Study on the Technique of Ellipse Excavation and Tilt Correction of the Stone Statues of the Northern Song Dynasty Imperial Mausoleum

: This article takes the stone statues of the Northern Song Dynasty imperial mausoleum as the research object. Aiming at the characteristics of the stone statues low weight and small building area, combined with the serious weathering of the stone statues, the reasons for the inclination and the defects of the traditional round soil excavation holes, an elliptical soil excavation correction method is proposed. Adopt the method of combining numerical simulation and experiment to carry out the research of elliptical excavation and tilt correction of stone statues. Research indicates: The settlement difference between the excavation side and the non-excavation side increases with the increase of the span-to-height ratio of the excavation hole; The shallower the depth of the digging hole, the greater the settlement difference between the digging side and the non-digging side; The settlement difference between the digging side and the non-digging side decreases with the increase of the hole spacing; The settlement of the superstructure mainly occurs within 4 to 5 hours after the soil is excavated, and then enters a slow growth stage, and finally gradually stabilizes; During the test, the failure of the digging hole belongs to plastic failure. The damage of the digging hole is firstly destroyed from both sides of the hole, and the upper part of the hole is destroyed immediately, and the upper structure edge is destroyed first.


1.Introduction
Tomb stone carvings, also known as "Stone Statues", are one of the main elements of the tomb [1] . At present, the surviving stone statues have caused various diseases due to natural erosion and man-made destruction. Among them, the tilt of the stone statues is one of the most important diseases affecting its overall stability. There are many research results in the field of tilt correction technology for existing buildings at home and abroad. Terracina [2] first proposed the idea of rectifying tilt to relieve the stress of the building foundation in the plan to save the Leaning Tower of Pisa. Tugaenko [3] successfully corrected the tilt of a 16-story residential building by using the flooding method. Green [4] studied the influence of multiple circular excavation holes with different diameters on the stress distribution of the foundation under different spatial conditions. Liu Zude [5] put forward the technique of rectification and reinforcement of foundation stress relief method. Qin Shanglin [6] used an engineering example in which a 6-story comprehensive building was seriously inclined due to the existence of a weak soil layer underneath the foundation, and proposed a combination of horizontal excavation and grouting reinforcement to correct inclination and reinforcement.Zhu Yanpeng [7] proposed an expansion correction method for inclined buildings in collapsible loess areas, and derives the calculation formula for the amount of expansion material with the aid of the pore compaction principle.Zhang Xuqiang [8] took the Elephant Temple Pagoda in Heyang, Shaanxi as the research object, and analyzed the relationship between the water content of loess and the amount of compression combined with the indoor compression test.Cheng Xiaowei [9] used the method of soil excavation combined with anchor cable pressure to correct the inclination of a high-rise residential building.At present, shallow excavation and forced landing in tilt correction projects often rely on experience to correct tilt, and most of the earth excavation holes are round earth excavation holes. However, when the upper load is small and the building area is small, it is often difficult to achieve the expected tilt correction goal for the circular soil excavation hole.
If the size of the soil excavation hole is too small, the correction will be very slow and the effect is not ideal. Excessive tilt correction caused the upper building to tilt in the opposite direction.Aiming at the above problems, this paper proposes an elliptical soil excavation correction method.By changing the ratio of the long and short axis of the elliptical soil excavation hole, the stress concentration coefficient of the soil around the excavation hole is controlled, so that the base soil is more susceptible to disturbance under low loads.
Compression deformation occurs.

