Earth-wood structure houses often cause large casualties and economic losses in historical earthquakes. Therefore, it is estimated that the seismic vulnerability of civil structures in areas that have not experienced earthquakes is of great significance for earthquake prevention and disaster reduction. In this paper, an analogy calculation method was proposed for calculating the seismic vulnerability of earth-wood structure houses in unknown regions from the seismic vulnerability of earth-wood structure houses in known regions. Firstly, the main factors affecting the seismic capacity of earth-wood structure houses were determined, and the weights of influence of influencing factors on the overall seismic capacities of buildings under different seismic intensities were determined by using the fuzzy analytical hierarchy approach; secondly, the relative seismic capacities of the main influencing factors are analogically scored by considering the differences in influencing factors in different regions. Finally, based on the vulnerability matrix of earth-wood structure houses in existing regions and comprehensive evaluation of relative seismic capacities of earth-wood structures, the vulnerability matrix of unknown earth-wood structures was calculated by analogy. The results of trial calculation showed that this method has higher reliability and effectiveness. At the end of the article, the vulnerability analysis of earth-wood structure houses in Shigatse, Tibet, was carried out using this method, and the vulnerability curve was initially given.
The seismic vulnerability of buildings is to estimate the degree of damage that may occur when buildings are affected by a certain intensity earthquake [
Although with the continuous development of social economy and the gradual reconstruction of houses in rural areas in China, the number of earth-wood structure houses is decreasing year by year in rural areas in China, and there are still more earth-wood structure houses in rural areas in economically backward regions and ethnic minority autonomous regions in China. Due to the fact that seismic fortification is not considered in these earth-wood structure houses and the building age is old, it is extremely easy for them to be damaged under the action of earthquakes, and their seismic resistances are poor. Therefore, it is still very important to study the seismic vulnerability of earth-wood structure houses to effectively carry out the work of earthquake prevention and disaster reduction [
Western China is an earthquake-prone area in China; multiple earthquakes of magnitude 7 and above have occurred in history, including the Wenchuan earthquake (
After field investigations, it was found that earth-wood structure houses were widely distributed in rural areas of Shigatse, Tibet. According to the structural characteristics of earth-wood structure houses in Shigatse, Tibet, this paper uses the method to analyze the vulnerability of earth-wood structure houses in this area.
It was assumed that the seismic vulnerability matrix of earth-wood structure houses in
As no seismic fortification measures are taken, earth-wood structure houses will suffer obvious seismic damages such as cracks in walls and destroyed internal supporting structures when the seismic intensity is above 6° [
Main influencing factors of seismic damage of earth-wood structure houses.
No. | |||
---|---|---|---|
Influencing factors | Number of floors | Load bearing wall | Internal support structure |
Through the study of the previous actual seismic damage data of earth-wood structures, it was found that the influences of influencing factors on the seismic capacities were different under different seismic intensities. For example, when the seismic intensity was 6°, the seismic damage of the earth-wood structure houses was mainly the damage of the wall, and the damage grade was mainly affected by the condition of the wall; however, when the seismic intensity was 8° or above, whether overall earth-wood structure houses collapsed was mainly determined by the supporting strength of the internal supporting structures, and the damage grade was mainly affected by the internal supporting structures. In order to determine the influences of the main factors on the seismic capacities under different intensities, the fuzzy analytical hierarchy approach was used in this paper to construct the fuzzy judgment matrix and determine the influence weights of the main factors on the seismic capacities under different seismic intensities.
Fuzzy analytical hierarchy approach [
Scale value and meaning of the fuzzy judgment matrix.
Scale value | Meaning | Notes |
---|---|---|
0.5 | Equally important | Two factors are compared; two factors are equally important |
0.6 | Slightly more important | Two factors are compared; one factor is slightly more important than the other one |
0.7 | Obviously more important | Two factors are compared; one factor is obviously more important than the other one |
0.8 | Much more important | Two factors are compared; one factor is much more important than the other one |
0.9 | Extremely important | Two factors are compared; one factor is extremely important than the other one |
0.1, 0.2, 0.3, 0.4 | Converse comparison | If the judgment |
Thereby, the judgment matrix of the evaluation index is constructed as
The fuzzy judgment matrix of the main influencing factors under different seismic intensities is shown in Tables
Fuzzy judgment matrix of the main seismic damage factors when the intensity was 6°.
