After multiple on-site surveys, we found that the wooden pagoda has not yet collapsed, although it is currently suffering from severe deformation. In order to preserve this precious ancient architectural heritage more effectively, we use the acquired point cloud data to simulate a real structural model for deformation analysis under long-term self-weight loading and natural aging process. We use multiple point deformation values of the column-architrave structure to identify the weak areas in the second layer, and then effectively reinforce these weak areas and analyze the effect of the reinforcement in detail. This approach aims to prevent potential structural problems in advance to ensure the long-term conservation of ancient buildings.
3.1 Validation of model accuracy and acquisition of weak areas of the model
The column-architrave structure of the wooden pagoda is made of North China larch, the wood has orthogonal anisotropy, and the column-architrave structure is mainly compressed by the longitudinal grain, which carries the vertical load transferred from the upper part. The wood property parameters were taken from Table 1 [33].
Table 1
Material parameters of wood
Material Density(Kg/m3) | Elastic modulus (Mpa) | Poisson's ratio |
Ex | Ey | Ez | µyz | µxz | µxy |
510.2 | 1000 | 275 | 650 | 0.3 | 0.02 | 0.035 |
First, we conduct finite element simulation analysis on the realistic model, excluding considerations of external environmental factors such as temperature, humidity, and wind speed. Our focus is on the effects of long-term self-weight loading, particularly on the second layer structure, which consists of 24 columns and 8 architraves.
Draw the example diagram on any one of the eight sides of the second layer, with the rest of the sides having the same location of the force points. Three analysis surfaces are taken at the top, middle and bottom of each column as A, B, C, and one analysis surface is taken at the middle of each architrave as a. The locations of the main analysis force points are shown in Fig. 10 below.
As the simulation we carried out was based on a realistic model of the wooden pagoda in its original condition, it took into account all aspects of the performance of the wooden pagoda during its original construction, as well as the good connection of the column and architrave components. Therefore, in the simulation, we considered the mortise and tenon joints as a whole, and the column foot were in direct contact with the ground, and fixed constraints were set at the column foot. This simulation assumption reflects the actual situation at the beginning of the construction of the wooden pagoda in order to analyze the performance of the structure more accurately.
In wooden pagoda structure, column components and architrave members mainly bear the vertical loads transmitted from the upper members such as Dougong brackets and wood-plate lintel. These loads are uniformly applied to the columns and architraves, including compressive and bending loads. Through simulation, we obtained the deformation cloud as shown in Fig. 11, based on which the behavior and performance of the structure is analyzed.
To verify the accuracy of the point cloud model, four column point locations, namely column M2W22-S, column M2W23-S, column M2W24-S and column M2W1-S, were selected from the simulated realistic model and compared and analyzed with the data obtained from the automated real-time 3D monitoring system. The results of the error comparison are presented in Table 2 below.
Table 2
Numerical simulation of deformation and automated real-time 3D monitoring system deformation data error statistics table
Column point | Numerical simulation of deformation results (mm) | Monitoring system deformation results (mm) | Absolute error (%) | Relative error (%) |
M2W1-S | 3.279 | 3.229 | 0.05 | 1.5 |
M2W22-S | 4.031 | 3.961 | 0.07 | 1.8 |
M2W23-S | 4.258 | 4.328 | -0.07 | -1.6 |
M2W24-S | 4.651 | 4.538 | 0.11 | 2.4 |
Numerically simulated deformation data is obtained by finite element simulation based on a realistic model constructed from real collected point cloud data. Deformation data from the monitoring system is derived from real-time readings from buried sensors. While there are relative errors in some parts of the numerical simulation, both the numerical simulation results and the relative error measurements from the monitoring system are quite small, all within 3%. The deformation errors at the four column locations are within 1mm for both types of data, confirming the accuracy of the point cloud model.
For the analysis of 24 columns, 10 critical points were selected at the top, middle and bottom of each column as shown in Fig. 8. The deformation values of each column at these three different locations were studied in detail and the results were obtained as shown in Fig. 12.
It is worth noting that the wooden pagoda is an octagonal structure and out of these eight sides, we observed that the deformation values of the four columns on the south-west side were significantly higher than those of the columns on the other sides. This may indicate that the columns on the south-west side were subjected to greater external forces or loads, resulting in their heavier deformation. Through the data in the figure, we can see that among the 24 columns, the column with the largest deformation value is column M2W23 located on the southwest side of the wooden pagoda. Its deformation value reaches 4.65 mm and this value occurs at the top position of the column (up to the position of one third of the height of the column from the top to the bottom). This means that the deformation of the column is significantly larger at the top, and further structural analysis and reinforcement may be required to ensure its stability and safety. For wooden pagoda structures, deformation analysis is crucial, especially for the columns on the south-west side. By analysis of the specific data information of the 24 columns, appropriate measures are required to address potential problems to ensure structural health and safety.
3.2 Reinforcement component design solutions for realistic models
There are generally two types of reinforcement for wooden structures, one is supplemental reinforcement and the other is residual reinforcement. Considering the current condition of the study subject, we believe that the primary focus should be on supplementary reinforcement. In the weak areas identified in section 3.1, it was observed that the wooden columns had irreversibly deformed due to compression. We implemented both traditional and modern reinforcement measures for these weak areas. The first traditional reinforcement we considered primarily involves using aluminum alloy to reinforce wooden columns, while the second modern reinforcement method involves the use of CFRP reinforcement.