The mechanism of elliptical excavation and tilt correction
The elliptical digging and tilting correction of the stone statue refers to the special design, by extracting a part of the soil from a certain depth of the soil under the foundation of the stone statue, forming a specific size, direction, depth and spatial distribution (single row or multiple rows) The elliptical hole reduces the pressure-bearing area of the foundation soil, so that the contact stress slowly increases, which promotes the collapse of the excavation hole, resulting in settlement of the upper foundation surface, forcing the foundation to sink, and causing the stone statue body to follow the established trajectory. The "rigid body" rotates to adjust the uneven settlement and achieve the purpose of tilt correction, which belongs to the digging and forced landing of tilt correction [10] . A schematic diagram of digging soil to correct tilt, as shown in Figure 1. Suppose the cross-section of the elliptical digging hole is the z-plane, and the z-plane has an elliptical digging hole with a semi-major axis a and a semi-minor axis b. The coordinate system is established with the center o of the digging hole as the origin 2 show.
First, conformal transformation is used to turn the boundary of the non-circular hole into a circular boundary, and the analytical solution obtained on the circular boundary is changed back, so that the solution of the original problem can be obtained. The conformal mapping function [11] is: In the formula:n=(a+b)/2；m=(a-b)/(a+b)。 The elliptical digging hole in the z-plane is mapped to the unit circle with a plane radius of 1 as shown in Figure 3. After transformation, the stress expression of the elliptical digging hole can be derived as: 2   2   2   2   2  cos  2  1   2  2  cos  2  1  2  cos  2  1   2  2  cos  2   In this paper, the method of combining stress component expression and stress coordinates is used to obtain the maximum and minimum principal stresses at the edge of the elliptical excavation hole, and the Mohr-Coulomb strength failure criterion is used to determine whether the excavation hole will fail.
(1) Stress coordinate conversion and principal stress solution The transformation relation of stress components from polar coordinates to rectangular coordinates is: (2) Mohr-Coulomb strength criterion judgment According to the geometric relationship between the shear strength line of the soil and the stress Mohr circle, the limit equilibrium condition of the soil is established [12] : In the formula: σ1 is the maximum principal stress; σ3 is the minimum principal stress; c is the cohesive force; φ is the angle of internal friction.
From equation (4), σmin can be obtained, and σmin=σ3 is substituted into equation(5) to obtain σ1. If σmax>σ1, the excavation hole starts to fail at this point.

Instability analysis of the failure of the elliptical cut hole
Based on the principle of load symmetry, this paper will select 1/4 soil excavation holes at 15°intervals in the counterclockwise direction on the z-plane to divide, as shown in Figure   4. Use equations (2) and (3) and use matlab to calculate the stress values of 7 key points on the sides of the soil hole a~g, and then make judgments based on the soil limit equilibrium condition equation (5). Figure4 The edge of the 1/4 elliptical digging hole is divided at 15°intervals

Calculation model and evaluation index
The values of relevant parameters in the calculation model are shown in Table1. In this paper, the ratio of the principal stress value σ1 of the soil under the limit equilibrium state to the maximum stress value σmax around the digging hole is used to judge the stability of the digging hole [13] , and the stability coefficient k is introduced: When the stability coefficient k<1, it indicates that the elliptical digging hole is unstable, that is, the digging hole is easy to deform, which can effectively disturb the foundation soil and cause foundation settlement. If the stability coefficient k≥1, it indicates that the elliptical digging hole is stable, the digging hole will not be deformed, and the tilt correction project will appear "digging without tipping", and auxiliary measures need to be taken to promote the damage of the digging hole .  Table 2. It can be seen from Table 2 that when the upper load is 70KPa, the elliptical excavation hole has the largest stress at point a, that is, this point has the least stability and is most prone to damage. The stress at point a increases as the ratio of the long and short axis of the excavation hole increases, and when the ratio of the long and short axis of the elliptical excavation hole is 1:2.5, tensile stress appears at the two points f and g of the excavation hole.
In order to more intuitively describe the influence of the ratio of the length of the elliptical digging hole on the stability of the digging hole, the stability coefficients of the elliptical digging hole under four working conditions are further calculated, and the settlement results are shown in Figure 5. It can be seen from Figure 5 that the stability of the digging hole is inversely proportional to the ratio of the long and short axis of the elliptical digging hole. Especially when the ratio of the long and short axis is 1:1, that is, when m=0, the elliptical digging hole degenerates into a circular digging hole. At this time, the stability coefficient of the digging hole is the largest, and it is not easy for the digging hole to be in a stable state damage.
Therefore, when the upper load is small, the elliptical digging hole is more prone to instability and deformation than the circular digging hole, which can effectively disturb the foundation soil and cause foundation settlement.  The top of the model is a free boundary, and the bottom is a fixed boundary. The lateral soil is constrained in the X and Y directions respectively. According to the geological survey report, the basic parameters of the foundation soil are shown in Table 3