Influencing factor | |||
---|---|---|---|
0.5 | 0.4 | 0.6 | |
0.6 | 0.5 | 0.8 | |
0.4 | 0.2 | 0.5 |
Fuzzy judgment matrix of the main seismic damage factors when the intensity was 7°.
Influencing factor | |||
---|---|---|---|
0.5 | 0.4 | 0.5 | |
0.6 | 0.5 | 0.6 | |
0.5 | 0.4 | 0.5 |
Fuzzy judgment matrix of the main seismic damage factors when the intensity was 8°.
Influencing factor | |||
---|---|---|---|
0.5 | 0.6 | 0.4 | |
0.4 | 0.5 | 0.4 | |
0.6 | 0.6 | 0.5 |
Fuzzy judgment matrix of the main seismic damage factors when the intensity was 9–10°.
Influencing factor | |||
---|---|---|---|
0.5 | 0.7 | 0.3 | |
0.3 | 0.5 | 0.2 | |
0.7 | 0.8 | 0.5 |
According to the obtained fuzzy judgment matrix, the general formula to solve the weight of the fuzzy judgment matrix proposed by Xu [
In formula (
The calculation results are shown in Table
Weights of various influencing factors under different seismic intensities.
Grade VI | Grade VII | Grade VIII | Grade IX | Grade X | |
---|---|---|---|---|---|
0.333 | 0.317 | 0.333 | 0.333 | 0.333 | |
0.400 | 0.367 | 0.300 | 0.300 | 0.250 | |
0.266 | 0.317 | 0.367 | 0.367 | 0.417 |
Whether the weight value calculated by the above formula is reasonable still needs to be checked for consistency. In this paper, according to the compatibility of the fuzzy judgment matrix [
Then, the weight compatibility index is
When the compatibility index
In this paper, formulas (
Calculation results of compatibility indexes.
Seismic intensity | Grade VI | Grade VII | Grade VIII | Grade IX | Grade X |
---|---|---|---|---|---|
Compatibility index | 0.066 | 0.028 | 0.044 | 0.099 | 0.099 |
All compatibility indexes of the weights of the main influencing factors under different intensities were less than 0.1, so it was considered that the fuzzy judgment matrices of the influencing factors under different intensities were consistent, and the distribution of the weights was reasonable.
Because there are some differences in the specific conditions of the main factors affecting the seismic capacities in different regions, for example, the thickness of the walls is different among some regions, the seismic capacities of earth-wood structure houses in different regions are different. According to the actual situation of the main influencing factors, the relative seismic capacities of the main influencing factors are determined by using the expert scoring method. Experts participating in scoring mainly come from the fields of structural engineering, earthquake engineering, and disaster prevention and mitigation engineering and have extensive experience in earthquake site inspections. In this paper, the relative seismic capacities of the main influencing factors were divided into five grades, and the better the relative seismic capacity was, the higher the score given by relevant experts was. For example, if the damage grade of the earth-wood structure with thick walls is lower than that of the earth-wood structure with thin walls during the earthquake [
Scoring standard for the relative seismic capacity of each influencing factor.
Relative seismic capacity | Worse | Bad | Ordinary | Good | Better |
---|---|---|---|---|---|
0–0.2 | 0.2–0.4 | 0.4–0.6 | 0.6–0.8 | 0.8–1 |
According to the housing census data, we could understand the specific situations such as the number of floors of earth-wood structures, bearing walls, and internal supporting structures in a certain region. Based on the specific conditions of the main influencing factors of earth-wood structures, relevant experts were consulted for evaluating the relative seismic capacities of the main influencing factors. According to the influence weights of the main influencing factors on the seismic capacities of the building under different intensities, the comprehensive scores of the relative seismic capacities of the earth-wood structures in a certain region under different intensities were obtained as follows:
In the formula,
Seismic engineering experts such as Hu [
Correlation between the seismic damage index and the seismic damage degree.
