Study on the Linear Vanishing Section Ratio of Earthen Sites and Anthropogenic Influence from the Perspective of Population Density


 Having extremely high artistic, scientific and social values, earthen sites are widely distributed in China, which are important cultural relic resources of mankind. Due to accumulated natural erosions and human activities, however, earthen sites have been greatly damaged and have even vanished many sections, so that they are seriously threatened by extinction. In the circumstances, acquiring the conservation status of earthen sites is a vital prerequisite for the subsequent targeted protection. In this paper, as a world-renowned heritage site, the castles of the Ming Great Wall located in Qinghai Province were selected as the research object. A novel indicator namely the linear vanishing section ratio (L-VSR) was proposed and its value was classified as five levels to quantitatively characterize the specific conservation status of such sites. Based on the assessment results, the castles at the excellent status constituted the minimum proportion, while the castles at the very poor status represented the largest percentage, reflecting the grave situation of earthen sites. Furthermore, applying population distribution models into the linear fitting combined with the population density (PD), the positive correlation between PD and L-VSR was obtained to reveal the anthropogenic influence on the destruction of earthen sites. This study provides a new thought to quantitatively characterize the preservation conditions of earthen sites and also indicates the effect of human activities on the damage of earthen sites from the population perspective. Hence, it is beneficial to the overall damage assessment of earthen sites, and also meaningful to their further preservation and protective planning.


Introduction
Earthen sites are a kind of typical architectural sites mainly built with soil materials, which are widely distributed in the whole world, such as Ajina Tepa, Tajikistan [1], Alhambra, Spain [2], Casa Grande Ruins National Monument, the United States [3], Çatalhöyük, Turkey [4], Great Wall [5] and Tulou, China [6]. Having extremely high artistic, scientific and social values, earthen sites in China have a long historical process stretched from the Palaeolithic Age to modern times, reflecting the evolution of Chinese civilization and the improvement of social productivity [7,8]. Undoubtedly, they are important cultural relic resources of mankind. Exposed to long-term natural forces including wind and rain erosions and human activities, however, earthen sites have developed many deteriorations such as sapping, cracks, scaling off, gullies, collapses, etc., severely threatening their safe occurrence [5,[9][10][11][12]. Under the circumstances, most earthen sites have been seriously damaged and even have vanished many sections due to the development of deteriorations and natural/human influences in the past thousands of years, so that they are greatly threatened by extinction. Consequently, taking targeted protection for earthen sites is very urgent, and acquiring the conservation status of earthen sites starting from these vanishing sections is a vital prerequisite for the protection work.
So far, many scholars mainly focused on the mechanisms of deterioration development of earthen sites. Four deterioration categories including property deterioration, structure damaging, structure collapse, and site destroying were summarized [10].
On the basis of field investigation and laboratory analysis, four main deterioration modes, namely wind-related deterioration, water-related deterioration, temperature-related deterioration and chemical-related deterioration in Jiaohe ruins in China were identified [12]. A model characterizing the deterioration at earthen sites of the Ming Great Wall in Qinghai Province was also proposed to reveal the mechanisms and evolution of deterioration from a macro perspective [5]. Based on these deteriorations development, the damage assessment of earthen sites was studied by means of multicriteria decision-making (MDCM) and machine learning methods combined with environmental factors and building materials indices, which has revealed earthen sites' local damages caused by the development of deteriorations [9,13]. However, a scientific approach to assess the overall damage of earthen sites was still lacked to quantitatively illustrate these sites' conservation status. The effects of natural factors on earthen sites such as wind, rain, earthquake, etc., have mostly been studied [11,14,15], but few researches focused on their quantitative influence of human activities.
In this paper, the authors selected 46 castles of the Ming Great Wall located in Qinghai Province, China as the research object, and proposed a novel indicator, namely the linear vanishing section ratio (L-VSR) to characterize such sites' conservation. Moreover, the anthropogenic influence on the L-VSR was researched from the perspective of population density (PD). By applying population distribution models, PD was further correlated with L-VSR to show the effect of human activities on the damage of earthen sites from the macroscopic perspective. As seen from the research results, it is potential to promote the indicator and model proposed in this study into earthen sites and other architectural types of the Ming Great Wall. The research findings have beneficial references to the overall damage assessment of earthen sites, and also meaningful to their further preservation and protective planning.

Study Objects
The Great Wall built in the Ming Dynasty, called the Ming Great Wall, was the most renowned military defensive project in ancient China, which has been designated as a World Heritage in 1987 [16]. The Ming Great Wall is a complex military network consists of walls, trenches, beacon towers, passes, castles, precipitous mountain areas, marine insurance, etc., and these building types played their respective roles and cooperated with each other in the military defense phase [17]. In the whole Great Wall system, the castle is a core element with multiple functions such as the exchange of military information, goods and people, and the management of important civil affairs [18,19].
Located independently from the Great Wall mainline in "nine towns", the Ming Great Wall in Qinghai Province is a significant section of the whole Great Wall, which was built from 1546 to 1596, surrounding Xining Wei with an arch shape [17,20]. As the rammed earth is the dominant building material vulnerable to climate, the Ming Great Wall in Qinghai Province has currently existed as a form of earthen sites exposed under environmental impacts for about 500 years [13,21]. Being a significant part of the Ming Great Wall, there are 46 castles located in Qinghai Province (Fig. 1), which were selected as the study object to research their conservation status. The information on these sites has been listed in Table 1. By collecting archaeological materials of such sites, the linear circumference and remaining length of walls can be acquired. Then L-VSR can be calculated to indicate the conservation status of castles.