Settlement analysis under different burial depth influencing factors
Set the size of the elliptical excavation hole: short axis b=80mm, long axis a=140mm, hole spacing 250mm, and excavation depth 1000mm; the buried depth h of the excavation hole is 200mm, 300mm, 400mm and 500mm. Analyze the situation. The settlement of the foundation soil under different hole buried depth conditions is shown in Figure 7~8.

Settlement analysis under different influencing factors of soil cut hole size
In order to analyze the influence of the size of the elliptical digging hole on the tilt correction effect, firstly define the parameter n=a/b, where a is the long axis of the elliptical digging hole and b is the short axis of the elliptical digging hole, that is, the parameter n is the elliptical The span-to-height ratio of the soil holes is designed to be 250mm, the buried depth of the soil holes is 300mm, the soil depth is 1000mm, b=80mm is fixed, a is 100mm, 120mm, 140mm, 160mm, 180mm and 200mm respectively n is 1.25, 1.5, 1.75, 2, 2.25, 2.5 six working conditions for analysis.
The settlement of foundation soil under different span-to-height ratios of cutout holes is shown in Figures 15-16. It can be seen from Figure 18 that the north-south settlement difference of the foundation soil increases with the increase of the span-to-height ratio of the excavation hole, but the growth rate is different. When the span-to-height ratio n of the cut hole increases from 1.25 to 1.75, the north-south settlement difference increases from 2.665mm to 5.793mm, an increase of about 117%; n increases from 1.75 to 2.5, the north-south settlement difference increases from 5.793mm to 22.953mm, an increase That's about 296%.  In order to ensure that the model soil is

Test loading and measurement plan
The test adopts the jacking method to load. A steel backing plate with a size of 700mm×500mm×15mm is made of I-beam instead of the stone lining and placed on the surface of the model soil; the distribution beam is 250mm×250mm×9mm×14mm I-beam with a length of 500mm; hydraulic jacks are used The height is 280mm, the running diameter is 100mm, and the maximum lifting force is 5t. Use No. 10 channel steel to make a simple reaction frame that meets the test loading requirements. When pressurized to 2 tons at a time, a uniform load of 57142N/㎡ can be obtained.
In order to obtain detailed changes in the settlement of the superstructure during the excavation process and after the excavation is completed, two electronic digital dial indicators are fixed on the steel backing plate to observe the vertical settlement of the superstructure. In the early stage of settlement, the change is large, and the data is recorded every 0.3h, while the later settlement change is small, and the data is recorded every 1h.

Design of elliptical soil excavation and tilt correction conditions
Set the burial depth of the excavation hole to 300mm, the hole spacing to 250mm, the excavation depth to 500mm, the short axis of the oval excavation hole b=80mm, the upper load to 2 tons, and the upper structure area to be 0.7m×0.5m. Details The parameter design of working conditions is shown in Table 5. Take working condition 1 as an example, the soil excavation process is the same for other working conditions. First, use a jack with a pressure gauge to pressurize to the design load at a time. When the data of the electronic digital dial indicator is stable, reset it to zero, and then carry out the soil excavation test. Hole digging is divided into two stages: centering the hole and digging the soil to form the hole.
Step 1: centering the hole Step 2: Dig the soil After the location of the hole center of the soil excavation hole is determined, a Luoyang shovel is used to manually excavate the soil. Digging should be carried out in phases and batches to avoid sudden sinking due to rapid or uneven digging. The sequence of digging holes is hole A, hole C, and hole B. The completed drawing of soil cutting is shown in Figure   21.
Figure 20 Layout of soil cut holes Figure 21 Completed drawing of soil cutting

