An Evaluation System Based on AHP Method for Preserve Situation in Guangyuan Thousand-Buddha Grotto of Tang Dynasty in Sichuan, China

Guangyuan thousand-buddha grotto is of great value in researching Buddhism spread in China. By joint effect of various factors, the grottos have developed serious diseases, which threaten the long-term preservation. To date, the existing study can neither reveal the contribution each disease makes to nor the grottos’ preserve situation in a quantized way. Therefore, establishing a scientific evaluation system to explore the effection of each disease and assess grottos’ preserve situation degree has been a significant topic for grotto’s conservation. In this research, the authors selected 11 grottos of middle Tang dynasty in Guangyuan thousand-buddha grotto as survey objects, traditional diseases investigation was taken and analytic hierarchy process (AHP method) was applied to build a system to calculate weight of 15 diseases and evaluate grottos’ preserve situation. The result shows, 15 diseases can be classified as two risk categories, and every disease has its own weight on effecting grotto’s preserve situation. AHP method is suitable for heritage assessment with complex structure. 3. This research characterizes the preserve situation in a quantized way of 11grottos of middle Tang dynasty in Guangyuan thousand-buhhdas grottos, and explores the vulnerability evaluate mode primarily. The result shows that AHP method can be used for the grottos’ preserve situation evaluation, and in the future study, it is necessary to take a consideration of the interaction of each factor.


Introduction
Grotto is a kind of valuable heritage in China with high history, art and science value, which is started from Han dynasty, and thriven from North Wei dynasty to Tang dynasty. It can be classified as Xinjiang grotto, north grotto, south grotto and Tibetan grotto according to the characteristic [1].
Among these four parts, the south grotto is account for 42.9%, and grotto in Sichuan and Chongqing is account for more than 80% of south grotto. A large number of grottoes with high value distributed in Sichuan province, southwest China. They are the outstanding representative of grotto in late time in Chinese history, which is meaningful to reconstruct the local history of southwest China [2]. After experiencing hundreds years of natural erosion and human destruction, most of these grottoes have developed serious deterioration that threaten their long term existence and preservation. The existing research reveals that most of grotto in Sichuan is suffering dangerous rock mass, sandstone degradation, water disease and biological disease, due to wet and rainy climate, soft property of sand stone and dense seismic zones [3]. Conservation research on sandstone grotto is in the primary stage. Grotto's deterioration is the result of the combined function of varies factors, such as sandstone properties, grotto's preserve situation and surrounding [4]. Among these factors, sandstone properties and grotto's preserve situation are internal causes and the surrounding is the external cause.
Vulnerability evaluation is derived from natural disaster risk assessment, which is widely used in assessing the loss caused by earthquake, debris flow, landslip and rainstorm [5][6][7][8]. Currently, the research on risk management in cultural heritage is still in the exploratory stage. Studies of risk forecast on specified types heritage to single factor were taken, such as rainstorm to historic building, flood to earthen site and earthquake to grotto [9][10][11]. These studies provide a good foundation to this research and emphasize the disaster' development degree and frequency, but they are unaware of the center position of cultural relics in risk event.
From dynamics aspect, the grotto's preserve situation is the result of the combined effect of varies factors, and from the performance is the joint contribution of the multiple diseases. Grotto's preserve situation is represented in kinds of diseases or quantity of diseases [12]. Neither of them can show the contribution of each disease to grotto's deterioration nor the grotto's preserve situation in a quantized way. So far, the research on grotto's preserve situation makes little contribution to assess the grotto's conserve necessary scientifically.
In this research, the authors selected 11 grottoes of Tang dynasty in Guangyuan Thousand-Buddha Grotto as the study objects. To explore the vulnerability evaluation mode and the quantification of preserve situation, the geological disaster risk assessment method is used for reference [13]. By the traditional diseases surveying and taking analytic hierarchy process (AHP method), the contribution of each disease to the grotto's preserve situation is determined.
Furthermore, the vulnerability evaluation mode, including grotto's value, sandstone properties, preserve situation and management, is basically established. This research proposes a new evaluation system to grotto's preserve situation, and is an important component of grotto's risk assessment, which is benefit for judging the urgency of the grotto's preserve situation in a quick and effective way and offering evidence for grotto's conservation and consolidation.

