Research on the eco-geological environment carrying capacity in pingwu county after the wenchuan earthquake based on the modified AHP

Many counties in southwestern China were devastated by the Wenchuan earthquake, and this earthquake also induced several geological hazards. Therefore, evaluation of the eco-geological environment in the disaster area is essential for county restoration and ecological remediation. This research considers Pingwu County, which is located 89 km from the epicenter of the Wenchuan earthquake, as the study area to evaluate the eco-geological environment carrying capacity. First, three evaluation index layers are built for an eco-geological environment carrying capacity model after the earthquake, including the geological, ecological and social environments. Then, the evolutionary algorithm is used to modify the analytic hierarchy process (AHP). By optimizing the consistency ratio of the AHP, the most consistent evaluation matrix can be obtained. Finally, we calculate the eco-geological environment carrying capacity in Pingwu via the best consistent evaluation matrix and obtain a hierarchical map of the eco-geological environment carrying capacity through grid rasterization. The results indicate that the current eco-geological environment carrying capacity in Pingwu County mainly contains two states, equilibrium and surplus states. According to the hierarchical map, this study suggests that focusing on ecological protection and disaster monitoring in the eastern and northern areas of Pingwu, large infrastructures should be built in the central and southern areas, and the land use capability should be further improved. Moreover, construction in the central area of Pingwu should be optimized, the scale of regional construction should be controlled, and the original ecological species in the natural protection area should be maintained.


Introduction
A strong earthquake, namely, the Ms8.0 Wenchuan earthquake, caused catastrophic disasters in most counties of Southwest China (Wang et al. 2011;Ye et al. 2011). At the same time, landslides, barrier lakes, and collapses induced by this earthquake seriously threatened stable development of the social economy and ecological environment in the disaster area (Zhang et al. 2010). The Fujiang River basin belongs to the severely afflicted area of the Ms7.2 Songping earthquake in 1976 and the Ms8.0 Wenchuan earthquake in 2008. The eco-geological environment in the basin is complicated and fragile. As a result, there occurred a large number of secondary disasters in the area after the earthquake. Pingwu County, one of the key towns in the Fujiang River basin, was rebuilt after the earthquake. With increasing human engineering activities during reconstruction, the geological environmental capacity in certain regions is rapidly decreasing but is not adapted to further construction and development. Therefore, it is essential to implement eco-geological environment carrying capacity assessment in the area to plan town development and provide long-term guidance for urban reconstruction in the disaster area.
The capacity of the geological environment for human activities is limited, and the maximum limit is referred to as the geological environmental capacity (Bishop 1974). Since this concept was proposed, the evaluation method of the carrying capacity of the geological environment has been improved. There are several evaluation models related to the environment carrying capacity: Rees (1992) proposed the ecological footprint method by measuring the ecological environment range required by human activities, which provides a basis for determining whether human activities occur within the adaptable range of the carrying capacity. Trevisan et al. (2000) developed a multi-index evaluation system to evaluate the geological environment carrying capacity in terms of various indices including water/soil pollution, land subsidence, land salinization, and desertification. Cherp (2001) and Vatn (2009) used systematic analysis methods to evaluate and compare the geological environment carrying capacity of countries located in Eastern Europe and Central Asia. They summarized several evaluation indices and methods for the geological environment carrying capacity. However, most of these methods are unilateral or qualitative static evaluation methods; for example, the ecological footprint method is primarily biased toward ecological evaluation, and systematic analysis methods are only used for qualitative evaluation. In recent years, the GIS-based analytic hierarchy process has been applied in geological environment carrying capacity evaluation. Zhu (2009) chose the Guangxi Beibu Gulf Economic Zone as the research object, using the AHP with a comprehensive index method and a coupling method of the environmental saturation, to obtain early warnings of resource and environmental constraints and formulated prevention and control measures. Wang et al. (2011) used the AHP-GIS coupling model to evaluate the carrying capacity of the geological environment in the Shandong Peninsula. Compared to other models, the AHP method is fully quantitative and highly accurate, so this method is widely used to evaluate the geological environment carrying capacity. However, after the Wenchuan earthquake, few research studies combined different eco-geological environment factors of key towns within the disaster area, and there was a lack of guidance for long-term eco-geological recovery from the perspective of the eco-geological environment carrying capacity.