Methods
In this research, the authors mainly referred to archaeological materials from the Qinghai provincial administration of cultural relics and the Qinghai Bureau of surveying and mapping to collect the plane graph of castles. Then the data castles' circumference length (CL) and remaining length (RL) can be acquired from the measurement of plane graphs in Auto CAD.
The authors proposed a novel indicator called the linear vanishing section ratio (L-VSR) which indicates how many sections of earthen sites in these castles have been vanished by the following calculation: where RL/CL is the remaining length ratio (RLR) shown in Eq. (2): The value of L-VSR can be classified as 5 levels to quantitatively characterize the specific conservation status of castles, including excellent (E) (0-10%), good (G) (10%-25%), fair (F) (25%-50%), poor (P) (50%-75%), and very poor (VP) (75%-100%). Because there has not been a uniform method of damage division for earthen sites so far, in this research the authors mainly referred to the classification approach used for the rock quality designation (RQD) to provide a quantitative estimate of rock mass quality from drill core logs [22].
After that, the authors introduced the index of population density (PD) into this research. The PD indicates the number of people living in each unit of area (such as a square kilometer), which is an important indicator to measure the distribution of population in a region [23]. Its formula was shown in Eq. (3): where PN is the number of population in a certain region, and RA is the area of that region.
Finally, four frequently-used single core population distribution models were applied to achieve positive correlations between PD and L-VSR, showing the influence of human activities on the conservation of earthen sites from a macroscopic perspective.

Linear Vanishing Section Ratio (L-VSR)
The authors firstly calculated the L-VSR value of the No.  Using the same procedures and methods, all 46 castles' L-VSR values were acquired. The data of RL and CL were collected and then L-VSR data were calculated based on Eq. (1), and the conservation status was also given according to the L-VSR values and classification levels, which were listed in Table 2.  (Fig. 3). Hence, the castles at the excellent status constituted the minimum proportion, while the castles at the very poor status represented the largest percentage. There are more than half of the castles in the poor condition or even worse. These grading evaluation results have reflected the grave situation of earthen sites.  Table 3.
Combined with castles' conservation status results acquired before, the authors averaged all PD data of villages where the castles in each same damage level are located. As shown in Fig. 4, with the increment of overall damage level, the average PD data steadily increased from 4860 number per km 2 in the G status to 8679 number per km 2 in the VP status. This means that the conservation status of earthen sites would worsen as the surrounding population grows. Thus, the influence of human activities on the conservation of earthen sites can be proved from the PD perspective. Note: There is no village close to the No. 5 castle so its related village population was not considered in this research.