Study object
Guangyuan Thousand-Buddha Grotto is located in Guangyuan, Sichuan province, which was excavated from NorthWei to Qing dynasty [14]. The Grotto distributed on the face of the cliff beside the east bank of Jialing River (Figure 1). The Jinniu road was under the cliff, which is the important path that Buddhism was spread from center plains area to Shu area. By the digital investigation, 949 caves and more than 7000 stone sculptures were found, most of which were made from Tang dynasty, presenting high level of history, art and science value in the southern part of China. Owing to the high value and serious preservation, Guangyuan Thousand-Buddha Grotto was honored as the first state-level key cultural relic preservation organ in 1961, and urgent repairing treatments were needed [14]. However, several important questions must be answered before starting the work: Which disease is the most common and which is the most serious? Which one affected the stability of the grotto and which one affected the value loss? Which conservation project should be conducted first? Therefore, it is very necessary to conduct a systematic and quantized diseases investigation on the grotto, not only for answering these questions, but also for offering a decision basis to conservation.

Field investigation
In this research, the authors surveyed the diseases on the grottos but didn't involve the dangerous rock of the surrounding. The diseases were named by referring the classification and legend on the deterioration of ancient stone objects (WW/T 0002-2007), issued by the State Administration of Cultural Heritage of People's Republic of China [15]. Based on the investigation, all the diseases can be classified as two major categories according to the risk. The one may cause safety risk involving scaling off, detachment, water disease, body loss, cracks and plant damage. These diseases may affect the grotto's safety directly, leading to the grotto's loss or disappearance. They have small quantity but develop fast and destructively. And the other one may cause value loss including rock powdering weathering, deep loss, salt crystallization, pigment layer peeled off, paint layer craquelure, scratch or graffiti, improper repairing, human pollution, microorganism pollution. These diseases exist on the grotto for a long time, and do not affect the grotto's safety in a short term, but will lead to the value loss for a long time. They distribute widely with slow development and have weak destructive. All these typical diseases almost exist all the survey objects ( Table 2). The diseases data were investigated and analyzed in Table 3 and Table 4. All data are from Guangyuan Thousand buddha Museum.

AHP method
The AHP method is a multi-objective decision analysis method combined qualitative and quantitative analysis, applying to the large complex system with complex target structure, or lack of certain data [16,17]. The basic principle is to decompose the decision goal according to different standard, then calculate the weight each element to a specific element in the above layer through calculating the matrix and eigenvector, finally conclude the weight of every element in this system [16]. The specific procedure includes 5 necessary steps [6][7][8]11,16]: clarify the decision goal, build hierarchical structure, construct judgment matrix, check consistency and make judgment. The finally goal of AHP method is to determine the relative weight every element in the system. The specific procedure of this method is shown in Figure 2.