In this study, the following aspects were considered to evaluate the eco-geological environment carrying capacity in Pingwu: (1) the AHP method was modified by using the evolutionary algorithm, which solved the problem whereby judgment based on expert scoring in the AHP method is not objective. (2) Through a geological survey of the geological structure and natural hazards, we determined ten factors related to the geological, ecological, and social environments. The current status of the geological environment bearing capacity in Pingwu County was calculated with the modified AHP method. (3) According to the obtained hierarchical map, we analyzed the geological environment carrying capacity threshold and capacity status in Pingwu County and provided a development suggestion for postearthquake development plans of the region.

Geological environmental background of the study area
The study area, Pingwu County, is located in the northwestern part of the Sichuan Basin, within the eastern edge of the transition from the Qinghai-Tibet Plateau to the Sichuan Basin (E103°50′ ~ E104°58′, N31°59′ ~ N33°02′; with a total area of 5974 km 2 ). Geographic location and elevation information of Pingwu County is shown in Fig. 1. The overall terrain in the study area is high in the northwest and low in the southeast. The altitude of Xuebaoding, the highest peak of Minshan Mountain in the northwest, reaches up to 5588 m, and the lowest altitude occurs in the southeast in the Jiaoyuanzi Valley of Erlangxia, Fujiang River, at just 600 m. The height difference between these two locations is nearly 5000 m.
As shown in Fig. 1, Pingwu County is located 89.7 km from the epicenter of the Ms8.0 Wenchuan earthquake, which belongs to the high-hazard area within the epicenter range, and the disasters in towns near Beichuan County were more serious than those in other areas. The 2008 earthquake sequence was distributed along the Wenchuan-Maowen fault, and half of the earthquakes passed through Pingwu. Most of the focal mechanism solution involved thrust, and the remainder involved strike-slip. At present, there remain many geological environmental problems in Pingwu County, including the following aspects: First, soil erosion widely occurs in this area due to earthquakes and human engineering activities, especially after the Wenchuan earthquake. Second, Pingwu County belongs to the mountainous area, and the mountain valley catchment capacity leads to highly serious flood disasters. There remained many collapse deposits in the valley after the above earthquake, blocking the channel, resulting in poor drainage and flooding-prone conditions during heavy rainfall. Moreover, the foundation of the Wuxian structure occurs on a soil foundation with different physical and mechanical properties, which is prone to uneven settlement. Last and most importantly, there are several active faults in the northwest triangular block of Pingwu, including the Minjiang fault, Huya fault, Songpinggou fault, and Jiaochang fault, and this area has experienced twenty Ms > 5 earthquakes and three Ms > 7 earthquakes since 1630.
On May 12, 2008, an Ms 8.0 magnitude earthquake occurred along the Longmenshan fault. The Pingtong-Xingyan-Nanba-Shikan area along the fault in Pingwu County is a meizoseismal area, and the seismic intensity reached as high as 11 degrees. A total of 27 Ms > 4 aftershocks occurred in Pingwu County and adjacent areas, and the maximum magnitude of these aftershocks in this area reached Ms 6.1. Therefore, numerous secondary geological disasters were induced by this earthquake. According to a detailed investigation of geological disasters (Qin et al. 2009), there are 406 geological hazards in Pingwu County. As shown in Fig. 2, landslides account for the highest proportion of all disasters, reaching 64.53% (262 sites). The second highest proportion involves debris flows at 66 sites, accounting for 16.26% of all sites. The other sites include 47 collapse sites (11.58%) and 31 unstable slope sites (7.64%). The threat of geological disasters mainly includes towns, settlements, schools, farmers' lands, and roads. Saaty and Kearns (1985) first proposed a multicriteria decision-making method, namely, the analytic hierarchy process (AHP), which is considered a reasonable and effective weighting method among existing weight evaluation methods (Saaty 2008). Because the AHP adopts the qualitative analysis approach of the expert scoring method and an appropriate mathematical model for quantitative analysis, multiple objectives and multiple criteria can be reasonably and quantitatively analyzed simultaneously (Saaty and Vargas 2012). This method includes four main steps: 1. establishment of an analytic hierarchy model; 2. construction of a model comparison matrix; 3. calculation of the weight of each factor in the model; 4. result consistency testing. However, the subjective influence of expert evaluation in the AHP leads to very large number of qualitative components, which reduces the reliability of this method (Zhao and Dan 2003). This study used evolutionary algorithms (EAs) to further optimize the weight determination process of the AHP and improve the rationality of quantitative evaluation of each factor. As described in Fig. 3, the modified AHP uses evolutionary algorithms to obtain the optimal comparison matrix with the best consistency (the black dotted line), instead of expert scoring and consistency testing in the traditional AHP (the red dotted line). As a result, the modified AHP method is more objective than is the traditional method.

