High and steep embankment semi-rigid combined supporting structure and design method thereof

Abstract

The invention discloses a high and steep embankment semi-rigid combined type supporting structure and a design method thereof, the embankment supporting structure comprises a balance weight type retaining wall, the balance weight type retaining wall is arranged on a moderately weathered slate of a slope toe, a reinforced area is arranged above the balance weight type retaining wall, and rib materials are laid in the reinforced area in a layered mode; a reinforced modified soil cushion layer is horizontally laid between the reinforced area and the top of the balance weight type retaining wall, rib materials are laid in the reinforced modified soil cushion layer in a full-section mode, and the rib materials in the reinforced modified soil cushion layer and the balance weight type retaining wall are not anchored. And the length of the rib material and the height of the retaining wall are optimized according to different failure modes until the anti-sliding stability coefficient and the anti-overturning stability coefficient meet the standard requirements. The gravity center of the wall body is moved backwards through the balance weight platform of the balance weight type retaining wall, the synergistic effect of the balance weight type retaining wall and rib materials is enhanced, the stability of the high and steep embankment supporting structure is improved, 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 semi-rigid composite support structure for high and steep embankments and its design method. Background Technology

[0002] The highway network is continuously extending into mountainous and hilly areas, forming numerous high and steep embankment sections. Existing reinforcement technologies for treating high and 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 high and steep embankment conditions, traditional counterweight retaining walls rely excessively on their own weight to resist earth pressure, and the increased wall height leads to a significant increase in material consumption and decreased economic efficiency; ③ High and steep embankments, due to their large filling height and steep slope, 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 high and steep embankments 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 high embankment with a counterweight retaining wall 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 the counterweight retaining wall foundation in complex and steep sections and improves its bearing capacity. However, it only considers the bearing capacity requirements of counterweight retaining walls with a height of 5m-6m in steep slope embankment support and does not fully consider the stability requirements.

[0005] In summary, existing methods for reinforcing high and steep embankments 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, gravity retaining walls rely excessively 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) Existing reinforcement methods often design retaining walls and reinforcement materials as independent components, lacking in-depth consideration of the working mechanism of the two, resulting in the inability to form an organic whole between the backfill soil, reinforced soil and retaining wall, and the overall stability potential of the structure is not fully mobilized. Summary of the Invention

[0009] To address the aforementioned issues, this invention provides a semi-rigid composite support structure for high and steep embankments, comprising a reinforced zone, a reinforced modified soil cushion layer, and a counterweight retaining wall. By utilizing the counterweight platform of the counterweight retaining wall to shift the wall's center of gravity backward, the synergistic effect between the counterweight retaining wall and the reinforcing material is enhanced, thereby improving the stability of the high and steep embankment support structure, reducing project costs, and achieving the dual goals of cost savings and optimized project performance.

[0010] Another objective of this invention is to provide a design method for a semi-rigid composite support structure for high and steep embankments.

[0011] The technical solution adopted in this invention is a semi-rigid composite support structure for high and steep embankments, including an embankment support structure and a drainage system. The embankment support structure includes a counterweight retaining wall with a counterweight platform on its back. The counterweight retaining wall is located on moderately weathered slate at the toe of the slope. A reinforcement zone is provided above the counterweight retaining wall, and reinforcement materials are laid in layers in the reinforcement zone.

[0012] A reinforced modified soil cushion layer is laid horizontally between the reinforced area and the top of the counterweight retaining wall. Reinforcing bars are laid in the reinforced modified soil cushion layer in a full-section manner. The reinforcing bars inside the reinforced modified soil cushion layer are not anchored to the counterweight retaining wall.

[0013] Furthermore, the reinforced area includes a modified portion and an unmodified portion. The modified portion extends from the surface of the embankment slope to the interior of the embankment to form a platform, while the remaining portion is the unmodified portion.

[0014] Furthermore, the area outside the moderately weathered slate on the gentle slope and steep slope above the reinforced area is a fill area, and the area between the counterweight retaining wall, the moderately weathered slate, and the reinforced modified soil cushion layer is a fill area. A stepped structure is provided at the connection between the fill area behind the counterweight retaining wall and the moderately weathered slate.

[0015] Furthermore, the unmodified portion of the reinforced zone is filled with plain soil in layers; the modified portion of the reinforced zone is filled with modified soil in layers, wherein the modified soil is a mixture of cement and plain soil in a mass ratio of 2:25 to 1:10.

[0016] 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 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.

[0017] The continuous drainage layer is located in the backfill area behind the counterweight retaining wall and is constructed using permeable materials.

[0018] 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.

[0019] A design method for a semi-rigid composite support structure for high and steep embankments includes the following steps:

[0020] S1 identifies the failure modes of overall instability;

[0021] S2, for mode 1: the sliding surface shears the reinforced area and the reinforcement is pulled out of the slope; the software searches for the most dangerous sliding surface of the embankment, divides the soil above the most dangerous sliding surface and inside the reinforced area into multiple vertical soil strips, and uses the unbalanced thrust method 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.