The correlation between PD and L-VSR
After acquiring the data of PD of villages and L-VSR of castles of the Ming Great Wall in Qinghai Province, the correlation between PD and L-VSR was studied in order to further reveal the anthropogenic influence on the conservation of earthen sites. In fact, many castles in this research are not located in villages but nearby those villages, so the population density attenuation along with the distance between castles and villages should be considered. The four frequently-used single core population distribution models were applied, including the models of Clark, Smeed, Newling, and Cubic [24][25][26][27], to calculate the population density of castles with the attenuation of the PD of villages which have a certain distance from castles.
The Clark model used a negative exponential function to indicate the relationship between PD and distance from the residence center, shown in Eq. (4): The Smeed model's formula is a power exponential function shown in Eq. (5): The Newling model is a quadratic exponential model shown in Eq. (6): PD r =PD 0 e br+cr 2 (6) The Cubic model is a cubic function from Eq. (7): PD r =PD 0 e br+cr 2 +dr 3 (7) where PD r is the population density of a place with the distance of r from the residence center, PD 0 is the population density of the residence center, and b, c and d are parameters. In this study, the authors simplified the village as a point and if a castle is located in the village, their distance can be regarded as 0 m. Furthermore, the PD r is the assumed population density of castles with the attenuation of the PD of villages, PD 0 is the population density of villages, and r is the distance between the castle and village.
Combined with related archaeological materials and the software of Rivermap X3, we collected and measured the data of distances between castles and villages in which they are located or nearby, listed in Table 4. After that, it is assumed that there is a linear positive correlation between PD r and L-VSR. During processing related data, the PD 0 and L-VSR of castles which have the same distance from villages where they are located have been calculated as the average value. Eventually, there are 17 groups of data to conduct the fitting, which have been shown in Table 5.   To achieve optimal fitting effects, the optimization algorithm of Levenberg-Marquardt (LM) was used to determine the parameters in Eqs (4)- (7). After that, PD r can be calculated and the correlation between PD r and L-VSR can be further determined, as shown in Fig. 5. From the correlation results, the Cubic model has the largest correlation coefficient (R=0.6415), compared to the other three models. Therefore, the positive correlation between PD and L-VSR can be proved, and the anthropogenic influence on the conservation of earthen sites was revealed from a macroscopic perspective.
In fact, human activities have very significant effects on the damage of earthen sites, and even artificial destruction in historical and contemporary processes has been regarded as one of the deterioration types of earthen sites [8,10,12]. For instance, local farmers directly dug soils from earthen sites (Fig. 6a), randomly added buildings along with earthen sites (Fig. 6b), and even dwelt behind earthen sites so that the earthen wall has to be used as their home enclosures ( Fig. 6c and Fig. 6d). Some farming activities (Fig. 6e) and road engineering (Fig. 6f) also brought apparent influences on the earthen sites' conservation.
However, to implement the Rules on the Great Wall Protection, the overall protective planning of the Ming Great Wall in Qinghai Province has been conducted orderly, which would effectively restrict human destruction under the joint efforts of government and individuals [28]. In this research, the aforementioned four population distribution models have a common assumption with the single core population distribution, meaning that the population density would generally decrease with the increment of distance from the residential center. Therefore, if the castle is much closer to the village, its conservation could be more obviously affected by more intense human activities, which has been proved from the fitting correlation results in Fig. 5. The flaw is that the correlation coefficient is not very large. The reason is that the population number has fluctuated with time. Especially, the Ming Great Wall has been built for about 500 years but the residential number in their locations each year is really hard to acquire.
However, the population number in this research is only collected from the archaeological materials in 2008 provided by the Qinghai Bureau of Cultural Heritage. And the L-VSR data can also reflect the destruction status of castles in 2008 as the overall survey of castles was carried out in that year. This means that a good corresponding relationship between PD and L-VSR has been studied in this paper; Except for human influence, the damage of earthen sites is also closely related to the erosions of wind and rain and the vulnerability of rammed earth materials [9,13]. But a positive tendency between PD and L-VSR can be apparently seen from our research results, and correlation coefficients have passed the significant test, having statistical significance. Therefore, the indicator and model proposed in this research have scientificity and accuracy. In our future research, the models of L-VSR and PD will be further promoted and applied into other sections of the Ming Great Wall in NW China, to acquire more scientific and precise assessment outcomes of the conservation status of earthen sites by constantly revising and improving related parameters. What's more, the volume reflection data including the remaining height and the top and bottom width of earthen sites will be collected, and then the volume vanishing section ratio (V-VSR) can be further studied in the future.

Conclusion
In this paper, 46 castles of the Ming Great Wall in Qinghai Province were chosen as research objects. The linear vanishing section ratio (L-VSR) was proposed to characterize such earthen sites' conservation status which can be divided into five levels including excellent (E) (0-10%), good (G) (10%-25%), fair (F) (25%-50%), poor (P) (50%-75%), and very poor (VP) (75%-100%). By means of plane graphs of these castles, the remaining length (RL) and circumference length (CL) of castles were collected, and then L-VSR data were acquired.
Based on L-VSR values and corresponding classification ranges, there are 0 castles at the E status, 10 castles at the G status making up 22% of the total castles, 9 castles at the F status accounting for 20%, 10 castles (22%) at the P status, and 16 castles (36%) at the VP status, respectively. Hence, the castles at the excellent status constituted the minimum proportion, while the castles at the very poor status represented the largest percentage. There were more than half of the castles in the poor condition or even worse. These grading evaluation results have reflected the grave situation of earthen sites. Moreover, the population density (PD) of villages in which castles are located or nearby was obtained. Combined with castles' conservation status results, the average PD data increased with the increment of overall damage level, meaning that the conservation status of earthen sites would worsen as the surrounding population grows.
By referring to four frequently-used single core population distribution models, namely the models of Clark, Smeed, Newling, and Cubic, a linear positive correlation between the population density of a position where the castle is located (PD r ) and L-VSR was determined, and the Cubic model has the best fitting result.
According to our research findings, the novel indicator i.e., L-VSR is significant and applicable to characterize the conservation status of earthen sites, and the anthropogenic influence on the damage of earthen sites has been revealed from a macroscopic perspective. It is potential to promote the indicator and model proposed in this research into earthen sites and other architectural types of the Ming Great Wall, to acquire more scientific and precise assessment results of their conservation status by constantly revising and improving related parameters. Therefore, the research is beneficial to the overall conservation assessment of earthen sites, and also meaningful to their further preservation and protective planning.   The conservation status of castles in Qinghai Province The tendency graph between PD and conservation status of castles in Qinghai Province The correlation graphs between PDr and L-VSR: a Clark model, b Smeed model, c Newling model, and d Cubic model. * and ** represent the values of signi cance at 90% and 95% levels by the student's t-test, respectively.

Figure 6
The human activities graphs: a digging, b randomly building, c an enclosure in a peasant household, d an enclosure in an urban housing estate, e farming activities, and f rail engineering.