Modified AHP involving evolutionary algorithms
Through improvement of the traditional AHP method, the modified AHP can be organized as follows: First, the evaluation indicators (X1, X2…, Xn) of judgment matrix X are determined. Then, the importance range is obtained via pairwise comparison of the determined indicators, as summarized in Table 1. Finally, a fuzzy judgment matrix is assembled based on the importance range. It should be noted that the importance of these two evaluation indicators varies between two scales, so we construct a fuzzy scoring matrix with the expert scoring interval method and determine the best comparison matrix with the optimal consistency within the scope of the fuzzy scoring matrix.
The boundaries of the evolutionary algorithm are defined by a fuzzy judgment matrix, similar to the traditional AHP method, and the consistency ratio CR is calculated with Eqs. 1-4 as the single EA optimization objective.
(1) The judgment matrix can be expanded by the row as: (2) The judgment matrix can be normalized as: (3) The maximum eigenvalue of the judgment matrix can be determined as: (4) The consistency indicator CR can be calculated as: CI is the consistency ratio, λ max is the maximum eigenvalue, and n is the matrix order. RI is the ratio of the average random consistency to the random consistency reflected in the number of evaluation indicators. The judgment matrix can be regarded as indicating a satisfactory consistency, and the weight values are reasonable for CR < 0.1 in the traditional method. However, for CR > 0.10, the data do not generate meaningful outcomes unless reexamined, which always complicates the evaluation procedure. Therefore, we can apply CR as the only optimization objective to determine a consistent optimal matrix, thus yielding a single-objective evolutionary problem, and directly calculate a Indicating that one factor is slightly more important than the other factor 5 Indicating that one factor is significantly more important than the other factor 7 Indicating that one factor is more important than the other factor 9 Indicating that one factor is extremely more important than the other factor 2, 4, 6, 8 Indicating a transition value between importance judgment levels Reciprocal Factor i is compared to j to obtain judgment b ij . Factor j is compared to i to obtain judgment b ji = 1/b ij consistent optimal judgment matrix with the evolutionary algorithm method. Therefore, the result of the modified AHP is more objective than that of the traditional method.

Building the evaluation index system
According to the postearthquake geological environment background, ecological environment, distribution of disaster points, and social development in the region, considering the characteristics of frequent geological disasters, vulnerable ecological environment and frequent human activities in the study area, an evaluation system of the geological environment carrying capacity is constructed based on ten evaluation index layers in the three aspects of the geological, ecological, and social environments, which is suitable for areas with geological disasters (Huang et al. 2008), and this method is widely used for carrying capacity evaluation in different areas (Qi et al. 2015;Liu and Ye 2015;Huang et al. 2011). Then, the content of the evaluation index system of the geological environment carrying capacity can be calculated at different levels. The Pingwu County geological environment carrying capacity evaluation index system structure, as shown in Figure 4, includes three subsystems: the geological environment subsystem, ecological environment subsystem, and socioeconomic subsystem. As shown in Fig. 4, construction of the AHP evaluation system requires that the selected factors are independent factors. Therefore, we selected four factors related to the geological environment carrying capacity in the geological environment criterion layer. Because the ecological environment constitutes an essential part of the environmental geology, the ecosystem was regarded as the second criterion layer, including water and land resources. The third criterion layer encompassed the social economy, including the population and basic facilities. Obviously, evaluating the regional geological environment carrying capacity considering the potential of natural hazards and environmental resources is not sufficiently comprehensive (Liu et al. 2009;Wang and Yi 2009). The social and ecological environments are also key criterion layers of the quantitative model of the eco-geological environment carrying capacity evaluation system. Therefore, we could comprehensively evaluate the eco-geological environment carrying capacity in the study area based on this new evaluation index system.

