Historical building lime-sand pile foundation reinforcement construction method based on counter-force calculation model

Abstract

The invention discloses a historical building lime-sand pile foundation reinforcement construction method based on a counter-force calculation model, and belongs to the technical field of foundation treatment and foundation engineering. The historical building lime-sand pile foundation reinforcement construction method comprises the steps that S1, current situation evaluation is conducted on a historical building, and construction preparation is made; s2, according to the data obtained in the S1, an elastic foundation beam model is established, and a counter-force threshold value needed by a reinforcing area is calculated; s3, the mix proportion, the pile length, the pile diameter and the pile distance of the lime-sand piles with the needed bearing capacity are determined; s4, cement-sand pile foundation reinforcement construction work is carried out; s5, detection in the construction process and after completion is carried out; s6, monitoring foundation settlement and stress change data in real time, and optimizing a construction scheme and a later maintenance strategy; according to the historical building lime-sand pile foundation reinforcement construction method based on the counter-force calculation model, through accurate calculation and a reasonable construction scheme, the foundation bearing capacity and stability of a historical building can be effectively improved on the premise that the original style and appearance of the historical building are not damaged, and the safety and durability of the building are ensured.

Description

Technical Field

[0001] The invention relates to the technical field of foundation treatment and basic engineering, and in particular to a construction method for reinforcing a lime-sand pile foundation of a historical building based on a reaction force calculation model. Background Art

[0002] Historical buildings usually have important cultural and historical values, but over time, their foundations may age and settle, affecting the safety and stability of the buildings. Therefore, strengthening the foundations of historical buildings is a key part of conservation and restoration work. However, due to the uniqueness and sensitivity of historical buildings, traditional reinforcement methods may not be applicable, and more sophisticated and technically demanding reinforcement solutions are needed.

[0003] Therefore, this paper designs a construction method for reinforcing the foundation of historical buildings with lime-sand piles based on a reaction force calculation model. Lime-sand piles are a common foundation reinforcement method, especially suitable for the treatment of soft soil foundations. It forms a composite foundation by driving a pile body made of a mixture of cement (or lime) and sand into the soft soil layer, thereby improving the overall performance of the foundation. For historical buildings, lime-sand pile reinforcement technology has the advantages of low vibration, high adaptability and economy. The reaction force calculation model is used to evaluate and design the foundation reinforcement scheme, helping engineers to accurately predict the bearing capacity and deformation characteristics of the reinforced foundation, and ensure the effectiveness and safety of the reinforcement scheme. Summary of the invention

[0004] The purpose of the present invention is to provide a construction method for reinforcing the foundation of a historical building with lime-sand piles based on a reaction force calculation model, so as to solve the problems existing in the above-mentioned background technology.

[0005] To achieve the above object, the present invention provides a construction method for reinforcing the foundation of a historical building with lime-sand piles based on a reaction force calculation model, comprising the following steps: S1. Conduct status assessment of historic buildings and prepare for construction; S2. According to the data obtained in step S1, an elastic foundation beam model is established to calculate the reaction force threshold required for the reinforcement area; S3. According to the required bearing capacity of the historical building, the lime-sand pile ratio, pile length, pile diameter and pile spacing of the required bearing capacity are determined by using the lime-sand pile reaction force tester; S4. Carry out lime-sand pile foundation reinforcement construction work; S5. Conduct quality control inspection during construction and inspection after completion; S6. Integrate IoT sensors to monitor foundation settlement and stress change data in real time, and optimize construction plans and subsequent maintenance strategies through big data analysis.

[0006] Preferably, the current status assessment in step S1 includes structural assessment, geological survey and risk assessment. The structural assessment includes assessment of the materials, structural form and bearing capacity of the historical buildings; the geological survey is used to obtain information such as foundation soil parameters, soil layer distribution, groundwater level and bearing capacity; the risk assessment is used to assess the risks that may arise during the construction process, such as settlement, tilting, cracking, etc., and to formulate corresponding emergency plans; the bearing capacity information is obtained by conducting collapsible tests and soil shear tests on the soil samples obtained.