Damage grade | Basically intact | Slightly damaged | Moderately damaged | Severely damaged | Destroyed |
---|---|---|---|---|---|
Seismic damage index | 0–0.1 | 0.1–0.3 | 0.3–0.55 | 0.55–0.85 | 0.85–1.0 |
The expected value of the seismic damage index is the average value of the seismic damage indexes of buildings in a region. The dispersion of the damage grade of buildings in a region can be expressed by the standard deviation of the seismic damage index. Therefore, the expected value and standard deviation of the seismic damage index of a certain type of structure can be obtained according to its vulnerability matrix.
Based on the difference in the comprehensive score of the relative seismic capacity between earth-wood structure houses in the benchmark region and the target region, the expected values and standard deviations of the seismic damage indexes in the benchmark region under different intensities were used to calculate inverse distance weighted (IDW) interpolation [
In the formula,
According to the relationship between the expected value and the standard deviation of parameters
Thereby, the beta probability density distribution of the seismic damage index under seismic intensity
According to formula (13), the damage probabilities of the earth-wood structure houses in the target region under different damage degrades can be fitted, and finally, the vulnerability matrix of the earth-wood structure houses in the target region can be obtained.
In the formula,
The vulnerability matrix of earth-wood structure houses in Gansu province was fitted using the calculation method proposed in this paper.
In this paper, Sichuan province, Xinjiang Uygur Autonomous Region, and Yunnan province in western China are selected as the benchmark regions, and the main factors affecting the seismic capacity of earth-wood structure houses in the benchmark regions and Gansu region are shown in Table
Specific conditions of the main influencing factors in the benchmark regions and Gansu region.
Number of floors | Load bearing wall | Internal support | |
---|---|---|---|
Sichuan province | The houses had one or two floors | The wall thickness was 30–50 cm, and the wall integrity was ordinary | Some houses had supporting structures such as wooden frames and wooden columns, and the internal supporting condition was ordinary |
Xinjiang Uygur Autonomous Region | The houses mainly had one floor | The wall thickness was 30–50 cm, and the wall integrity was relatively poor | Fewer houses had internal supporting structures, and the internal supporting condition was poor |
Yunnan province | Most houses had two floors, and a few houses had one floor | The wall thickness was 60–120 cm and was 80 cm in most cases, with good wall integrity | Most houses had wooden posts, wooden beams, and mortise and tenon connection between beams and columns, with better internal supporting condition |
Gansu province | The houses mainly had one floor | The wall thickness was 30–50 cm, and the wall integrity was ordinary | Some houses had supporting structures such as wooden frames and wooden columns, and the internal supporting condition was good |
According to the specific conditions of the main influencing factors in each region in Table
Scores of the main influencing factors of the benchmark regions and Gansu region.
Number of floors | Load bearing wall | Internal supporting structure | |
---|---|---|---|
Sichuan | 0.6 | 0.6 | 0.5 |
Xinjiang | 0.8 | 0.3 | 0.3 |
Yunnan | 0.4 | 0.8 | 0.8 |
Gansu | 0.8 | 0.4 | 0.7 |
According to formula (
Comprehensive scores of relative seismic capacities of the benchmark regions and Gansu region.
Grade VI | Grade VII | Grade VIII | Grade X | |
---|---|---|---|---|
Sichuan | 0.533 | 0.532 | 0.533 | 0.533 |
Xinjiang | 0.467 | 0.458 | 0.467 | 0.467 |
Yunnan | 0.667 | 0.673 | 0.667 | 0.667 |
Gansu | 0.613 | 0.622 | 0.643 | 0.658 |
Based on the scores and the expected values and standard deviations of the seismic damage indexes under different intensities in each benchmark region in Table
Expected values and standard deviations of seismic damage indexes in each benchmark region.