[0022] S3, for Mode 2: Soil slides out from the top of the counterweight retaining wall; calculate the remaining sliding force under different combinations of reinforced modified soil cushion thickness and counterweight retaining wall height, and then determine the optimal combination of reinforced modified soil cushion thickness and counterweight retaining wall height.

[0023] S4, for mode 3: the counterweight retaining wall overturns or slides; based on the height of the counterweight retaining wall determined in mode 2, determine the inclination angles of the hypothetical back wall, upper back wall, and lower back wall, and then calculate the inclination angles of the three potential rupture surfaces corresponding to the hypothetical back wall, upper back wall, and lower back wall, namely the inclination angles of the second rupture surface, the first rupture surface, and the lower rupture surface.

[0024] For the soil between the second and first rupture surfaces, a moment balance equation is established. Based on the results of Mode 1 and Mode 2, the number of reinforcing bars that the most dangerous sliding surface passes through is determined, and then the resistance of the reinforcing bars on the left side of the first rupture surface is solved. Establish static equilibrium equations in the horizontal and vertical directions, and solve for the earth pressure at the second rupture surface. Earth pressure at the first rupture surface ;

[0025] For the soil between the second rupture surface and the back of the retaining wall, based on the earth pressure at the second rupture surface... The earth pressure on the back of the upper wall is solved by using the static equilibrium equations in the horizontal and vertical directions. Earth pressure of the balance platform ;

[0026] For the soil between the first fracture surface and the lower wall fracture surface, establish a moment equilibrium equation and solve for the resistance of the reinforcement on the left side of the lower wall fracture surface. Establish static equilibrium equations in the horizontal and vertical directions, based on the earth pressure at the first rupture surface. Resistance of the reinforcement on the left side of the first fracture surface Resistance of the reinforcement on the left side of the fractured surface of the lower wall Solve for the earth pressure on the back of the wall. ;

[0027] S5. Calculate the sliding stability coefficient and overturning stability coefficient based on the calculation results of S4. If they do not meet the requirements of the specifications, adjust the size of the counterweight retaining wall or the reinforcement arrangement until the sliding stability coefficient and overturning stability coefficient meet the requirements of the specifications.

[0028] Furthermore, in S4, the earth pressure at the first rupture surface is selected. Earth pressure at the second rupture surface The intersection of the lines of action of the resultant forces is taken as the center of the moment, and the resistance of the reinforcement on the left side of the first fracture surface is... Calculate according to the following formula:

[0029]

[0030] in, , and They are , and The perpendicular distance from the line of action to the center of the moment. The weight of the soil between the second rupture surface and the first rupture surface. For the resistance of the reinforcement on the right side of the second fracture surface, The allowable tensile force of the reinforcing bar is taken in the calculation. The tensile strength of the reinforcement is the product of the allowable tensile strength of the reinforcement and the total width of the reinforcement. The total width of the reinforcement is the product of the width of a single reinforcement and the number of reinforcements that the most dangerous sliding surface passes through. The thickness of the reinforced modified soil cushion is obtained through Mode 2, and the number of reinforcements that the most dangerous sliding surface passes through the reinforced modified soil cushion is determined by combining the reinforcement spacing. The length of the reinforcement inside the reinforced area is obtained through Mode 1, and the number of reinforcements that the most dangerous sliding surface passes through in the reinforced area above the reinforced modified soil cushion is determined by combining the position of the most dangerous sliding surface.

[0031] Earth pressure at the second rupture surface Calculate according to the following formula:

[0032]

[0033] Earth pressure at the first rupture surface Calculate according to the following formula:

[0034]

[0035] in, This represents the internal friction angle of the imaginary wall back; The dip angle of the first fracture surface; The angle of inclination of the second fracture surface.

[0036] Furthermore, in S4, the earth pressure on the back of the upper wall... Calculate according to the following formula:

[0037]

[0038] Earth pressure of the counterweight platform Calculate according to the following formula:

[0039]

[0040] in, The angle of inclination of the wall back; This represents the weight of the soil between the second rupture surface and the back of the retaining wall.

[0041] Furthermore, in S4, the resistance of the reinforcing bars on the left side of the fracture surface of the lower wall... Calculate according to the following formula:

[0042]

[0043] in, Indicates the resistance of the reinforcement on the left side of the first fracture surface. The perpendicular distance from the line of action of the torque to the center of the moment; Indicates the earth pressure at the first rupture surface The perpendicular distance from the line of action to the center of the moment; This represents the weight of the soil between the first rupture surface and the rupture surface of the lower wall. The perpendicular distance from the line of action to the center of the moment; Indicates the resistance of the reinforcement on the left side of the fracture surface of the lower wall. The perpendicular distance from the line of action to the center of the moment;

[0044] Earth pressure behind the wall Calculate according to the following formula:

[0045]

[0046] in, The angle of inclination of the fracture surface of the lower wall; Indicates the internal friction angle of the lower wall back; The angle of inclination of the lower wall back.