[0007] Preferably, step S2 specifically includes: S21, obtaining soil layer distribution and physical and mechanical properties of the foundation according to the geological survey in step S1, and clarifying foundation parameters for subsequent calculations; S22. Calculate the loads transferred from the superstructure of the historic building to the foundation; S23. Calculation of foundation loads of historic buildings and requirements for considering deformation characteristics; S24. Calculate the reaction force threshold required for the foundation reinforcement area based on the reaction balance relationship between the superstructure load on the foundation and the foundation soil.

[0008] Preferably, the calculation of the foundation bearing capacity in step S23 is specifically as follows: the foundation bearing capacity is determined by a plate load test, and the calculation formula of the soil deformation modulus is obtained according to the elastic semi-infinite surface loading principle: ; in, is the coefficient, is the Poisson's ratio of the foundation soil, is the pressure on the bottom of the pressure plate, For load The corresponding settlement, is the diameter of the circular bearing plate, or the side length of the square bearing plate; the ultimate bearing capacity of the foundation is calculated based on the soil deformation modulus, and the formula is: ; in, is the shear strength, , , is the coefficient calculated based on its characteristic parameters, is the effective stress, For the base bottom heavy, is the base area; in actual use, a safety factor is introduced to calculate the allowable bearing capacity used in the actual design. The calculation formula is: ; in, is the safety factor.

[0009] Preferably, the specific implementation steps of analyzing the deformation characteristics of the foundation in step S23 are as follows: ① Determine the foundation parameters, load conditions and foundation parameters, which can be obtained through field tests or laboratory tests; ②, Establish the Boussinesd solution elasticity theory model and its corresponding mathematical equations; ③. Calculate the settlement according to the mathematical equation in step ②, including single-point settlement and multi-point settlement. For single-point settlement, calculate the settlement of each specific point; for multi-point settlement, repeat the calculation for multiple points within the entire foundation range to obtain a complete settlement distribution map; ④. Draw the calculated settlement values ​​of each point into a graph to form a settlement curve, which is used to intuitively understand the distribution law of settlement; ⑤. Evaluate the overall stability and potential risks of the building by comparing the settlement amounts at different locations; at the same time, calculate the inclination based on the settlement difference at the four corners of the building to determine whether it exceeds the allowable value in the specification; ⑥ Considering the secondary consolidation effect and creep phenomenon, use empirical formulas or numerical simulation methods for long-term prediction.

[0010] Preferably, the mathematical equation in step ② includes a stress component and a displacement component, and the stress component expression is: Vertical normal stress: , the negative sign indicates compressive stress; Radial normal stress: ; Shear force: ; in, is the load, specifically the concentrated force applied vertically downward to a point on the ground surface; For load A rectangular coordinate system established for the origin; is the distance from the load point to the calculation point; The displacement component expression is: Vertical displacement: ; Radial displacement: .

[0011] Preferably, the reaction force threshold value of step S24 is calculated as: ; in, is the foundation reaction force, is the design value of the vertical force transmitted from the superstructure to the top surface of the foundation, The weight of the foundation and the weight of the soil on the foundation. is the base area; and .

[0012] Preferably, step S3 specifically includes: S31. According to the structural characteristics of the historical building and the reaction force threshold calculated in step S2, the target bearing capacity to be achieved after the lime-sand pile foundation reinforcement is determined. The formula is: ; S32. Conduct field tests on lime-sand piles with different mix ratios, pile lengths, pile diameters, and pile spacings using a lime-sand pile reaction force tester, monitor the reaction force changes of the lime-sand piles in real time, and record the test data under different working conditions; S33. Analyze the test data, analyze the relationship between the lime-sand pile ratio, pile length, pile diameter, pile spacing and bearing capacity, and determine the lime-sand pile ratio, pile length, pile diameter and pile spacing required for the foundation reinforcement of historical buildings.

