Method for calculating equivalent pile length of long and short piles of foundation pit in non-limit state
By equating long and short piles to piles of equal length, and utilizing the principle of overall equivalence of the stress on the retaining structure, the problem of lack of theoretical guidance for long and short pile foundation pit engineering was solved, thus achieving safety assessment and reduction of construction costs.
Patent Information
- Application Number
- CN202511518169.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-23
- Publication Date
- 2026-01-27
AI Technical Summary
Existing technologies lack unified theoretical guidance for long and short pile foundation pit engineering, making it impossible to effectively assess their safety, resulting in high construction costs for long and short piles and limited promotion and application.
The equivalent pile length calculation method for long and short piles in non-limit state foundation pits is adopted, which converts long and short piles into piles of equal length. The equivalent pile length is calculated by formula (1-10) using the principle of overall equivalence of the retaining structure's stress, and then the safety assessment is carried out by applying the existing design specifications.
This study provides a theoretical analysis of the safety of both long and short piles, overcoming the lack of theoretical guidance, guiding the construction of both types of piles, and reducing construction costs.
Smart Images
Figure CN121413067A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of foundation pit support technology, and in particular relates to a method for calculating the equivalent pile length of long and short piles in foundation pits under non-limit state conditions. Background Technology
[0002] With the rapid increase in my country's urban population, the need for developing and utilizing urban space resources is growing. Deep foundation pit engineering, as a crucial step in urban high-rise buildings, rail transit, and large-scale municipal facilities, is becoming increasingly widespread. During the construction of retaining piles for foundation pits, especially in deep soft soil layers or layers with a soft upper layer and a hard lower layer, drilling is difficult and pile driving costs are high. The long-short pile support method, by leveraging the synergistic mechanism of "long piles controlling depth and stability, and short piles controlling shallowness and variation," reduces the grouting depth of the pile foundation, significantly saving construction costs, and has gradually become a common foundation pit support method. Although the long-short pile construction process has significant economic benefits, current design and construction specifications are all for piles of equal length, and cannot assess the safety of long and short piles. Furthermore, current theoretical calculations mostly use limit state analysis, while the soil in actual foundation pit engineering is usually in a non-limit state. These factors combined result in a lack of unified theoretical guidance for the practice of long-short pile engineering, greatly limiting its widespread application. Therefore, this invention provides a method for calculating the equivalent pile length of long and short piles in a non-limit state foundation pit. By utilizing the principle of overall equivalence of the stress on the retaining structure, long and short piles are equivalent to piles of equal length, and then the equivalent pile length is calculated, thereby enabling theoretical analysis of the safety of long and short piles. Summary of the Invention
[0003] In view of the lack of standardized guidelines for the design and construction of long and short piles in foundation pits, and the inability to conduct theoretical analysis on their safety, this invention proposes a method for calculating the equivalent pile length of long and short piles in foundation pits under non-limit state conditions. This method can convert long and short piles into piles of equal length, thereby using the standards for piles of equal length to guide the design and construction.
[0004] A method for calculating the equivalent pile length of long and short piles in a non-limit state foundation pit includes the following steps: S1: Based on the displacement of the pile top in the middle of the foundation pit s max The side length of the foundation pit is 2 a Spacing of retaining piles b and the numbering of retaining piles n The displacement of the pile top of any numbered retaining pile is calculated using formula (1). ; (1) S2: Further based on the pile top displacement of different numbered retaining piles Length of retaining piles L and foundation pit depth h Formula (2) is used to calculate the horizontal displacement at any depth of retaining piles with different numbers. ; (2) Among them, the bottom displacement of the retaining piles with different numbers is The calculation formula is as follows: (3) S3: Calculate the active earth pressure on retaining piles of different numbers based on the magnitude of the pile top displacement. When the pile top displacement of the retaining pile is less than or equal to the active limit displacement ( The active earth pressure on the retaining piles under non-limit state is calculated using formula (4): (4) In the formula: K a The active earth pressure coefficient, K 0 represents the coefficient of earth pressure at rest. s a This is an active limit displacement. z Depth from the ground, γ The unit weight of the soil; When the pile top displacement of the retaining pile is greater than the active limit displacement ( The active earth pressure on the retaining piles is calculated in segments using formula (5): (5) S4: Based on the magnitude of the pit bottom displacement of the retaining piles, calculate the passive earth pressure on retaining piles with different numbers. When the pit bottom displacement of the retaining piles is less than or equal to the passive limit displacement ( The passive earth pressure on the retaining piles in the non-limit state is calculated using formula (6): (6) In the formula: K p This is the passive earth pressure coefficient; When the bottom displacement of the retaining pile is greater than the passive limit displacement ( The passive earth pressure on the retaining piles is calculated in segments using formula (7): (7) S5: Based on the active and passive earth pressures in steps S3 and S4, the overall stress of the long and short piles in the foundation pit is calculated using formula (8): (8) S6: Based on the active and passive earth pressures in steps S3 and S4, the overall stress of the long and short piles in the foundation pit is calculated using formula (9): (9) S7: Based on the principle of equivalent stress of retaining piles, formulas (8) and (9) are combined to calculate the equivalent pile length of the long and short piles in the non-limit state foundation pit: (10) Among them, the active earth pressure coefficient K a The Coulomb active earth pressure coefficient is calculated using the following formula: (11) (12) In the formula: φ The internal friction angle of the soil. φ D To account for the equivalent internal friction angle of soil cohesion, δ It is the friction angle between the retaining structure and the soil.
