mixture of cement and plain soil in a mass ratio of 2:25-1:

10.

4. The combined support structure of reinforced subgrade and gravity retaining wall for steep slopes according to claim 1, characterized in that, The drainage system includes longitudinal drainage ditches on the embankment slope, a continuous drainage layer, and drainage holes in front of the wall. The longitudinal drainage ditches are located on the surface of the embankment slope and are set at fixed intervals along the longitudinal direction of the embankment slope, extending from the top of the slope to the bottom of the slope. The continuous drainage layer is located between the backfill layer (1) and the gravity retaining wall (6), and is filled with permeable material; The drainage hole in front of the wall is a row of PVC pipes with a diameter of 50~100mm, which are set at a fixed distance above the embankment base. The outer end is inclined downward and the inner end is embedded with a continuous drainage layer. The pipe body is wrapped with reverse filter geotextile.

5. The design method for a combined support structure of reinforced subgrade and gravity retaining wall on steep slopes as described in claim 1, characterized in that, Includes the following steps: S1 identifies the failure modes of overall instability; S2, for mode one: the sliding surface shears the unmodified reinforced area (3) and the modified reinforced area (4), and the reinforcement is pulled out of the slope; by searching the most dangerous sliding surface (7) through software, the soil above the most dangerous sliding surface (7) and located inside the reinforced area is divided into multiple vertical soil strips, and the unbalanced thrust method is used to calculate the unbalanced thrust transmitted by the soil strips close to the reinforced area, so as to determine the length of reinforcement inside the reinforced area that is sufficient to resist the unbalanced thrust; S3, for mode 2: the soil slides out from the top of the gravity retaining wall (6); calculate the remaining sliding force under different combinations of the thickness of the reinforced modified soil cushion (5) and the height of the gravity retaining wall (6), and then determine the best combination of the thickness of the reinforced modified soil cushion (5) and the height of the gravity retaining wall (6); S4. For Mode 3: Overturning or sliding of gravity retaining wall (6); considering the earth pressure behind the wall, the weight of the soil wedge and the tension of the reinforcement material on gravity retaining wall (6) transmitted through the reinforced modified soil cushion layer (5), establish static equilibrium equations in the X and Y directions, and verify the anti-sliding and anti-overturning stability of gravity retaining wall (6).

6. The design method for a combined support structure of reinforced subgrade and gravity retaining wall on steep slopes according to claim 5, characterized in that, In S2, the method for calculating the length of the reinforcing bar is as follows: S21, the intersection point Q of the most dangerous sliding surface (7) and the reinforced area is cut vertically. The outer side of the cutting line is the soil strip block of the reinforced area, and the inner side of the cutting line is cut vertically with equal width to obtain multiple soil strip blocks; S22, the anti-sliding force of the reinforced soil strip. Calculate according to formula (1): （1） In the formula, This represents the area of ​​the soil strip in the reinforced zone; The unit weight of the soil in the reinforced area; The angle between the lower part of the reinforced soil strip and the horizontal direction; The internal friction angle of the soil strip in the reinforced zone; The cohesion of the sliding surface of the soil strip in the reinforced zone; The length of the soil strip in the reinforced zone; The pull-out resistance of the reinforcing bars in the reinforced zone is calculated according to formula (2) based on the pull-out resistance generated by the upper and lower surfaces of the reinforcing bars: （2） In the formula, This refers to the pull-out resistance of the reinforcing steel. This refers to the vertical earth pressure above the reinforcing steel. Width of the reinforcing bar; This refers to the length of the reinforcing bar. The coefficient of friction; To balance the landslide thrust transmitted from adjacent reinforced soil blocks to the reinforced soil blocks, the required anti-sliding force of the reinforced soil blocks is... Calculate according to formula (3): （3） In the formula, The safety factor for sliding down the most dangerous sliding surface (7); The landslide thrust transmitted from adjacent reinforced soil blocks to the reinforced soil blocks is calculated using the unbalanced thrust method. By combining equations (1), (2), and (3), the length of the reinforcing bar can be obtained. .

7. The design method for a combined support structure of reinforced subgrade and gravity retaining wall on steep slopes according to claim 6, characterized in that, The calculation of the landslide thrust transmitted from adjacent reinforced soil blocks to the reinforced soil blocks using the unbalanced thrust method is as follows: （4） In the formula, Indicates the first The first block of earth is sent to the second... The thrust of the first soil strip is parallel to the first... The bottom surface of each soil block; The landslide safety factor; For the first The weight of a single soil block; Indicates the first The angle between the lower part of the soil strip and the horizontal direction; Indicates the first The length of each soil strip; Indicates the first The internal friction angle of each soil block; Indicates the first Cohesion of the sliding surface of the soil strip; Indicates the first The first block of earth is sent to the second... The thrust of each soil block; Indicates the thrust from the first The first block of earth is sent to the second... The transfer coefficient of each soil block; Transmission coefficient Calculated using equation (5): （5） In the formula, Indicates the first -1 The angle between the lower part of the soil strip and the horizontal direction.

8. The design method for a combined support structure of reinforced subgrade and gravity retaining wall on steep slopes according to claim 5, characterized in that, In S3, the method for calculating the residual sliding force of the combined structure of the reinforced modified soil cushion (5) and the gravity retaining wall (6) is as follows: S31, the pull-out resistance of the reinforcing material. and tensile strength The smaller value represents the anti-slip force generated by the reinforcing material. ; When the most dangerous sliding surface (7) passes through the reinforced modified soil cushion layer (5) at S32, considering the contribution of the reinforcement layer, the resulting anti-slip force is calculated according to formula (6): （6） This represents the resistive force of the i-th soil block; For the first The self-weight of each soil block; Indicates the first The angle between the lower part of the soil strip and the horizontal direction; Indicates the first The internal friction angle of each soil block; Indicates the first Cohesion of the sliding surface of the soil strip; Indicates the first The length of each soil strip; S33, the remaining sliding force on the reverse slope section is calculated according to formula (7): （7） Indicates the first The first block of earth is sent to the second... The thrust of each soil block Indicates the first The first block of earth is sent to the second... The thrust of each soil block Indicates the thrust from the first The first block of earth is sent to the second... The transfer coefficient of a soil strip, For the first The downward force of each soil block.

9. The design method for a combined support structure of reinforced subgrade and gravity retaining wall on steep slopes according to claim 8, characterized in that, The method for determining the reverse slope section is as follows: Starting from the vertex N of the gravity retaining wall (6), draw an initial ray that is angled downwards at a fixed angle to the horizontal direction. The initial ray intersects the arc of the most dangerous sliding surface (7) at point N. The reverse extension lines intersect the lower surface of the reinforced modified soil cushion layer (5) at point [point missing]. It intersects the slope surface at point ; Using N as the base point, the initial ray is rotated clockwise at fixed angles to generate a series of new rays, which intersect the arc of the most dangerous sliding surface (7) at points a, b, c, d, and e, respectively. The reverse extension lines intersect the reinforced modified soil cushion layer (5) at point... , , , and The slope surface intersects at point , , , and ; Connect the intersection of the most dangerous sliding surface (7) and the slope surface to form a line segment. , , , and That is, the reverse slope section.

10. The design method for a combined support structure of reinforced subgrade and gravity retaining wall on steep slopes according to claim 8, characterized in that, Calculate the pull-out force of the reinforcing bar. When the length of the reinforcing bar is the length of the reinforcing bar anchorage section after the most dangerous sliding surface (7) passes through the reinforcing bar.

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