[0013] Preferably, step S4 specifically includes: S41. According to the reinforcement plan, accurately mark the position of each pile on the ground, use a drilling rig to drill holes according to the designed depth, and ensure that the hole diameter and verticality meet the requirements; S42. After the drilling is completed, the hole is cleaned to remove the mud and debris in the hole to ensure that the bottom of the hole is clean; S43, mixing the lime sand according to the ratio determined in step S33, stirring evenly to ensure the uniformity and fluidity of the mixture, injecting the mixed lime sand into the hole through a pouring device, and vibrating while pouring to ensure that the lime sand densely fills the hole; S44. After pouring is completed, treat the top of the pile to ensure that it is flat and dense to prevent water loss.

[0014] Preferably, step S5 specifically includes: S51. During the construction process, the deformation of the foundation is monitored in real time to ensure that the construction process is smooth and controllable. According to the monitoring results, the construction parameters, including the lime-sand ratio and the pouring speed, are adjusted in time to ensure the construction quality; S52. Conduct static load tests on completed ash-sand piles to check whether their bearing capacity meets the design requirements; use non-destructive testing technology (such as ultrasound, radar, etc.) to check the internal quality of ash-sand piles to ensure their integrity; and conduct regular settlement observations within a period of time after construction to record the settlement of the building and ensure the reinforcement effect.

[0015] Therefore, the present invention adopts the above-mentioned historical building lime-sand pile foundation reinforcement construction method based on the reaction force calculation model, which has the following beneficial effects: (1) Through the reaction force calculation model, accurate acquisition of basic data, establishment of mathematical model, solution of foundation bearing capacity, calculation of deformation characteristics, and the use of numerical simulation methods, the performance of the foundation can be effectively predicted and controlled; (2) Through the elastic theory model, accurate acquisition of foundation and subgrade parameters, establishment of mathematical models, solution of settlement, drawing of settlement curves, analysis of uneven settlement, long-term settlement prediction, and the use of numerical simulation methods, the performance of the reinforced foundation can be effectively predicted and controlled.

[0016] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of the construction method for reinforcing the foundation of a historical building with lime-sand piles based on a reaction force calculation model of the present invention; Figure 2 A schematic diagram of calculating the threshold value of the reaction force required for the reinforcement area according to an embodiment of the present invention; Figure 3 Schematic diagram of the reaction force calculation model according to an embodiment of the present invention. DETAILED DESCRIPTION

[0018] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0019] See also Figure 1-Figure 3 The construction method for reinforcing the foundation of historical buildings with lime-sand piles based on the reaction force calculation model includes the following steps: S1. Conduct status assessment of historical buildings and make preparations for construction; status assessment includes structural assessment, geological survey and risk assessment. Structural assessment includes assessment of materials, structural forms and bearing capacity of historical buildings; geological survey is used to obtain information such as foundation soil parameters, soil layer distribution, groundwater level and bearing capacity; risk assessment is used to assess risks that may arise during construction, such as settlement, tilting, cracking, etc., and formulate corresponding emergency plans; bearing capacity information is obtained by conducting collapsible tests and soil shear tests on the soil samples obtained.

[0020] S2. According to the data obtained in step S1, an elastic foundation beam model is established to calculate the reaction force threshold required for the reinforcement area; specifically, the following steps are included: S21, obtaining soil layer distribution and physical and mechanical properties of the foundation according to the geological survey in step S1, and clarifying foundation parameters for subsequent calculations; S22. Calculate the loads transferred from the superstructure of the historic building to the foundation; S23. Calculate the foundation load of historical buildings and consider the requirements of deformation characteristics; the calculation of foundation bearing capacity is as follows: determine the foundation bearing capacity through a plate load test, and obtain the calculation formula of soil deformation modulus based on the elastic semi-infinite surface loading principle: ; in, is the coefficient, is the Poisson's ratio of the foundation soil, is the pressure on the bottom of the pressure plate, For load The corresponding settlement, is the diameter of the circular bearing plate, or the side length of the square bearing plate; the ultimate bearing capacity of the foundation is calculated based on the soil deformation modulus, and the formula is: ; in, is the shear strength, , , is the coefficient calculated based on its characteristic parameters, is the effective stress, For the base bottom heavy, is the base area; in actual use, a safety factor is introduced to calculate the allowable bearing capacity used in the actual design. The calculation formula is: ; in, is the safety factor.