Calculating the index weight via evolutionary algorithms
According to the chosen evaluation indices of the eco-geological environment carrying capacity in the previous section and standards for quantitative judgment listed in Table 1, we determined the fuzzy judgment matrix referring to the expert scoring method of AHP Fig. 4 Evaluation index system structure for the geological eco-environment carrying capacity in Pingwu County evaluation indices in previous studies (Chen et al. 2004;Wang and Yi 2009). The fuzzy scoring matrix reflects the advantages of quantitative evaluation of the expert scoring results and reduces the objectivity due to human factors in the scoring process. Table 2 provides details on the fuzzy judgment matrix.
In fact, the original complex process could be reduced to a single-objective optimization problem by selecting the consistent optimal matrix with the fuzzy matrix. CR is the evolutionary algorithm optimization objective in this study. We set the number of individuals to 1000 and increased the evolutionary generations step by step. As shown in Fig. 5, with increasing evolutionary generations, the mean and standard deviation of CR continuously decreased from those of the last evolutionary generations.
(a) 50 generations; (b) 100 generations; (c) 200 generations; (d) 500 generations. Indeed, the optimal solution and standard deviation of CR remain stable, while the number of generations increases to five hundred (< 10 −4 ). Therefore, we use the comparison matrix corresponding to the minimum CR value of these five hundred generational evolutionary algorithm as the optimal comparison matrix to calculate the weight of each parameter. The calculation results are listed in Table 3.

Results of the geological eco-environment carrying capacity in Pingwu County
Based on the nine evaluation indices in the three criterion layers of the geological, ecological, and social environments, Fig. 6 shows the results of GIS raster visualization. Then, we determined the weight of each index with the modified AHP method involving evolutionary algorithms. We calculated and superimposed multiple indicator values through the GIS grid and finally obtained a geological environment carrying capacity map of Pingwu County.
(a) Lithology; (b) topography; (c) natural hazards; (d) geological structure. There are four indices in the geological environment criterion layer, as shown in Fig. 6. The topography and geological structure indices contain two secondary factors. The geological structure mainly includes the influence of seismic faults, and this index can be quantified based on the fault distance and classification of the ground shock. Similarly, the slope and elevation were selected to represent the characteristics of the topography. The other indices could be directly expressed by a single factor, including the natural hazard density and lithology.
According to the genetic type, material composition, structural characteristics, and physical and mechanical properties of strata, the lithology could be divided into five geological rock groups, namely, clastic, carbonate, metamorphic, magmatic rocks and pebbles, which could be considered hard rock, medium-hard rock, hard/soft interphase, soft rock and pebble soil, respectively. The topography index includes the slope range from 0° to 90°and the elevation range from 600 to 5440 m, and these factors could be divided into four levels. The main purpose of this study was to better understand the geological carrying capacity after the Wenchuan earthquake, so the natural disaster index system analyzes the disaster density distribution after the earthquake, mainly including debris flows, landslides, collapses and other disasters, and the geological structure index includes the fault distance and ground shock, which are quantitative indicators directly related to earthquakes. Figure 7 shows the visualization results of the two indices in the ecological environment criterion layer, including water and land resources. Water resources mainly originate from the Fujiang River running through Pingwu County with a total length of 157 km, which is the largest tributary of the Jialing River. Moreover, there are 15 Fujiang tributaries  and 428 streams in the region, such as the Qingyi River and Duobu River, and the total river network density reaches up to 0.3 km/ km 2 . Pingwu County experiences abundant rain with an average annual precipitation of 806.0 mm, which supplies water resources for rivers, and all rivers contain enough water to support both human and economic activities. Therefore, the river distance is a critical criterion for water resources. There are sufficient cultivated land resources in the study area, mainly including dry land, paddy fields and vegetable fields. The total sown area is 25,231.47 hectares, and the food production of all fields reaches up to 101,190.88 tons each year. Major agricultural products include rice, corn, and rapeseed. Land resources for food production are important to sustain the population, and these resources represent another critical criterion for the ecological environment. The population density and basic facilities belong to the social economy criterion layer. The population density reflects the degree of population aggregation in Pingwu County. As shown in Fig. 7, the population of Pingwu is mainly concentrated in Longan town, Crystal town, and Nanba town, and radial reduction in the population density was centered on these areas. The population density in Tucheng town and Xiangyan town sharply decreased to below 50 people per square kilometer. The infrastructure in Pingwu County is mainly distributed along the river basin, in which Longan town exhibits the highest concentration. Infrastructure is distributed linearly along the main river channel and tributaries of the Fujiang River. Infrastructure projects mainly include highway traffic, town construction, and ancillary facilities.