Fig. 2 AHP Method procedure
In existing investigation, the grotto's preserve situation is often characterized through quantity and variety of diseases [12], this expression depends on the investigator's subjective judgement.
Although most of the investigators are professional, the disease data is lack of objective. Since of the significant value of these survey objects, it is very important to consider experts' opinions when studying the preserve situation and conservation. In this research, we selected AHP method because it can reflect the subjective intension of the decision maker, provide the hierarchical structure, facilitate decomposition and pairwise comparison, reduce inconsistencies and generate priority vectors [11,16]. The AHP method was used to establish a system for evaluating the grotto's preserve situation, in order to calculate its degree of disease development in each grotto, because of its combination of subjectivity and objectivity in this research.
The AHP method procedures are as follow: Step 1: Clarify the decision goal. In this research, the decision goal is to evaluate all survey subjects' preserve situation in a quantized way.
Step 2: Build hierarchical structure. According to the grotto's diseases, the hierarchical structure of the grotto's preserve situation is established.
Step 3: Construct judgement matrix. In this step, the weight of the indexes in the hierarchical structure are calculated.
First, compare the element of particular layer pairwise in accordance with the experts' opinion, then the matrix A can be given as follows (Eq 1): n is the number of elements compared, and is governed by the rules: is the element of the matrix A, and the value of is from the judgement of a pair of elements and , which indicate the relative importance between two elements. The value of is defined from a 9-point scale ( Table 5). In this table, the value of relative importance is expressed as pairwise weight of 1, 3, 5, 7 and 9, which means the relative importance between elements is equally, moderately, strongly, very strong and extremely. While the value of 2, 4, 6, and 8 are intermediate value [17].
In equation (2)， ′ is the element of matrix A' which is normalized from matrix A, is the relative importance value of and in matrix A, ∑ is the sum of each column in matrix A.
The eigenvector of each column in matrix A can be calculated according to Eq (3). Finally, normalizing the eigenvector of each column according to Eq (4), the weight of each index can be calculated.
In equation (4), ̅̅̅ is the eigenvector of each column, ∑ is the sum of eigenvalue in matrix A.
Step 4: Check consistency. To avoid the inconsistency of the decision system, it is necessary to verify the consistency of the matrix. When the coincidence indicator (C.I) and the random consistency index (C.R) are both less than or equal to 0.1, it means the matrix can be regarded as consistent. The C.I can be calculated according to Eq (5), and C.R can be calculated according to Eq (6) [16].
. . = . . . ⁄ In equation (5), is the largest eigenvalue of matrix A, n is the scale of matrix, R.I is average random consistency index which is a constant according to the scale of matrix (Table 6). Step 5: Make judgement. By calculating the weight and normalizing the quantity of disease in each grotto, the grottos' preserve situation can be calculated in a subjective and objective way, and the grottos' vulnerability assessing mode can be established primarily.

Result
In this part, the authors established a hierarchical structure of the grottos' preserve situation, calculated the weight of the indices in the hierarchical structure and finally obtained the preserve situation of each grotto.

Building hierarchical structure
The grottos' degradation is the joint effect of various diseases. According to the survey, the diseases may lead to safe risk, have less quantity, but develop fast and more dangerously, while the diseases resulting in value loss distribute widely but develop at a low speed, exiting in a long term. The two categories' diseases have different contribution to grottos' preserve situation and further effecting.
It is necessary to consider both the quantity and the weight of disease when defining the grottos' preserve situation. The authors build the hierarchical structure of 15 diseases two categories ( Figure   3). By calculating the weight, the contribution of each disease to grottos' preserve situation can be determined. Combined with the quantity of each disease, the grottos' preserve situation can be characterized in a respect quantitively way. And then the vulnerability of each grotto is determined which offers the evidence of priority level of conservation.

Fig. 3
The hierarchical structure of grotto's preserve situation assessment

Constructing judgement matrix
In this research, the grottos' preserve situation is the goal layer, the safety risk and value loss risk are criterion layer. The index layer includes scaling off, detachment, water disease, body loss, cracks and plant damage, rock powdering weathering, deep loss, salt crystallization, the pigment layer peeled off, paint layer craquelure, scratch or graffiti, improper repairing, human pollution, microorganism pollution.
Three experts who are well acquainted with the preservation of grottos in China were invited to provide the final comparison results for the structure pairwise comparison matrices, as shown in Table 7 to Table 9. Table 7 is the comparison result of criterion layer, and Table 8 and Table 9 are the index layer to particular criterion above.    According to the Eq (3), the eigenvector ̅̅̅ of each column in matrix A', matrix B1' and matrix B2' can be calculated. And according to Eq (4), the normalized eigenvector ̅̅̅ and comprehensive weight of every criterion and index can be calculated. The result in this research is shown in Table   10.

Checking consistency
Avoiding to the inconsistency of the index pairwise in the system, the consistency checking is necessary. Only the C. I and C. R both less than or equal to 0.1, the result above is approved. When the matrix is a second order matrix (scale n=2), its' C.I and C. R both are 0, and the matrix is naturally consistent. According to Eq (5) and Eq (6), the consistency of matrix B1 and matrix B2 is checked (Table 11).

Assessing the preserve situation
The weight shows the contribution of each disease makes to the grotto's preserve situation. Here, the authors started to evaluate the grottos' preserve situation. Owing to the various units of 15 diseases, there are no comparability between different diseases, and the disease data cannot be weighted sum. It is necessary for dimensionless process of diseases data to solve the incomparable between different diseases. In this research, equalization method is adopted according to Eq (7).
In equation (7), xi` is the dimensionless processing data, xi is the initial disease data from Table 3 and Table 4, and ̅ is average of every column in Table 3 and Table 4. The proceed data are in Table 12 and Table 13.