[0047] Furthermore, in S5, the anti-slip stability coefficient Calculate according to the following formula:

[0048]

[0049] Anti-overturning stability coefficient Calculate according to the following formula:

[0050]

[0051] in, The coefficient of friction, This represents the weight of the counterweight retaining wall. Indicates the earth pressure on the back of the wall. Horizontal component of force; Indicates the earth pressure on the back of the wall. The vertical component of the force; Indicates the earth pressure behind the lower wall. Horizontal component of force; Indicates the earth pressure behind the lower wall. The vertical component of the force; , and They are respectively , and The vertical distance from the line of action to the toe of the counterweight retaining wall; and They are respectively and The vertical distance from the line of action to the toe of the counterweight retaining wall; express The vertical distance from the line of action to the toe of the counterweight retaining wall.

[0052] The beneficial effects of this invention are:

[0053] (1) The present invention utilizes the counterweight platform of the counterweight retaining wall to shift the center of gravity of the wall backward, thereby enhancing the synergistic effect between the counterweight retaining wall and the reinforcement. The top of the counterweight retaining wall is provided with a reinforced modified soil cushion layer to prevent the soil from sliding out from the top of the wall. The reinforcement greatly reduces the thrust transmitted from the top of the slope, resulting in a reduction in the soil pressure on the back of the retaining wall, thereby improving the overall stability and enhancing the anti-sliding and anti-overturning capabilities.

[0054] (2) This invention uses the unbalanced thrust method to calculate stability, optimizes the length of the reinforcement material, and reduces the height of the retaining wall based on the relationship between the thickness of the reinforced modified soil cushion layer and the height of the retaining wall. This effectively solves the problems of excessive cross-sectional size, material waste, and local instability of traditional gravity retaining walls in high and steep embankment scenarios.

[0055] (3) The counterweight retaining wall provided by the present invention uses the backfill soil on the counterweight platform and the self-weight of the wall to resist the soil pressure. It innovatively introduces the reinforcement synergistic working mechanism, which significantly improves the anti-sliding and anti-overturning stability. Attached Figure Description

[0056] 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.

[0057] Figure 1 This is a zoning diagram of a high embankment in an embodiment of the present invention.

[0058] Figure 2 This is a cross-sectional view of a high-fill embankment according to an embodiment of the present invention.

[0059] Figure 3 This is a diagram showing the arrangement of reinforcing bars in an embodiment of the present invention.

[0060] Figure 4 This is a simplified diagram of the calculation of the residual sliding force in the calculation model of this invention embodiment.

[0061] 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.

[0062] Figure 6 This is a simplified diagram illustrating the trial calculation of wall height in the calculation model of this invention embodiment.

[0063] Figure 7 This is a cross-sectional angle diagram of the counterweight retaining wall in an embodiment of the present invention.

[0064] Figure 8 This is a stress diagram of the cross-section of the counterweight retaining wall in an embodiment of the present invention.

[0065] Figure 9 These are force polygon diagrams of soil at different locations in embodiments of the present invention; (a) represents the soil between the first rupture surface and the second rupture surface, (b) represents the soil between the second rupture surface and the back wall of the retaining wall, and (c) represents the soil between the first rupture surface and the back wall of the retaining wall.

[0066] Figure 10 This is a schematic diagram of the location of the gravity retaining wall drainage design in an embodiment of the present invention.

[0067] In the diagram, 1. Filled area; 2. Moderately weathered slate; 3. Reinforced area; 4. Reinforced modified soil cushion layer; 5. Counterweight retaining wall; 6. 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 semi-rigid composite support structure for high and steep embankments 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 zone 3 (1:1, 9.5m high), a reinforced modified soil cushion layer 4, and a counterweight retaining wall 5. 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 moderately weathered slate 2, reinforced modified soil cushion layer 4, counterweight retaining wall 5, reinforced zone 3, and fill zone 1. Moderately weathered slate 2 serves as the roadbed. The counterweight retaining wall 5 is located on the moderately weathered slate 2 at the toe of the slope. The reinforced zone 3 is located above the counterweight retaining wall 5. The reinforced zone 3 includes modified and unmodified parts. The modified part extends 2m from the surface of the embankment slope to the interior of the embankment, and the remaining part is the unmodified part. The reinforced modified soil cushion layer 4 is fully covered with reinforcing material (geogrid). The area between the moderately weathered slate 2 and the reinforced modified soil cushion layer 4 is the fill zone 1. The connection between this area and the moderately weathered slate 2 is provided with a stepped structure. The fill is plain soil, specifically silty clay.

[0072] Reinforced zone 3 is constructed by layering fill and modified soil. The modified soil is a mixture of cement and plain soil in a mass ratio of 2:25-1:10, layered from bottom to top at a height of 0.5m, for a total of 19 layers, each layer being compacted and leveled. Subsequently, a layer of reinforcing material (geogrid) is laid flat on the top surface of each layer of fill and modified soil. The reinforcing material of the reinforced modified soil cushion layer 4 is only adjacent to the counterweight retaining wall 5, without extending into the retaining wall. It is anchored to the underlying fill layer along its length and edges using U-shaped nails. The reinforcing material does not need to penetrate the counterweight retaining wall 5, avoiding complex construction steps, reducing construction difficulty and cost, and avoiding maintenance difficulties caused by the connection between the reinforcing material and the counterweight retaining wall 5. Because in this design scheme, the function of the reinforcing material is to resist the lateral deformation of the soil in reinforced zone 3, rather than directly bearing the earth pressure transmitted by the counterweight retaining wall 5, no anchoring connection is required between the reinforcing material and the counterweight retaining wall 5.