[0021] The specific steps for analyzing foundation deformation characteristics are as follows: ① Determine the foundation parameters, load conditions and foundation parameters, which can be obtained through field tests or laboratory tests; ② Establish the Boussinesd solution elastic theory model and its corresponding mathematical equation. The mathematical equation includes stress component and displacement component. The stress component expression is: Vertical normal stress: , the negative sign indicates compressive stress; Radial normal stress: ; Shear force: ; in, is the load, specifically the concentrated force applied vertically downward to a point on the ground surface; For load A rectangular coordinate system established for the origin; is the distance from the load point to the calculation point; The displacement component expression is: Vertical displacement: ; Radial displacement: ; ③, according to the mathematical equation of step S2, the settlement is calculated, including single-point settlement and multi-point settlement. For single-point settlement, the settlement of each specific point is calculated; for multi-point settlement, the calculation is repeated for multiple points within the entire foundation range to obtain a complete settlement distribution map; ④. Draw the calculated settlement values ​​of each point into a graph to form a settlement curve, which is used to intuitively understand the distribution law of settlement; ⑤. Evaluate the overall stability and potential risks of the building by comparing the settlement amounts at different locations; at the same time, calculate the inclination based on the settlement difference at the four corners of the building to determine whether it exceeds the allowable value in the specification; ⑥ Considering the secondary consolidation effect and creep phenomenon, use empirical formulas or numerical simulation methods for long-term prediction.

[0022] S24. According to the reaction balance relationship between the upper structure load and the foundation soil, the reaction threshold required for the foundation reinforcement area is calculated. The calculation formula is: ; in, is the foundation reaction force, is the design value of the vertical force transmitted from the superstructure to the top surface of the foundation, The weight of the foundation and the weight of the soil on the foundation. is the base area; and .

[0023] S3. According to the required bearing capacity of the historical building, use the lime-sand pile reaction force tester to determine the lime-sand pile mix ratio, pile length, pile diameter, and pile spacing of the required bearing capacity; specifically including: S31. According to the structural characteristics of the historical building and the reaction force threshold calculated in step S2, the target bearing capacity to be achieved after the lime-sand pile foundation reinforcement is determined. The formula is: ; S32. Conduct field tests on lime-sand piles with different mix ratios, pile lengths, pile diameters, and pile spacings using a lime-sand pile reaction force tester, monitor the reaction force changes of the lime-sand piles in real time, and record the test data under different working conditions; S33. Analyze the test data, analyze the relationship between the lime-sand pile ratio, pile length, pile diameter, pile spacing and bearing capacity, and determine the lime-sand pile ratio, pile length, pile diameter and pile spacing required for the foundation reinforcement of historical buildings.

[0024] S4. Carry out lime-sand pile foundation reinforcement construction work; specifically including: S41. According to the reinforcement plan, accurately mark the position of each pile on the ground, use a drilling rig to drill holes according to the designed depth, and ensure that the hole diameter and verticality meet the requirements; S42. After the drilling is completed, the hole is cleaned to remove the mud and debris in the hole to ensure that the bottom of the hole is clean; S43, mixing the lime sand according to the ratio determined in step S33, stirring evenly to ensure the uniformity and fluidity of the mixture, injecting the mixed lime sand into the hole through a pouring device, and vibrating while pouring to ensure that the lime sand densely fills the hole; S44. After pouring is completed, treat the top of the pile to ensure that it is flat and dense to prevent water loss.