Indeed, we used the weight of each index (Table 3) obtained with the optimal comparison matrix and implemented grid superposition to obtain a geological eco-environment  Table 4. The data sources were mainly based on file collection from the government, open-access databases, and field surveys of this project. In addition, to fully utilize high-resolution data, we unified all grid sizes to 5 × 5 m via interpolation, which is the smallest grid size across all indices, and obtained the eco-geological environment carrying capacity in Pingwu County, as shown in Fig. 8.
The carrying capacity of the eco-geological environment in Pingwu County involves four categories: high, medium, low, and very low. Furthermore, these categories could be divided into two states: equilibrium (critical overload) and surplus (nonoverload). The equilibrium state includes high and medium carrying capacity levels, which suggests that the geological disasters in the region are relatively widely developed, but the development area is limited. Moreover, both low and very low carrying capacity levels indicate the surplus state, and the areas exhibiting this state are usually less developed with a low population density. As shown in Fig. 8, high-carrying capacity areas were mainly located along the Fujiang River and both sides of the Pingtong River, including slope sections on both sides of the valley and human activities close to the buffer zone of nature reserves, as well as low-mountain and hilly landform areas. The critical overload capacity in these areas could be mainly attributed to frequent geological disasters and human activities. Similarly, the areas in Pingwu County with a low population  Data sources Geological structure 1:50,000 regional geological survey report of Pingwu Lithology 1:50,000 regional geological survey report of Pingwu Topography 1:50,000 regional geological survey report of Pingwu Natural hazards 1. Emergency investigation of geological disasters after the Wenchuan earthquake by the Sichuan Provincial Bureau of Metallurgical Geology 2. Survey of geological disasters in Pingwu County by the Sichuan Geological Survey 3. Investigation of geological disasters in Pingwu County by the Sichuan Geological and mineral Resources Group Co., Ltd Water resources Fujiang environmental geological in situ survey project Land resources Resource and environment science center of the chinese academy of sciences Population Fujiang environmental geological in situ survey project Basic facilities Fujiang environmental geological in situ survey project density and fewer geological disasters belonged to the surplus state, mainly including nature reserve areas in Baima town, Tucheng town, and Huya town.

Discussion
Pingwu County is located in the upper reaches of the Yangtze River, where the regional geological structure is complex. Especially after the Wenchuan earthquake, the unique geological structure, earthquakes, debris flows, landslides, and other natural hazards in coastal areas become significant barriers to the recovery and development of cities and towns (Song et al. 2016;Yao and Yuan 1994). The multi-index comprehensive evaluation method of the geological environment carrying capacity can be used to quantitatively evaluate the geological conditions in Pingwu. The analytic hierarchy process (AHP) is the standard multi-index quantitative analysis method. However, the expert scoring step of the AHP is greatly influenced by subjective factors, so we combined a fuzzy scoring matrix and evolutionary algorithms to obtain the comparison matrix with the minimum consistency ratio.
According to previous studies on environment carrying capacity evaluation with the AHP method (Dai et al. 2001;Liu and Li 2020;Bozdağ et al. 2016), most consistency ratio CR values ranged from 0.01 to 0.07. As shown in Fig. 9, compared to the result of the modified AHP method yielding a consistency ratio of CR < 10 −4 , the other CR results are much higher, and the judgment matrices are not consistent enough, even though they all pass the consistency test. As a result, the modified AHP can evaluate multi-index quantification problems more objectively and reasonably than can traditional methods.