[0073] The arrangement of reinforcing bars (reinforcing bars) is as follows: Figure 2As shown, the reinforcing steel and the counterweight retaining wall 5 together constitute the support system for the high and steep embankment, achieving coordinated support for the embankment. The unit weight of the subgrade soil... internal friction angle Cohesion The unit weight of modified soil internal friction angle The cohesion is The safety factor for the embankment slope is 1.35.

[0074] like Figure 10 As shown, 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 slope surface has longitudinal drainage ditches. These ditches are spaced 4m apart along the longitudinal direction of the embankment slope, extending from the top to the bottom. The width of the longitudinal drainage ditches is 10m, and the depth is 0.2m-0.4m. The continuous drainage layer is located in the backfill area 1 behind the wall. It is constructed with permeable material (gravel or crushed stone) to drain water from the backfill material. The top and bottom of the continuous drainage layer are sealed with 0.4m thick mortar (or other impermeable material) to prevent water infiltration. The drainage holes in front of the wall use PVC pipes with a diameter of 50-100mm. A row of these holes is installed 30cm above the embankment base, with a spacing of 2m-3m. The outer ends are slightly inclined downwards at a slope of 5%, and the inner ends are embedded in the continuous drainage layer. The pipe body is wrapped with geotextile to prevent clogging.

[0075] Example 2,

[0076] The design method for the semi-rigid composite support structure of high and steep embankments described in Example 1 includes the following steps:

[0077] S1: Semi-rigid composite support structure for high and steep embankments, with a total height of 22.25m (from the bottom of the retaining wall to the top of the reinforced zone).

[0078] S2: The height of each layer of reinforced zone 3 is 0.5m.

[0079] S3: The reinforcing materials located in the middle of each soil layer in the reinforced zone 3 are named sequentially from the top of the embankment to the bottom of the embankment: Reinforcing Material 1, Reinforcing Material 2, ... Reinforcing Material 18.

[0080] S4: Based on the most dangerous sliding surface 6, calculate the minimum length of the reinforcement required using the target pull-out stability coefficient to ensure that the reinforcement zone 3 has sufficient pull-out capacity, thereby optimizing the total length of the reinforcement.

[0081] S5: Based on the failure mode of soil sliding out from the top of the retaining wall, the structural stability under different combinations of cushion layer thickness and retaining wall 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.

[0082] S6: Based on the overturning or sliding failure mode of the counterweight retaining wall 5, the overall stability of the semi-rigid composite support structure of the high and steep embankment is verified.

[0083] 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. Therefore, the support structure designed in this invention exhibits better overall stability under the synergistic effect of the reinforcing steel.

[0084] Calculation example:

[0085] For the first failure mode of this embankment slope instability: the soil within a certain range below the embankment slope shears the fill and modified soil along the sliding surface, while the reinforcement is pulled out of the slope; firstly, the slide software is used to automatically search for the most dangerous sliding surface 6 of the embankment, and the most dangerous sliding surface 6 sliding horizontally from each layer of modified soil is determined.

[0086] like Figure 3 As shown, the most dangerous sliding surface is cut into 10 soil strips from top to bottom. The first 9 soil strips (①~⑨) are obtained by vertically cutting the most dangerous sliding surface 6 with equal width. The 10th soil strip is obtained by vertically cutting the boundary Q between the most dangerous sliding surface 6 and the reinforced zone 3. The soil mass of each strip is simplified as follows: Figure 4 As shown, the thrust is calculated using the unbalanced thrust method, and the derived formula is obtained:

[0087] (1)

[0088] In equation (1), Indicates the first Transmit the soil strip to the first The thrust of the soil strip is parallel to the first The bottom slip surface of the soil block; For the landslide safety factor, take ; The weight of the soil strip; Indicates the first The angle between the lower part of the soil strip and the horizontal direction; Indicates the length of the soil strip; Indicates the first soil layer The cohesion of the side of the soil strip Indicates the first soil layer The inner friction angle of the side of the soil strip; Indicates the first Transmit the soil strip to the first The thrust of the soil strip is parallel to the first The bottom surface of the soil block.

[0089] Transmission coefficient Calculated using equation (2):

[0090] (2)

[0091] Indicates the first -1 The angle between the lower part of the soil strip and the horizontal direction.

[0092] The landslide thrust of soil blocks 1 to 9, which slid out of the most dangerous sliding surface of the slope from the 19th layer of reinforced soil, was calculated. As shown in Table 1.

[0093] 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.

[0094]

[0095] 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.

[0096] 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.

[0097] The anti-sliding force of soil block No. 10 Calculate according to formula (3):

[0098] (3)

[0099] 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.

[0100] 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:

[0101] (4)

[0102] In equation (4): as reinforcement Its 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; Let be the coefficient of friction, which is set here. 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.

[0103] In order to balance the landslide thrust transmitted from soil block No. 9 to soil block No. 10 The required anti-sliding force for the No. 10 soil block Calculate using the following formula:

[0104] (5)

[0105] In equation (5), The safety factor for the soil sliding down the circular arc surface is 1.35, which is taken here.