Tab. 12 Dimensionless processing data of safety risk
No.
C1, C2, C3…C15 is dimensionless processing disease data, and 1 、 2 … 15 is the weight of disease. D is grottos' preserve situation. Using the procedure and equations above, the value of preserve situation of 11 grottos can be calculated and result is shown in Table 14.

Vulnerability assessment
Vulnerability is origin from risk management [18][19][20]. In this research, the authors define the grotto's risk, which is the possibility of grotto destructed by various factors, including the possibility, and the loss destruction may lead to geological hazard. All the behaviors may lead to safety risk or value loss to grotto and its' surrounding can be treated as risk, and we use risk degree to characterize its' value, and the expression of risk degree is as Eq (9) [5,13].
In equation 9, R means risk degree and H stands for hazard. In this research, hazard, referring to the external causes, may lead to grotto's degradation, such as geologic environment, meteorological environment, biological environment, and these factors does not involve in this research. V is vulnerability, and we define it as the internal causes resulting in the grotto's degradation, including According to the analysis, safety risk has more effect on grottos' preserve situation, and value of safety risk weight in the system is 0.75. While value loss risk affects grottos' preserve situation less, effect weight is 0.25. In fact, safety risk in these 11 survey objects often develop fast with a small quantity, which means they are more destructive than other diseases. All of them may directly or indirectly lead to grottos' stability problems. Especially Guangyuan is near to the Longmenshan fault zones, it means once earthquake occurs, the safety risk may result in grottos' destructive damage or disappearance. The physical remains of grottos is the most important physical carrier of value. Value loss risk affects the grotto at a low speed with a long time and distributes widely. In short terms, it will not bring an obvious change to grottos' appearance, but in a long term, this risk may lead to grottos' weathering and value loss even disappearance.
Grottos' vulnerability is a multi-factor, hierarchical structure complex system which involves grottos' value, stone property, existed preserve situation and management. When assessing the grottos' vulnerability, every factor should be considered and the factors are interacted with each other. In this research, we try to explore the vulnerability evaluate mode primarily and under current research condition, the specific expression of the function in equation 10 and 11 is not clear which is for further research.
The AHP method can be used for studying other parameters of grottos' vulnerability or hazard, and this research can offer a useful reference for further study. The grottos' preserve situation assessment mode and vulnerability evaluation mode is still needed to be verified by using other grottos' diseases data. Only keeping adjusting the construction and constitute of matrix in further practice, the assessing indexes and weight can be more reasonable and the evaluation mode can be more reliable. The result can reflect the degree of vulnerability and hazard more effectively, while offering effective evidence for conservation.
There are some deficiencies in this research. One important aspect is geologic environment.
Geologic environment plays a crucial role in determining grottos' vulnerability because of most grottos in Sichuan excavated in mountains. In this study, we treat it as the external cause of grottos' degradation, which may lead to dangerous rock mass problem. And then reducing the degree of vulnerability to a certain extent. So, in the future study, it is necessary to research the mode of hazard.
Only combining the grottos' vulnerability and hazard, can the risk grottos' facing to be reflected reliably and objectively.

Conclusion
The authors surveyed 11 grottos of middle Tang dynasty in Guangyuan thousand-buddhas grottos in the field to determine the contribution of each disease, making to grottos' preserve situation. By building hierarchical structure and constructing judgement matrix, weight of every disease is calculated, and the preserve situation degree of 11 grottos can be shown in a quantized way. From the result, we can conclude the following: 1. A hierarchical structure of the preserve situation is established: the preserve situation of grotto is defined as goal layer, two categories' risks made up criterion layer, the index layer includes 15 diseases, namely, body loss (C4), scaling off (C1), cracks (C5), water diseases (C3), detachment (C2), rock powdering weathering (C7), deep loss (C8), salt crystallization (C9), plant damage (C6), pigment layer peeled off (C10), paint layer craquelure (C11), scratch or graffiti (C12), improper repairing (C13), human pollution (C14), and microorganism pollution (C15). The weight in the evaluate system is descending order.