[0005] Furthermore, the passive earth pressure coefficient K p The Coulomb passive earth pressure coefficient is calculated using the following formula: (13) Furthermore, the displacement of the pile top in the middle of the foundation pit s max The final horizontal displacement to be monitored.
[0006] Furthermore, the numbering of the foundation pit retaining piles. n The size is 10~20, and the foundation pit has no internal support structure.
[0007] Furthermore, the retaining piles of the foundation pit are rigid structures, and the retaining structure does not deform, but only rotates around the bottom of the piles.
[0008] Compared with the prior art, at least one embodiment of the present invention has the following beneficial effects: by utilizing the principle of overall equivalence of the stress of the foundation pit retaining pile structure, the long and short piles of the foundation pit can be equivalent to piles of equal length, and then the safety of them can be evaluated using existing design and construction specifications. This overcomes the dilemma of lack of theoretical guidance in the engineering practice of long and short piles, and can better guide the construction of long and short piles in foundation pits, which has certain value for its promotion and application. Attached Figure Description
[0009] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying 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.
[0010] Figure 1 This is a flowchart of the calculation process of the present invention; Figure 2 This is a plan view of the foundation pit; Figure 3 This is a longitudinal cross-sectional view of the foundation pit; Figure 4 This is a schematic diagram of the stress on the long and short piles in the foundation pit; Figure 5 This is a schematic diagram of the stress on piles of equal length in the foundation pit.
[0011] Among them: 1-retaining pile, 2-bottom of foundation pit, 3-soil layer, 4-edge of foundation pit, 5-ground surface. Detailed Implementation
[0012] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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 skilled in the art without creative effort are within the scope of protection of the present invention.
[0013] This embodiment provides a method for calculating the equivalent pile length of long and short piles in a non-limit state foundation pit. The calculation process is as follows: Figure 1 As shown, the specific calculation steps are as follows: S1: As Figure 2 As shown, number 1 represents the retaining piles, and number 4 represents the edge of the foundation pit. The displacement of the pile tops in the middle of the foundation pit is considered. s max The side length of the foundation pit is 2 a Spacing of retaining piles b and the numbering of retaining piles n The displacement of the pile top of any numbered retaining pile is calculated using formula (1). ; (1) S2: As Figure 3 As shown, number 2 represents the bottom of the foundation pit, and number 3 represents the stratum. The displacement of the top of the retaining piles with different numbers is shown in the figure. Length of retaining piles L and foundation pit depth h Formula (2) is used to calculate the horizontal displacement at any depth of retaining piles with different numbers. ; (2) Among them, the bottom displacement of the retaining piles with different numbers is The calculation formula is as follows: (3) S3: Calculate the active earth pressure on retaining piles of different numbers based on the magnitude of the pile top displacement. When the pile top displacement of the retaining pile is less than or equal to the active limit displacement ( The active earth pressure on the retaining piles in the non-limit state is calculated using formula (4): (4) In the formula: K a The active earth pressure coefficient, K 0 represents the coefficient of earth pressure at rest. s a This is an active limit displacement. z Depth from the ground, γ The unit weight of the soil; When the pile top displacement of the retaining pile is greater than the active limit displacement ( The active earth pressure on the retaining piles is calculated in segments using formula (5): (5) S4: Based on the magnitude of the pit bottom displacement of the retaining piles, calculate the passive earth pressure on retaining piles with different numbers. When the pit bottom displacement of the retaining piles is less than or equal to the passive limit displacement ( The passive earth pressure on the retaining piles in the non-limit state is calculated using formula (6): (6) In the formula: K p This is the passive earth pressure coefficient; When the bottom displacement of the retaining pile is greater than the passive limit displacement ( The passive earth pressure on the retaining piles is calculated in segments using formula (7): (7) S5: As Figure 4 As shown, where label 5 represents the ground surface, the overall stress on the long and short piles in the foundation pit is calculated using formula (8) based on the active and passive earth pressures in steps S3 and S4: (8) S6: As Figure 5 As shown, based on the active and passive earth pressures in steps S3 and S4, the overall stress on the long and short piles in the foundation pit is calculated using formula (9): (9) S7: Based on the principle of equivalent stress of retaining piles, formulas (8) and (9) are combined to calculate the equivalent pile length of the long and short piles in the non-limit state foundation pit: (10) Among them, the active earth pressure coefficientK a The Coulomb active earth pressure coefficient is calculated using the following formula: (11) (12) In the formula: φ The internal friction angle of the soil. φ D To account for the equivalent internal friction angle of soil cohesion, δ It is the friction angle between the retaining structure and the soil.