[0025] S5. Conduct quality control inspections during the construction process and inspections after completion; specifically include: S51. During the construction process, the deformation of the foundation is monitored in real time to ensure that the construction process is smooth and controllable. According to the monitoring results, the construction parameters, including the lime-sand ratio and the pouring speed, are adjusted in time to ensure the construction quality; S52. Conduct static load tests on completed ash-sand piles to check whether their bearing capacity meets the design requirements; use non-destructive testing technology (such as ultrasound, radar, etc.) to check the internal quality of ash-sand piles to ensure their integrity; and conduct regular settlement observations within a period of time after construction to record the settlement of the building and ensure the reinforcement effect.

[0026] S6. Regularly inspect the reinforced foundation and buildings to check for any abnormalities. If any abnormalities are found, take timely measures to carry out repairs and maintenance to ensure the safety and stability of the building. Integrate IoT sensors to monitor foundation settlement and stress change data in real time. Optimize construction plans and post-maintenance strategies through big data analysis, thereby conducting long-term monitoring of the building. The accumulated data can be used for subsequent analysis. By regularly analyzing the monitoring data, the reinforcement effect can be evaluated to provide a basis for future maintenance and management.

[0027] A historical building in a certain city was built in the late Qing Dynasty and early Republic of China. The courtyard faces south and north, is 33 meters long from east to west, 32 meters wide from north to south, covers an area of ​​about 1,050 square meters, and has a construction area of ​​485 square meters. It adopts a combination of Chinese and Western construction techniques, Western-style floor plan and indoor and outdoor decoration, and Chinese-style roof tile roof. The main structure of the building was reinforced and repaired. After three months of construction, the construction of all lime sand piles was completed. The following reinforcement results can prove the effectiveness of this embodiment: 1. Settlement control Before construction, the predicted single-point settlement of the four corners of the building were: 15mm at corner A, 18mm at corner B, 16mm at corner C, and 14mm at corner D. The overall settlement trend was uneven, and the calculated inclination was close to 0.3%, close to the edge of danger, reflecting the worrying stability of the foundation. After the reinforcement construction was completed, after a period of settlement observation, the settlement of the four corners tended to be stable, and the final settlement was: 3mm at corner A, 4mm at corner B, 3.5mm at corner C, and 2.5mm at corner D. The inclination was reduced to less than 0.1%, meeting the extremely high requirements of ancient buildings for stability. The building no longer had an obvious tilt on the exterior, and restored its due solemnity and beauty.

[0028] 2. Carrying capacity improvement Before construction, the characteristic value of the original foundation soil bearing capacity was determined to be 120kPa through flat plate load tests and other means. Taking into account the weight of the building's superstructure and possible subsequent usage scenarios, the reaction force calculation model showed that the foundation bearing capacity needed to be increased to at least 200kPa to ensure the safety and stability of the building.

[0029] After reinforcement with lime-sand piles, static load tests showed that the foundation bearing capacity reached above 220kPa, meeting and exceeding the expected target, ensuring that the building's structural bearing capacity was effectively enhanced. The subsequent building structure did not experience problems such as cracking and deformation due to insufficient bearing capacity.

[0030] 3. Quality inspection of lime sand piles Non-destructive testing (such as ultrasonic testing) of the ash-sand piles during the construction process showed that the pile body had good integrity, without common quality defects such as broken piles and neck shrinkage. The concrete density of the pile body reached more than 95% of the design requirements, ensuring that each ash-sand pile can effectively play its role in bearing and transferring loads.

[0031] The lime-sand piles were sampled after tests on combinations of different mix ratios, pile lengths, pile diameters and pile spacings, and the optimal mix ratio was determined to be cement: sand: lime = 3:2:5 (mass ratio), with a pile length of 8m, a pile diameter of 0.5m and a pile spacing of 1.2m. The lime-sand piles constructed according to these parameters performed stably in the reaction force test, with the average single pile reaction force exceeding 300kN, providing solid support for the overall foundation reinforcement effect.