Grade VI | Grade VII | Grade VIII | Grade IX | Grade X | ||
---|---|---|---|---|---|---|
Sichuan | Expected value | 0.172 | 0.358 | 0.592 | 0.770 | 0.900 |
Standard deviation | 0.168 | 0.258 | 0.270 | 0.207 | 0.091 | |
Xinjiang | Expected value | 0.250 | 0.405 | 0.632 | 0.806 | 0.909 |
Standard deviation | 0.216 | 0.262 | 0.276 | 0.185 | 0.084 | |
Yunnan | Expected value | 0.137 | 0.332 | 0.559 | 0.755 | 0.900 |
Standard deviation | 0.166 | 0.250 | 0.276 | 0.221 | 0.094 |
Expected values and standard deviations of seismic damage indexes under different intensities in Gansu province.
Grade VI | Grade VII | Grade VIII | Grade IX | Grade X | |
---|---|---|---|---|---|
Expected value | 0.156 | 0.343 | 0.562 | 0.755 | 0.900 |
Standard deviation | 0.152 | 0.249 | 0.276 | 0.220 | 0.094 |
Formulas (
Probability density distribution curves of seismic damage indexes under different seismic intensities.
According to the beta probability density distribution of the obtained seismic damage indexes, the vulnerability matrix was fitted by using formula (
Vulnerability matrix of earth-wood structure houses in Gansu province fitted by the proposed method.
Grade VI | Grade VII | Grade VIII | Grade IX | Grade X | |
---|---|---|---|---|---|
Basically intact | 48 | 20 | 5 | 0 | 0 |
Slightly damaged | 35 | 30 | 16 | 3 | 0 |
Moderately damaged | 14 | 28 | 26 | 14 | 0 |
Severely damaged | 3 | 19 | 36 | 41 | 22 |
Destroyed | 0 | 3 | 17 | 42 | 78 |
Actual seismic vulnerability matrix of earth-wood structure houses in Gansu province.
Grade VI | Grade VII | Grade VIII | Grade IX | Grade X | |
---|---|---|---|---|---|
Basically intact | 55 | 18 | 4 | 0 | 0 |
Slightly damaged | 30 | 29 | 10 | 1 | 0 |
Moderately damaged | 13 | 32 | 32 | 18 | 0 |
Severely damaged | 2 | 18 | 31 | 27 | 10 |
Destroyed | 0 | 3 | 23 | 54 | 90 |
In order to verify the reliability and effectiveness of this method, the vulnerability results of earth-wood structure houses estimated by this method were compared with the actual vulnerability results of seismic damage investigation. As shown in Table
Comparison between the expected value of the seismic damage index obtained by simulation and the expected value of the actual seismic damage index.
Grade VI | Grade VII | Grade VIII | Grade IX | Grade X | |
---|---|---|---|---|---|
Simulation value | 0.156 | 0.343 | 0.562 | 0.755 | 0.900 |
Actual value | 0.157 | 0.357 | 0.588 | 0.767 | 0.903 |
Error | 0.001 | 0.014 | 0.026 | 0.012 | 0.003 |
Through field research, it was found that the earth-wood structure houses in Shigatse, Tibet, were mainly two-story traditional Tibetan-style buildings with thick walls and good internal support structure, as shown in Figure
(a) Structural appearance of earth-wood structure houses in Shigatse region. (b) Internal support structure.
Based on the actual situation of earth-wood structure houses in Shigatse, Tibet, the method of this paper is used to analyze the vulnerability of earth-wood structure houses in this area. Sichuan province, Xinjiang Uygur Autonomous Region, and Yunnan province in western China are selected as the benchmark regions, and the main factors affecting the seismic capacity of earth-wood structure houses in the benchmark regions and Shigatse, Tibet, are shown in Tables
Specific conditions of the main influencing factors in Shigatse region.
Number of floors | Load bearing wall | Internal support | |
---|---|---|---|
Shigatse region | The houses mainly had two floors | The wall thickness was 80–100 cm, and the wall integrity was good | Most houses had wooden posts, wooden beams, and normal connection between beams and columns, with better internal supporting condition |
According to the specific conditions of the main influencing factors in Shigatse region in Table
Scores of the main influencing factors of Shigatse region.