3.2.1 Aluminum alloy double ring reinforcement
The subject of our study is the external column of the wooden pagoda, which is exposed to the external environment. Therefore, we need to consider factors like material corrosion due to external elements such as rainwater, and the chosen material should not impose additional stress on the wooden column. Aluminum alloy has properties similar to steel and is more suitable for enhancing the overall performance of wooden columns. Furthermore, its corrosion resistance is stronger than that of steel, which is why we have chosen aluminum alloy for reinforcing the wooden columns. We have opted for a double-ring type of reinforcement. The specific construction measures involve using two irregular ring-shaped aluminum alloy components, one positioned at the top and the other at the bottom, along with a 95cm long bar. The long bar primarily serves the purpose of securing the two irregular rings. The aluminum alloy tube has a wall thickness of 7mm, and the height of the two rings is 40cm. The upper and lower rings are positioned at one-third and two-thirds of the height of the wooden columns M2W23, respectively. 3D printing technology can be used for real wood member dimensions to process the reinforcement method. Detailed design dimensions are shown in Fig. 13 below.
3.2.2 CFRP reinforcement in different thicknesses
After on-site exploration and extensive literature research, we have implemented an innovative reinforcement method using CFRP of different thicknesses for the existing wooden columns, many of which exhibit significant damage. This method of reinforcement, primarily achieved through adhesive bonding, is unique in that it provides multiple benefits. Firstly, the CFRP material itself is very light, which helps to maintain the original structural stability of the wooden columns without placing excessive additional loads on them. This is crucial to maintaining the structural integrity of the building. Secondly, CFRP strips can be custom edge-cut as needed, making them flexible enough to accommodate a wide range of wooden column shapes and sizes, regardless of how complex their geometric features may be. This makes the reinforcement process more precise and controllable. Furthermore, CFRP materials exhibit excellent plastic properties and can accommodate the deformation of wooden columns, thereby mitigating issues related to uneven stress distribution during the reinforcement process. This ensures that the reinforced wooden columns are better equipped to withstand external loads. Most importantly, this type of reinforcement is flexible enough to address situations involving uneven damage to the wooden columns. Regardless of where the damage occurs, CFRP strips can be applied as needed to ensure a uniform distribution of strength throughout the wooden column. No matter where the damage is located, CFRP strips can be reinforced as needed, ensuring a uniform distribution of strength throughout the wooden column. Detailed reinforcement was carried out by bonding CFRP around the entire surface of the M2W23 wooden column, with thicknesses varying from 0.167mm to 10mm, depending on the extent of the damage. In order to match the dimensions of real wood components, 3D printing can be used to design and implement reinforcement methods. An example is shown in Fig. 14.
3.3 Simulation study to analyze the effect of post-reinforcement
The same parameter settings as in Table 1 were used for the simulation of the realistic model for both types of reinforcement. The material parameters of the aluminum alloy material are shown in Table 3. The material parameters of CFRP strips are shown in Table 4. CFRE is then set by line elasticity. A contact gap of 0.001mm was set for the wooden columns and architraves to simulate the unavoidable small gaps and non-linear contact behavior. Adhesive slippage between wood and CFRP strip is not taken into account. The boundary conditions in the model will match those used in the experiments. Node displacements within the section will be constrained at both ends of the model. At one end, degrees of freedom in the parallelepiped direction will be constrained, while at the other end, node displacements in the parallelepiped direction will be applied with coupled node degrees of freedom.
Table 3
Material parameters of aluminum alloys
Tensile strength /Mpa | Elastic modulus/Mpa | Poisson's ratio |
273.1 | 70698 | 0.32 | |
Table 4
Material parameters of CFRP strips
Tensile strength /Mpa | Elastic modulus/Mpa | Elongation/% |
3483 | 231 | 1.7 | |
We carried out finite element simulations for the second layer of the column- architrave structure and investigated two different reinforcement methods, as shown in Fig. 15 below. For the M2W23 wooden column, both reinforcement methods show significant results in enhancing the structural stability. After reinforcement with aluminum alloy material, the top deformation of the wooden columns was reduced to 3.5 mm, the reinforced wooden columns were more stable and less deformed with a reduction of 1.15 mm, and the top deformation of the wooden columns was reduced by about 24.7% compared to that before the unreinforced columns. The top deformation of the wooden columns was reduced from 4.65mm to 2.8mm after reinforcement with CFRP strips, which showed a stronger performance with less deformation compared to reinforcement with aluminum alloy material, and the top deformation of the wooden columns was reduced by about 39.7% compared to that before reinforcement. Although both types of reinforcement are effective in reducing deformation, different thicknesses of CFRP reinforcement are more applicable in this structure as the CFRP reinforcement method is more finely tuned to take into account the uniformity of the residual damage distribution. Both types of reinforcement have achieved significant results in enhancing stability, but the selection of an appropriate reinforcement method requires a combination of several factors, including regional precipitation, cost, performance requirements and feasibility. Depending on the object and resources, different thicknesses of CFRP reinforcement may be more suitable for this structure.