[0032] At the same time, inspection personnel were arranged to conduct regular observations. After observation, it was found that the B and C corners of the building had an upward trend within 2 weeks after implementation, which were 1mm and 2mm respectively, and then stopped developing and no longer changed. The A corner has stabilized and no longer settled. After that, the settlement was observed within 1-2 years after completion. The foundations in the reinforced area were basically all stable, proving that the implementation of this method can effectively reinforce the foundation.

[0033] Therefore, the present invention adopts the above-mentioned historical building lime-sand pile foundation reinforcement construction method based on the reaction force calculation model, which not only helps to protect and repair historical buildings, but also improves the safety and stability of their structures.

[0034] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A construction method for reinforcing the foundation of a historical building using lime-sand piles based on a reaction force calculation model, characterized in that: The following steps are involved: S1. Assess the current status of historic buildings and prepare for construction; S2. According to the data obtained in step S1, an elastic foundation beam model is established to calculate the reaction force threshold required for the reinforcement area; S3. According to the required bearing capacity of the historical building, the lime-sand pile ratio, pile length, pile diameter and pile spacing of the required bearing capacity are determined by using the lime-sand pile reaction force tester; S4. Carry out lime-sand pile foundation reinforcement construction; S5. Conduct quality control inspection during construction and inspection after completion; S6. Integrate IoT sensors to monitor foundation settlement and stress change data in real time, and optimize construction plans and subsequent maintenance strategies through big data analysis.

2. The method for reinforcing the foundation of a historical building using lime-sand piles based on a reaction force calculation model according to claim 1 is characterized in that: The current status assessment in step S1 includes structural assessment, geological survey and risk assessment. The structural assessment includes the assessment of the materials, structural form and bearing capacity of the historical buildings; the geological survey is used to obtain foundation soil parameters, soil layer distribution, groundwater level and bearing capacity information; the risk assessment is used to assess the risks arising during the construction process and formulate corresponding emergency plans; the bearing capacity information is obtained by conducting collapsible tests and soil shear tests on the soil samples obtained.

3. The method for reinforcing the foundation of a historical building using lime-sand piles based on a reaction force calculation model according to claim 2 is characterized in that: Step S2 specifically includes: S21, obtaining soil layer distribution and physical and mechanical properties of the foundation according to the geological survey in step S1, and clarifying foundation parameters for subsequent calculations; S22. Calculate the loads transferred from the superstructure of the historic building to the foundation; S23. Calculation of foundation loads of historic buildings and requirements for considering deformation characteristics; S24. Calculate the reaction force threshold required for the foundation reinforcement area based on the reaction balance relationship between the superstructure load on the foundation and the foundation soil.

4. The method for reinforcing the foundation of a historical building using lime-sand piles based on a reaction force calculation model according to claim 3 is characterized in that: The calculation of the foundation bearing capacity in step S23 is specifically as follows: the foundation bearing capacity is determined by a plate load test, and the calculation formula of the soil deformation modulus is obtained according to the elastic semi-infinite surface loading principle: ； in, is the coefficient, is the Poisson's ratio of the foundation soil, is the pressure on the bottom of the pressure plate, For load The corresponding settlement, is the diameter of the circular bearing plate, or the side length of the square bearing plate; the ultimate bearing capacity of the foundation is calculated based on the soil deformation modulus, and the formula is: ； in, is the shear strength, , , is the coefficient calculated based on its characteristic parameters, is the effective stress, For the base bottom heavy, is the base area; in actual use, a safety factor is introduced to calculate the allowable bearing capacity used in the actual design. The calculation formula is: ； in, is the safety factor.