[0106] By combining the sliding resistance of soil block No. 10 with the sliding resistance of the reinforced fill and modified soil, as well as 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 through inversion. .

[0107] By combining (3), (4), and (5), we obtain the length. The calculation formula is as follows:

[0108] (6)

[0109] In Mode 1, the calculated length of the reinforcing bar is... It is the length of the reinforcing bars inside reinforced zone 3.

[0110] The lengths of the reinforcing bars in each layer were calculated, as shown in Table 2.

[0111] Table 2 Length of reinforcement material in each layer of the reinforced zone

[0112]

[0113] 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 4 is a key parameter affecting the location and shape of the most dangerous sliding surface 6 and the overall safety factor of the embankment. Therefore, to ensure design safety, it is necessary to determine the optimal retaining wall height that matches the specific cushion layer thickness through stability analysis.

[0114] Taking a reinforced modified soil cushion layer 4 with a thickness of 1.5m and a retaining wall height of 12m as an example. First, the most dangerous sliding surface 6 is automatically searched and determined using slide software, such as... Figure 6 As shown, the most dangerous sliding surface 6 was cut into 14 soil strips (see...). Figure 6 In Among them, soil strip 11 located in the cushion section 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). ,like Figure 5 As shown in Table 3, the specific results are as follows.

[0115] Table 3. Residual sliding force values ​​at the intersection of the sliding surface and the reverse slope section

[0116]

[0117] 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) (Representing the internal friction angle of the fill), an initial ray sloping downwards, intersecting the arc of the sliding surface at point [point missing]. The reverse extension lines intersect the surface of the cushion layer at points in succession. 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. , , , , That is, the reverse slope section.

[0118] 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 permissible 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.

[0119] The anti-slip force generated by the tie rods (the reinforcing bars in the padding layer) Calculate using the following formula:

[0120] (7)

[0121] In the formula, Indicates the total number of reinforcing layers; Indicates the first time when the sliding surface passes through the reinforcing bar. Pull-out force on the layered reinforcement; Indicates the first Allowable tensile strength for layered reinforcement.

[0122] 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:

[0123] (8)

[0124] In the formula, This indicates the effective anchorage length of the reinforcing bar. The most dangerous sliding surface 6 passes through the reinforcing bar twice, dividing it into three segments, namely the left anchorage segment. Non-anchored section and the right anchorage section The anchorage section refers to the anchorage force between the reinforcement and the soil. The effective length of the reinforcement 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. .

[0125] Permissible tensile strength of reinforcing bars The direction is opposite to the direction of soil sliding, and its main function is to limit soil sliding. It is calculated using the following formula:

[0126] (9)

[0127] In the formula, Indicates the allowable tensile strength of the reinforcing steel; Indicates the width of the reinforcing bar, here .

[0128] The reinforcing bars are made with ultimate tensile strength. For reinforcing bars with a strength of 233 kN / m, the allowable tensile strength is... for:

[0129] (10)

[0130] 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.

[0131] When the most dangerous sliding surface 6 passes through the reinforced modified soil cushion layer 4, the resulting resistance force is calculated using the following formula:

[0132] (11)

[0133] This represents the resistance force of the i-th soil block.

[0134] Under the condition that the thickness of the reinforced modified soil cushion layer 4 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.

[0135] Table 4 Residual sliding force values ​​on the reverse slope section

[0136]

[0137] The peak residual sliding force of the reverse slope section under different retaining wall heights was calculated when the thickness of the reinforced modified soil cushion layer 4 was 1.5m, as shown in Table 5.

[0138] Table 5. Peak Residual Sliding Force at Various Retaining Wall Heights

[0139]

[0140] 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 anti-sliding force provided by the retaining wall is insufficient, and the wall height needs to be increased; conversely, if the peak value is excessively negative, it indicates that the retaining wall structure is too conservative and there is room for optimization, and 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. As shown in Table 5, when the cushion layer thickness is 1.5m, the optimal retaining wall height is 12m.

[0141] For the third failure mode, the parameters in the calculation model are as follows:

[0142] like Figure 7 As shown, for a counterweight retaining wall, the inclination angle of the hypothetical wall back is... =50.19°, the inclination angle of the upper wall back =34.99°, the inclination angle of the lower wall back =11.31°, slope inclination angle =23.57°, height above the wall Lower wall height When the inclination angle of the imaginary wall is greater than a certain critical value, a second fracture surface will be formed. The positions of the second fracture surface and the first fracture surface are related to the internal friction angle of the imaginary wall. , and These are the inclination angles of the second fracture surface, the first fracture surface, and the lower wall fracture surface, respectively.

[0143] like Figure 8 As shown, , and These are the earth pressures on the upper back wall, the lower back wall, and the counterweight platform, respectively. , and These are the earth pressures on the first rupture surface, the second rupture surface, and the rupture surface of the lower wall, respectively; The weight of the soil between the second rupture surface and the upper wall back. The weight of the soil between the second rupture surface and the first rupture surface. The weight of the soil between the first rupture surface and the rupture surface of the lower wall.