Number of floors | Load bearing wall | Internal supporting structure | |
---|---|---|---|
Shigatse region | 0.4 | 0.9 | 0.6 |
Based on the scores and the expected values and standard deviations of the seismic damage indexes under different intensities in each benchmark region in Table
Expected values and standard deviations of seismic damage indexes under different intensities in Shigatse region.
Grade VI | Grade VII | Grade VIII | Grade IX | Grade X | |
---|---|---|---|---|---|
Expected value | 0.156 | 0.343 | 0.562 | 0.755 | 0.900 |
Standard deviation | 0.152 | 0.249 | 0.276 | 0.220 | 0.094 |
Formulas (
Seismic vulnerability matrix of earth-wood structure houses in Shigatse region.
Grade VI | Grade VII | Grade VIII | Grade IX | Grade X | |
---|---|---|---|---|---|
Basically intact | 54 | 21 | 4 | 0 | 0 |
Slightly damaged | 31 | 31 | 15 | 4 | 0 |
Moderately damaged | 12 | 27 | 26 | 13 | 0 |
Severely damaged | 3 | 18 | 37 | 39 | 22 |
Destroyed | 0 | 3 | 18 | 44 | 78 |
According to the vulnerability matrix of earth-wood structure houses in Shigatse region calculated using the method in this paper, the vulnerability curve of earth-wood structure houses in this region can be obtained, as shown in Figure
Vulnerability curve of earth-wood structure houses in Shigatse region.
The calculation results show that the moderate and above damage degree of earth-wood structure houses in Xigaze area occupied the main part when the earthquake intensity is 8°; when the earthquake intensity is 10°, the earth-wood structure houses in the area are basically destroyed. Comparing the expected values of the earthquake damage index of earth-wood structures in Shigatse and other benchmark regions, because the load bearing wall of the earth-wood structure is thicker and good overall condition in Xigaze, the expected value of the earthquake damage index of earth-wood structure houses in Xigaze is relatively low in low-intensity areas; in high-intensity areas, due to the poor internal support structure compared with Yunnan, the expected value of the earthquake damage index for structural houses is higher than Yunnan.
It can be seen that the vulnerability analysis of the earth-wood structure houses in Shigatse, Tibet, using this method meets the expected results.
The vulnerability matrix of earth-wood structure houses in Gansu province was fitted using the calculation method proposed in this paper. In this paper, according to the needs of vulnerability estimation of earth-wood structure houses, a quick calculation method for fitting the vulnerability matrix of earth-wood structure houses is proposed. Based on the vulnerability matrix of the earth-wood structures in the benchmark region, considering the influence weights of the main influencing factors on the seismic capacity of the building under different seismic intensities and the difference in the actual situation of the influencing factors in different regions, the comprehensive scores of relative seismic capacities of the earth-wood structure houses in the benchmark region and the target region are calculated, respectively, and then, the expected values and standard deviations of the seismic damage indexes in the target are obtained by using the inverse distance weighted interpolation method. Finally, the beta distribution function is used to fit the seismic damage matrix in the simulated region. The earth-wood structures in Gansu province are checked by using the method in this paper, and the error between the calculated results and the actual seismic damage results is within a reasonable range.
The method proposed in this paper can quickly evaluate the vulnerability of earth-wood structure houses in a certain region, which considers the influence of different influencing factors on the seismic capacities of the structures under different seismic intensities compared with the previous methods. The accuracy of this method is affected by the selection of the benchmark region and the reasonableness of the relative seismic capacity scores evaluated by relevant experts on the main influencing factors. Generally, the region with earth-wood structures similar to those of the target region should be selected as the benchmark region, and the average value of the scores of multiple relevant experts should be used for evaluation. In this paper, only the vulnerability of earth-wood structures is evaluated, and how this analogy method can also be applied to houses of other types of structures needs further study.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest regarding the publication of this paper.
This study was supported by Special Fund for Basic Scientific Research Expenses of Institute of Engineering Mechanics (2018A02), National Key R&D Program of China (2018YFC1504602), and Business Expenses of China Earthquake Administration (19024205).