5. The method for reinforcing the foundation of a historical building using lime-sand piles based on a reaction force calculation model according to claim 3 is characterized in that: The specific implementation steps of analyzing the foundation deformation characteristics in step S23 are as follows: ① Determine the foundation parameters, load conditions and foundation parameters, which can be obtained through field tests or laboratory tests; ②, Establish the Boussinesd solution elasticity theory model and its corresponding mathematical equations; ③. Calculate the settlement according to the mathematical equation in step ②, including single-point settlement and multi-point settlement. For single-point settlement, calculate the settlement of each specific point; for multi-point settlement, repeat the calculation for multiple points within the entire foundation range to obtain a complete settlement distribution map; ④. Draw the calculated settlement values ​​of each point into a graph to form a settlement curve, which is used to intuitively understand the distribution law of settlement; ⑤. Evaluate the overall stability and potential risks of the building by comparing the settlement amounts at different locations; at the same time, calculate the inclination based on the settlement difference at the four corners of the building to determine whether it exceeds the allowable value in the specification; ⑥ Considering the secondary consolidation effect and creep phenomenon, long-term prediction is carried out using empirical formulas or numerical simulation methods; The calculated settlement under load is used to adjust the reaction force threshold to ensure that the foundation deformation does not exceed the allowable value.

6. The method for reinforcing the foundation of a historical building using lime-sand piles based on a reaction force calculation model according to claim 5 is characterized in that: The mathematical equation in step ② includes stress component and displacement component. The stress component expression is: Vertical normal stress: , the negative sign indicates compressive stress; Radial normal stress: ; Shear force: ; in, is the load, specifically the concentrated force applied vertically downward to a point on the ground surface; For load A rectangular coordinate system established for the origin; is the distance from the load point to the calculation point; The displacement component expression is: Vertical displacement: ; Radial displacement: .

7. The method for reinforcing the foundation of a historical building using lime-sand piles based on a reaction force calculation model according to claim 3 is characterized in that: The reaction force threshold of step S24 is calculated as: ； in, is the foundation reaction force, is the design value of the vertical force transmitted from the superstructure to the top surface of the foundation, The weight of the foundation and the weight of the soil on the foundation. is the base area; and .

8. The method for reinforcing the foundation of a historical building using lime-sand piles based on a reaction force calculation model according to claim 7 is characterized in that: Step S3 specifically includes: S31. According to the structural characteristics of the historical building and the reaction force threshold calculated in step S2, the target bearing capacity to be achieved after the lime-sand pile foundation reinforcement is determined. The formula is: ； S32. Conduct field tests on lime-sand piles with different mix ratios, pile lengths, pile diameters, and pile spacings using a lime-sand pile reaction force tester, monitor the reaction force changes of the lime-sand piles in real time, and record the test data under different working conditions; S33. Analyze the test data, analyze the relationship between the lime-sand pile ratio, pile length, pile diameter, pile spacing and bearing capacity, and determine the lime-sand pile ratio, pile length, pile diameter and pile spacing required for the foundation reinforcement of historical buildings.

9. The method for reinforcing the foundation of a historical building using lime-sand piles based on a reaction force calculation model according to claim 1, characterized in that: Step S4 specifically includes: S41. According to the reinforcement plan, mark the position of each pile on the ground and use a drilling rig to drill holes according to the designed depth; S42. After the drilling is completed, the hole is cleaned to remove the mud and debris in the hole to ensure that the bottom of the hole is clean; S43, mixing the lime sand according to the ratio determined in step S33, stirring evenly, injecting the mixed lime sand into the hole through a pouring device, and vibrating while pouring; S44. After pouring is completed, the pile top is processed.

10. The method for reinforcing the foundation of a historical building using lime-sand piles based on a reaction force calculation model according to claim 1, characterized in that: Step S5 specifically includes: S51. During the construction process, the deformation of the foundation is monitored in real time, and the construction parameters, including the lime-sand ratio and the pouring speed, are adjusted in a timely manner according to the monitoring results; S52. Conduct static load tests on completed lime sand piles to check whether their bearing capacity meets the design requirements; use non-destructive testing technology to check the internal quality of lime sand piles; and conduct regular settlement observations within a period of time after construction to record the settlement of the building.

Images