[0144] To simplify calculations, earth pressure is assumed to be triangularly distributed with its force located at 1 / 3 of the distance, while the force of reinforcement is assumed to be rectangularly distributed with its force located at the midpoint.

[0145] According to the fourth type of formula in Table 3-2-2 of the "Highway Subgrade Design Manual" (JTG D30-2015), the dip angle of the second fracture surface can be obtained. :

[0146] (12)

[0147] in, Indicates intermediate parameters. ; Let the internal friction angle of the hypothetical wall be... .

[0148] because It can be determined that a second fracture surface exists, and the dip angle of the second fracture surface is... .

[0149] The angle between the line connecting the outer edge of the weighing platform and the top of the slope and the vertical direction ,but According to the fourth type of formula in Table 3-2-2 of the "Highway Subgrade Design Manual" (JTG D30-2015), the dip angle of the first fracture surface can be calculated. :

[0150] (13)

[0151] and It can be seen that the first fracture surface intersects the slope.

[0152] According to the fifth type of formula in Table 3-2-3 of the "Highway Subgrade Design Manual" (JTG D30-2015), the inclination angle of the lower wall fracture surface can be calculated. :

[0153] (14)

[0154] in, , Indicates intermediate parameters. This indicates the internal friction angle of the lower wall back (38°).

[0155] but ,

[0156] because > The fracture surface of the lower wall intersects with the slope. This indicates the horizontal distance from the top of the back of the counterweight retaining wall to the top of the slope.

[0157] like Figure 8 As shown, the soil between the second and first rupture surfaces is first analyzed, and its gravity is:

[0158] (15)

[0159] in, Indicates the unit weight of the soil; This indicates the area of ​​the soil.

[0160] like Figure 8 As shown, a moment equilibrium equation is established, and the resistance of the reinforcement on the left side of the first fracture surface is solved based on this equation. :

[0161] (16)

[0162] To simplify the calculation, we select and The intersection of the lines of action of the resultant forces is taken as the center of the moment. , and They are , and The perpendicular distance from the line of action of the torque to the center of the moment is obtained through geometric construction. For the resistance of the reinforcement on the right side of the second fracture surface, , For the pull-out resistance of the reinforcing material, Permissible tensile strength for reinforcing bars; In the calculation, take The tensile strength of the reinforcement is the product of the allowable tensile strength of the reinforcement and the total width of the reinforcement. The total width of the reinforcement is the product of the width of a single reinforcement and the number of reinforcements that the most dangerous sliding surface 6 passes through. Mode 2 obtains the thickness of the reinforced modified soil cushion layer 4, and the number of reinforcements that the most dangerous sliding surface 6 passes through the reinforced modified soil cushion layer 4 can be determined by combining the spacing of the reinforcements. Mode 1 obtains the length of the reinforcements inside the reinforced area 3, and the number of reinforcements that the most dangerous sliding surface 6 passes through in the reinforced area 3 above the reinforced modified soil cushion layer 4 can be determined by combining the position of the most dangerous sliding surface 6. The sum of the two is the number of reinforcements that the most dangerous sliding surface 6 passes through.

[0163] The force exerted by the reinforcing material at the first fracture surface is obtained. .

[0164] like Figure 9 As shown in Figure (a), a static equilibrium equation in the vertical direction is established, and the earth pressure on the second rupture surface is solved based on this equation. :

[0165] (17)

[0166] in, The earth pressure at the first rupture surface. Formed with the normal of the first fracture surface horn( (The internal friction angle of the hypothetical wall back). The earth pressure at the second rupture surface. Formed with the normal of the second fracture surface horn.

[0167] get .

[0168] Establish the static equilibrium equation in the horizontal direction, and solve for the earth pressure at the first rupture surface based on this equation. :

[0169] (18)

[0170] get ;

[0171] but , , .

[0172] Secondly, analyze the soil between the second rupture surface and the back of the retaining wall, and its gravity. for:

[0173]

[0174] like Figure 9 As shown in Figure (b), a static equilibrium equation in the horizontal direction is established, and the earth pressure on the back of the upper wall is solved based on this equation. :

[0175] (19)

[0176] get ;

[0177] Establish the static equilibrium equations in the vertical direction, and solve for the earth pressure on the counterweight platform based on these equations. :

[0178] (20)

[0179] get ;

[0180] but , , , , , , .

[0181] in, , and They are respectively , and The vertical distance from the line of action to the toe of the counterweight retaining wall.

[0182] Finally, the soil between the first fracture surface and the lower wall fracture surface is analyzed, and its gravity is:

[0183] .

[0184] like Figure 8 As shown, a moment balance equation is established, and the resistance of the reinforcement on the left side of the fracture surface of the lower wall is solved based on this equation. :

[0185] (twenty one)

[0186] To simplify the calculation, we select and The intersection of the lines of action of the resultant forces is taken as the center of the moment. , , and They are , , and The perpendicular distance from the line of action of the torque to the center of the moment is obtained through geometric construction. This indicates the resistance of the reinforcing steel on the left side of the fractured surface of the lower wall.

[0187] get .