The eco-geological carrying capacity results for Pingwu provide a reference for postearthquake reconstruction and ecological restoration in the future. As shown in Fig. 10, high-carrying capacity areas up to 1087.39 km 2 , which account for 18.38% of the total area of Pingwu, were mainly located along the Fujiang River and both sides of the Pingtong

Area Ratio of the Eco-Geological Environment Carrying Capacity in Pingwu
High Medium Low Very low 1 3 River. The advantages of these areas are convenient transportation conditions, abundant water and soil resources, and multiple town gathering places. Moreover, the disadvantages include that these areas belong to the Zhongshan landform structure, so there are many geological disasters threatening the safety of towns and highways. Furthermore, it is suggested that these areas should strengthen the combination of engineering and ecological management measures to implement ecological slope management measures, which are both beautiful and effective. Reconstruction plans should give more attention to the optimization of the design of critical towns and should fully manifest the characteristics of the geological environment in towns. Medium-carrying capacity areas accounted for 37.35% (2210.23 km 2 ) of the total area, primarily located on both sides of the valley and the transition area from regions of human activities to nature reserve areas. The area belongs to the hilly landform zone, and there are plenty of mineral resources and fewer human engineering activities in this area. However, it is difficult to restore engineering areas and mitigate the aggregation of local geological disasters. Planning proposals for this region should focus on the scientific and rational exploitation of resources. For instance, environmental restoration of abandoned mining areas, control of secondary disasters due to mining, and reclamation of mining areas.
The areas with low and very low eco-geological environment carrying capacities accounted for 30.56% (1808.27 km 2 ) and 13.71% (811.46 km 2 ), respectively, of the total area, both located in nature reserves, with fewer human engineering activities and a low geological disaster risk. It is necessary to optimize construction in the central region, control the scale of regional construction, and maintain the original nature of ecological species in nature reserves. Table 5 provides postearthquake development plans for the different areas based on the eco-geological environment carrying capacity in Pingwu. To illustrate the validity and reliability of the application of the eco-geological environment carrying capacity in Pingwu based on the modified AHP method, Fig. 11 shows the distribution of natural hazards, as reported by the Department of Natural Resources of Sichuan Province after evaluation (http:// dnr. sc. gov. cn/ scdnr/ scgsgg/ 2021/4/ 29/ 20837 32f5a 29418 4b764 d271f ee7b9 b6. shtml). More than seventy percent of all natural hazards are located in areas with a low or very low capacity, and major newly built or ongoing municipal infrastructure construction projects (> one million dollars), including the first PPP (Public-Private Partnership) project of Mianyang city after 2018, are all located in areas with a high or medium capacity. It is illustrated that our results could provide a reference for reconstruction safety and disaster prevention.

Conclusion
Considering the severe threat of earthquakes and geological disasters to the towns in the mountainous areas of Southwest China and the characteristics whereby urban construction is tightly restricted by geological environment conditions and the susceptibility to geological disasters, this paper selected Pingwu County, a key town in the typical and representative Fu River Basin, as the study area. Based on many field investigations and collected data pertaining to Pingwu, we conducted a scientific evaluation of the eco-geological environment carrying capacity in selected towns with the modified AHP method involving evolutionary algorithms. This study provides a scientific basis for long-term planning and development of Pingwu County after the Wenchuan earthquake. The results are as follows: (1) the traditional AHP was modified by evolutionary algorithms. The fuzzy scoring matrix was used to determine the optimal consistent weight coefficient matrix, which avoids the difficulties of consistency testing and the influence of subjective factors associated with expert scoring. (2) The modified AHP method and spatial processing technology support the evaluation of the geological environment carrying capacity. The results indicated that this method is reasonable. However, due to the effect of strong geological tectonic motion, the evaluation system is only applicable in similar areas containing cities and towns in southwestern mountainous areas.
(3) According to the classification results of the eco-geological environment carrying capacity after the Wenchuan earthquake, the eastern and northern areas of Pingwu with a low and very low carrying capacity should be considered for ecological protection and disaster monitoring, and the earthquake resistance level of new infrastructure should be enhanced. Large infrastructures should be built in central and southern Pingwu with a high or medium carrying capacity, and the land use capability should be further improved.