[0014] Furthermore, the passive earth pressure coefficient K p The Coulomb passive earth pressure coefficient is calculated using the following formula: (13) Furthermore, the displacement of the pile top in the middle of the foundation pit s max The final horizontal displacement to be monitored.
[0015] Furthermore, the numbering of the foundation pit retaining piles. n The size is 10~20, and the foundation pit has no internal support structure.
[0016] Furthermore, the retaining piles of the foundation pit are rigid structures, and the retaining structure does not deform, but only rotates around the bottom of the piles, such as... Figure 3 As shown.
[0017] Implementation Case: To verify the rationality of the above formula for calculating the equivalent pile length of long and short pile foundation pits, the following calculation example is analyzed. The soil stratum is a single layer, silty clay, with specific parameters shown in Table 1. The foundation pit is a square pile pit with equal-length piles, with specific parameters shown in Table 2. Based on the method for selecting monitoring and early warning values in the monitoring technical standards, the monitoring and early warning values for the retaining structure are selected. s max The length is 40 mm. Substituting the relevant parameters into the above calculation formula, the equivalent pile length of the long pile (12 m) and short pile (8 m) is 10.29 m.
[0018] Table 1 Soil parameters
[0019] Table 2 Excavation Pit Parameters
[0020] The above embodiments are merely illustrative examples of the present invention and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all embodiments here, and obvious variations or modifications derived therefrom are still within the scope of protection of this invention.
Claims
1. A method for calculating the equivalent pile length of long and short piles in a non-limit state foundation pit, characterized in that, Includes the following steps: S1: Based on the displacement of the pile top in the middle of the foundation pit s max The side length of the foundation pit is 2 a Spacing of retaining piles b and the numbering of retaining piles n The displacement of the pile top of any numbered retaining pile is calculated using formula (1). ; （1） S2: Further based on the pile top displacement of different numbered retaining piles Length of retaining piles L and foundation pit depth h Formula (2) is used to calculate the horizontal displacement at any depth of retaining piles with different numbers. ; （2） Among them, the bottom displacement of the retaining piles with different numbers is The calculation formula is as follows: （3） S3: Calculate the active earth pressure on retaining piles of different numbers based on the magnitude of the pile top displacement. When the pile top displacement of the retaining pile is less than or equal to the active limit displacement ( The active earth pressure on the retaining piles under non-limit state is calculated using formula (4): （4） In the formula: K a The active earth pressure coefficient, K 0 represents the coefficient of earth pressure at rest. s a This is an active limit displacement. z The depth from the ground. γ The unit weight of the soil; When the pile top displacement of the retaining pile is greater than the active limit displacement ( The active earth pressure on the retaining piles is calculated in segments using formula (5): （5） S4: Calculate the passive earth pressure on retaining piles of different numbers based on the magnitude of the pit bottom displacement of the retaining piles. When the pit bottom displacement of the retaining piles is less than or equal to the passive limit displacement ( The passive earth pressure on the retaining piles in the non-limit state is calculated using formula (6): （6） In the formula: K p This is the passive earth pressure coefficient; When the bottom displacement of the retaining pile is greater than the passive limit displacement ( The passive earth pressure on the retaining piles is calculated in segments using formula (7): （7） S5: Based on the active and passive earth pressures in steps S3 and S4, the overall stress of the long and short piles in the foundation pit is calculated using formula (8): （8） S6: Based on the active and passive earth pressures in steps S3 and S4, the overall stress of the long and short piles in the foundation pit is calculated using formula (9): （9） S7: Based on the principle of equivalent stress of retaining piles, formulas (8) and (9) are combined to calculate the equivalent pile length of the long and short piles in the foundation pit under non-limit state: （10）。 2. The method for calculating the equivalent pile length of long and short piles in a non-limit state foundation pit according to claim 1, characterized in that, The active earth pressure coefficient K a The Coulomb active earth pressure coefficient is calculated using the following formula: （11） （12） In the formula: φ The internal friction angle of the soil. φ D To account for the equivalent internal friction angle of soil cohesion, δ It is the friction angle between the retaining structure and the soil.
3. The method for calculating the equivalent pile length of long and short piles in a non-limit state foundation pit according to claim 1, characterized in that, The passive earth pressure coefficient mentioned above K p The Coulomb passive earth pressure coefficient is calculated using the following formula: （13）。 4. The method for calculating the equivalent pile length of long and short piles in a non-limit state foundation pit according to claim 1, characterized in that, The displacement of the pile top in the middle of the foundation pit s max The final horizontal displacement to be monitored.
5. The method for calculating the equivalent pile length of long and short piles in a non-limit state foundation pit according to claim 1, characterized in that, The foundation pit retaining pile number n The size is 10~20, and the foundation pit has no internal support structure.
6. The method for calculating the equivalent pile length of long and short piles in a non-limit state foundation pit according to claim 1, characterized in that, The aforementioned foundation pit retaining piles are rigid structures, and the retaining structure does not deform, but only rotates around the bottom of the piles.