[0188] like Figure 9 As shown in Figure (c), establish the static equilibrium equations in the horizontal direction:

[0189] (twenty two)

[0190] in, The earth pressure on the back of the lower wall is perpendicular to the normal to the back of the lower wall. horn; Indicates the internal friction angle of the lower wall back. ; The earth pressure on the fracture surface of the lower wall is perpendicular to the normal to the fracture surface of the lower wall. horn.

[0191] Establish the static equilibrium equations in the vertical direction:

[0192] (twenty three)

[0193] Based on the static equilibrium equations in the horizontal and vertical directions, the earth pressure behind the lower wall is solved. :

[0194] get ;

[0195] but , , , , , .

[0196] in, and They are respectively and The vertical distance from the line of action to the toe of the counterweight retaining wall.

[0197] The sliding stability and overturning stability of the counterweight retaining wall 5 are now being verified:

[0198] Gravity of retaining wall :

[0199]

[0200] in, express The vertical distance from the line of action to the toe of the counterweight retaining wall; The area is represented by the height of the counterweight retaining wall obtained from Mode 2.

[0201] Based on the above calculations, the parameters of the retaining wall section are summarized in Table 6.

[0202] Table 6 Cross-sectional parameters of gravity retaining wall

[0203]

[0204] Anti-slip stability coefficient :

[0205] (twenty four)

[0206] in, Let be the coefficient of friction, and take . .

[0207] Anti-overturning stability coefficient :

[0208] (25)

[0209] Anti-overturning stability coefficient and anti-slip stability coefficient The requirements must be met simultaneously.

[0210] This invention overcomes the limitations of traditional designs that treat reinforcement and retaining walls as independent components. It establishes a coupled interaction model between the two under complex stress states, quantifies the synergistic support effect, and transforms it into optimized parameters that can guide construction. This solves the difficulty of accurately incorporating the reinforcement resistance into stability calculations for the counterweight retaining wall 5 under limit equilibrium conditions. In the failure mode calculation of the counterweight retaining wall 5, the synergistic effect between the reinforcement and the counterweight retaining wall 5 is fully considered, significantly reducing the thrust transmitted from the slope crest, thus reducing the earth pressure on the back of the retaining wall.

[0211] 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 semi-rigid composite support structure for high and steep embankments, comprising an embankment support structure and a drainage system, characterized in that, The embankment support structure includes a counterweight retaining wall (5), the back of which has a counterweight platform. The counterweight retaining wall (5) is located on the moderately weathered slate (2) at the toe of the slope. A reinforced area (3) is provided above the counterweight retaining wall (5), and reinforcing bars are laid in layers in the reinforced area (3). A reinforced modified soil cushion layer (4) is laid horizontally between the reinforced area (3) and the top of the counterweight retaining wall (5). Reinforcing materials are laid in the reinforced modified soil cushion layer (4) in a full-section manner. The reinforcing materials inside the reinforced modified soil cushion layer (4) are not anchored to the counterweight retaining wall (5).

2. The semi-rigid composite support structure for high and steep embankments according to claim 1, characterized in that, The reinforced area (3) includes a modified part and an unmodified part. The modified part extends from the surface of the embankment slope to the interior of the embankment to form a platform, and the remaining part is the unmodified part.

3. The semi-rigid composite support structure for high and steep embankments according to claim 1, characterized in that, The area outside the moderately weathered slate (2) on the gentle slope and steep slope above the reinforced area (3) is the fill area (1). The area between the counterweight retaining wall (5), the moderately weathered slate (2) and the reinforced modified soil cushion layer (4) is the fill area (1). A stepped structure is provided at the connection between the fill area (1) behind the counterweight retaining wall (5) and the moderately weathered slate (2).

4. The semi-rigid composite support structure for high and steep embankments according to claim 2, characterized in that, The unmodified part of the reinforced zone (3) is filled with plain soil in layers; the modified part of the reinforced zone (3) is filled with modified soil in layers, wherein the modified soil is a mixture of cement and plain soil in a mass ratio of 2:25-1:

10.

5. The semi-rigid composite support structure for high and steep embankments 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 in the backfill area (1) behind the counterweight retaining wall (5) 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.