Settlement analysis of working condition 1 (span-height ratio of soil excavation hole n=1.75)
It can be seen from Fig. 22 that the settlement of the superstructure changes rapidly at first, and then enters a stage of slow change, and finally the settlement gradually stabilizes.
The entire excavation work took 1.1 hours. Before the excavation work was completed, the settlement of the superstructure was small. The settlement changes mainly occurred after the excavation work was completed, and the superstructure was between 1.1h and 5.5h. The settlement of the slab is linearly changed. After 5.5h, the settlement changes steadily and gradually stays in a stable state, and the settlement difference between monitoring point 1 and

Analysis of Deformation of Digging Hole
Due to the small size of the excavation hole in the working condition 1, the clear distance between the holes is large, and the soil strips between the excavation holes form a stable soil arch, that is, there is no obvious around the excavation hole during the entire excavation test process. The digging hole remains the same as the shape when the digging is completed, as shown in Figure 26. can be seen that after the soil cutting hole A and the soil cutting hole C are completed, because the distance between the two holes is too large and the amount of soil is small, the soil cutting hole does not collapse. Appears, the A cutting hole is accompanied by the B cutting hole, and the A cutting hole is slightly falling on the right side at a distance of 300mm from the hole, as shown in Figure 27. When the second working condition is completed, as time goes by, the B-cut hole is about 250mm away from the hole, that is, there are obvious signs of collapse at the edge of the steel backing plate made of I-shaped steel, such as Shown in Figure 28. it can be seen that: compared with the first three working conditions, the size of the cutting hole and the amount of cutting are greatly increased, and the net distance between holes is also reduced from 110mm to 50mm. . When the excavation work of soil excavation hole A and soil excavation hole C is completed, the hole spacing between hole A and C is relatively large, the amount of inclination of the steel backing plate is small, the model soil settlement is small, and the deformation of the excavation hole is not obvious . When the excavation of hole B is completed, the net spacing of the three holes is reduced to 50mm, the inclination of the steel backing plate gradually increases, and the stress around the hole increases, resulting in the excavation hole and the soil between two adjacent excavation holes. The strips are severely deformed, such as cracks and staggered damage in the soil strips between holes A and B, as shown in Figure 31. The B soil-cutting hole was about 280mm away from the orifice, that is, a large area collapsed at the edge of the steel backing plate made of I-shaped steel, and the upper rigid backing plate of the model soil was exposed, as shown in Figure32.  Please see the Manuscript PDF le for the complete gure caption Please see the Manuscript PDF le for the complete gure caption Figure 5 Please see the Manuscript PDF le for the complete gure caption Figure 6 Please see the Manuscript PDF le for the complete gure caption Please see the Manuscript PDF le for the complete gure caption Figure 8 Please see the Manuscript PDF le for the complete gure caption Please see the Manuscript PDF le for the complete gure caption Figure 10 Please see the Manuscript PDF le for the complete gure caption Figure 11 Please see the Manuscript PDF le for the complete gure caption Figure 12 Please see the Manuscript PDF le for the complete gure caption Figure 13 Please see the Manuscript PDF le for the complete gure caption Figure 14 Please see the Manuscript PDF le for the complete gure caption Figure 15 Please see the Manuscript PDF le for the complete gure caption Figure 16 Please see the Manuscript PDF le for the complete gure caption Figure 17 Please see the Manuscript PDF le for the complete gure caption Figure 18 Please see the Manuscript PDF le for the complete gure caption Figure 19 Please see the Manuscript PDF le for the complete gure caption Please see the Manuscript PDF le for the complete gure caption Figure 21 Please see the Manuscript PDF le for the complete gure caption Please see the Manuscript PDF le for the complete gure caption Figure 28 Please see the Manuscript PDF le for the complete gure caption Figure 29 Please see the Manuscript PDF le for the complete gure caption Figure 30 Please see the Manuscript PDF le for the complete gure caption Figure 31 Please see the Manuscript PDF le for the complete gure caption Figure 32