6. The design method for a semi-rigid composite support structure for high and steep embankments 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 reinforced area (3), and the reinforcement is pulled out of the slope; by searching the most dangerous sliding surface (6) of the embankment through software, the soil above the most dangerous sliding surface (6) and located inside the reinforced area (3) 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, thereby determining the length of reinforcement inside the reinforced area (3) required to resist the unbalanced thrust; S3, for mode 2: the soil slides out from the top of the counterweight retaining wall (5); calculate the remaining sliding force under different combinations of the thickness of the reinforced modified soil cushion (4) and the height of the counterweight retaining wall (5), and then determine the best combination of the thickness of the reinforced modified soil cushion (4) and the height of the counterweight retaining wall (5). S4, for mode 3: the counterweight retaining wall (5) overturns or slides; based on the height of the counterweight retaining wall (5) determined in mode 2, determine the inclination angles of the hypothetical back wall, upper back wall, and lower back wall, and thus calculate the inclination angles of the three potential fracture surfaces corresponding to the hypothetical back wall, upper back wall, and lower back wall, namely the inclination angles of the second fracture surface, the first fracture surface, and the lower fracture surface; For the soil between the second and first rupture surfaces, a moment balance equation is established. Based on the results of Mode 1 and Mode 2, the number of reinforcing bars that the most dangerous sliding surface (6) passes through is determined, and then the resistance of the reinforcing bars on the left side of the first rupture surface is solved. Establish static equilibrium equations in the horizontal and vertical directions, and solve for the earth pressure at the second rupture surface. Earth pressure at the first rupture surface ; For the soil between the second rupture surface and the back of the retaining wall, based on the earth pressure at the second rupture surface... The earth pressure on the back of the upper wall is solved by using the static equilibrium equations in the horizontal and vertical directions. Earth pressure of the balance platform ; For the soil between the first fracture surface and the lower wall fracture surface, establish a moment equilibrium equation and solve for the resistance of the reinforcement on the left side of the lower wall fracture surface. Establish static equilibrium equations in the horizontal and vertical directions, based on the earth pressure at the first rupture surface. Resistance of the reinforcement on the left side of the first fracture surface Resistance of the reinforcement on the left side of the fractured surface of the lower wall Solve for the earth pressure on the back of the wall. ; S5. Calculate the sliding stability coefficient and overturning stability coefficient based on the calculation results of S4. If they do not meet the requirements of the specification, adjust the size or reinforcement arrangement of the counterweight retaining wall (5) until the sliding stability coefficient and overturning stability coefficient meet the requirements of the specification.

7. The design method for a semi-rigid composite support structure for high and steep embankments according to claim 6, characterized in that, In S4, the earth pressure at the first rupture surface is selected. Earth pressure at the second rupture surface The intersection of the lines of action of the resultant forces is taken as the center of the moment, and the resistance of the reinforcement on the left side of the first fracture surface is... Calculate according to the following formula: ； in, , and They are , and The perpendicular distance from the line of action to the center of the moment. The weight of the soil between the second rupture surface and the first rupture surface. For the resistance of the reinforcement on the right side of the second fracture surface, The allowable tensile force of the reinforcing bar is taken in the calculation. , is the product of the allowable tensile strength of the reinforcement and the total width of the reinforcement. The total width of the reinforcement is the product of the width of a single reinforcement and the number of reinforcements that the most dangerous sliding surface (6) passes through. The thickness of the reinforced modified soil cushion (4) is obtained through mode 2. The number of reinforcements that the most dangerous sliding surface (6) passes through the reinforced modified soil cushion (4) is determined by combining the spacing of the reinforcements. The length of the reinforcement inside the reinforced area (3) is obtained through mode 1. The number of reinforcements that the most dangerous sliding surface (6) passes through in the reinforced area (3) above the reinforced modified soil cushion (4) is determined by combining the position of the most dangerous sliding surface (6). Earth pressure at the second rupture surface Calculate according to the following formula: ； Earth pressure at the first crack Calculate according to the following formula: ； in, This represents the internal friction angle of the imaginary wall back; The dip angle of the first fracture surface; The angle of inclination of the second fracture surface.

8. The design method for a semi-rigid composite support structure for high and steep embankments according to claim 7, characterized in that, In S4, the earth pressure on the back of the upper wall Calculate according to the following formula: ； Earth pressure of the counterweight platform Calculate according to the following formula: ； in, The angle of inclination of the wall back; This represents the weight of the soil between the second rupture surface and the back of the retaining wall.

9. The design method for a semi-rigid composite support structure for high and steep embankments according to claim 8, characterized in that, In S4, the resistance of the reinforcement on the left side of the fracture surface of the lower wall. Calculate according to the following formula: ； in, Indicates the resistance of the reinforcement on the left side of the first fracture surface. The perpendicular distance from the line of action of the torque to the center of the moment; Indicates the earth pressure at the first rupture surface The perpendicular distance from the line of action to the center of the moment; This represents the weight of the soil between the first rupture surface and the rupture surface of the lower wall. The perpendicular distance from the line of action to the center of the moment; Indicates the resistance of the reinforcement on the left side of the fracture surface of the lower wall. The perpendicular distance from the line of action of the torque to the center of the moment; Earth pressure behind the wall Calculate according to the following formula: ； in, The angle of inclination of the fracture surface of the lower wall; Indicates the internal friction angle of the lower wall back; The angle of inclination of the lower wall back.

10. The design method for a semi-rigid composite support structure for high and steep embankments according to claim 6, characterized in that, In S5, the anti-slip stability coefficient Calculate according to the following formula: ； Anti-overturning stability coefficient Calculate according to the following formula: ； in, The coefficient of friction, This indicates the gravity of the counterweight retaining wall (5). Indicates the earth pressure on the back of the wall. Horizontal component of force; Indicates the earth pressure on the back of the wall. The vertical component of the force; Indicates the earth pressure behind the lower wall. Horizontal component of force; Indicates the earth pressure behind the lower wall. The vertical component of the force; , and They are respectively , and The vertical distance from the line of action to the toe of the counterweight retaining wall; and They are respectively and The vertical distance from the line of action to the toe of the counterweight retaining wall; express The vertical distance from the line of action to the toe of the counterweight retaining wall.

Images