Assessment of the physical vulnerability of buildings affected by slow-moving landslides

: Physical vulnerability is a challenging and fundamental issue in landslide risk assessment. The previous studies mostly focus on generalized vulnerability assessment from landslides or other types of slope failures, such as debris flow and rock fall, while the long-term damages induced by slow-moving landslides are usually ignored. In this study, a method was proposed to construct physical vulnerability curves for masonry buildings by taking Manjiapo landslide as an example. Landslide force acting on the buildings’ foundation is calculated by applying landslide residual thrust calculation method.


Introduction
Physical vulnerability is a fundamental and indispensable item in the risk definition presented by Varnes (1984).It can be defined as the degree of loss to a given element or set of elements within an area affected by a hazard (UNDRO, 1984).Physical vulnerability is measured on a continuous scale ranging from 0 (no loss) to 1 (total loss).For quantifying physical loss, such as the structural damage, the physical vulnerability of the elements at risk can be achieved by assessing the damage degree, resulting from the occurrence of a landslide of a given type and intensity (Van Westen et al., 2006).
Recently, physical vulnerability is still a challenge, and there has been a growing interest in quantifying risk due to natural hazards (Van Westen et al., 2006).To quickly and easily analyze the physical vulnerability, researchers have developed various types of tools or software such as HAZUS-MH (FEMA, 2003), RiskScape (King and Bell, 2005), ARMAGEDOM (Sedan et al., 2013), and CAPRA (https://ecapra.org/).HAZUS-MH (FEMA, 2003) is considered to be the initially introduced and the most popularly applied software.RiskScape is a national-scale multi-hazard impact model in New Zealand, and ARMAGEDOM is a tool for seismic risk assessment that has three different precision levels (regional territorial scale, districtscale, and the district-scale with more detailed hazard description and physical vulnerability estimation).The majority of the software is employed to analyze the physical vulnerability of earthquakes or multi-hazards, and very few can be utilized for landslide hazard assessment.To solve this problem, Papathoma-Köhle et al. (2015) developed an integrated toolbox designed for buildings subjected to landslides.
In the past decades, researchers have worked on landslide physical vulnerability assessments techniques, which can be grouped into four main approaches as follows: expert judgment (Sterlacchini et al., 2007;Winter et al., 2014;Godfrey et al., 2015;Guillard-Goncalves et al., 2016), statistical (Ciurean et al., 2013;Ciurean et al., 2017), mechanics-based (Luna et al., 2014;Liang and Xiong, 2019;Nicodemo et al., 2020), and integrated (Li et al., 2010;Uzielli et al., 2015b).The results of these approaches include matrices, indicators, and fragility, or physical vulnerability curves or functions.For example, by utilizing the procedures motivated by the seismic risk analysis, Negulescu and Foerster (2010) introduced a simplified methodology to evaluate the mechanical performances of buildings subjected to landslide hazards.Also, Totschnig et al. (2011) presented physical vulnerability curves for debris flow and torrent hazards.Wu et al. (2011) constructed physical vulnerability curves for landslides by considering the landslides' impact energy and impact impulse as the intensity indicators.By utilizing FLO-2D (a hydrologic and hydraulic modeling software of debris flow propagation), Luna et al. (2014) discussed the physical vulnerability functions of buildings at debris flow risk.Based on the physical vulnerability assessments proposed by Li et al. (2010), Uzielli et al. (2015b) modified the method by integrating the assessment of landslide intensity and buildings resilience.Papathoma-Köhle (2015) related hazard intensity (debris-flow depth) with the loss of buildings' damage to buildings' physical vulnerability curves.Soldato et al. (2017) studied the empirical physical vulnerability curves for buildings by considering the debris-flow depth, the flow velocity, and the impact pressure.Mavrouli et al. (2017) quantified the masonry-buildings' damage induced by rockfalls by calculating the impact force of falling rocks on masonry buildings.
The slow-moving landslides may cause partial damage to buildings due to local displacement.The assessment methods for the physical vulnerability of slow-moving landslides are still limited.The aforementioned approaches are not very suitable since slow-moving landslides have different intensity indicators and different types of damages as compared to that from debris flows, rockfalls, or fast-moving landslides.
The performance analysis of buildings during the landslide and the inventory of the observed damage is a feasible methodology (Faella and Nigro, 2003).To investigate the physical vulnerability of the buildings impacted by landslides, numerous studies have been conducted regarding the acquisition of landslide deformation displacement or finding the statistical relation between the damage degree of buildings and landslide intensity (Mansour et al., 2011;Abdulwahid and Pradhan, 2017;Nicodemo et al., 2017;Peduto et al., 2017;Chen et al., 2016;Peduto et al., 2018).For example, Mansour et al. (2011) investigated the relationship between the movement and the expected extent of damage to urban settlements.Based on the persistent scatterer interferometry, Lu et al. (2014) obtained the slow-moving landslides velocity for estimating buildings' economic risk with a total affected area of more than 800 km 2 .Ferlisi et al. (2015) reported that combining the differential interferometry (DInSAR) data and the results of supplementary damage surveys on the slow-moving landslides allowed the preliminary generation of a (maximum velocity) cause-effect (damage) relation.Peduto et al. (2017) applied landslide deformation (cumulative surface displacement and differential settlement) as the input variables to construct the empirical fragility and physical vulnerability curves for buildings.By applying the horizontal strains and angular distortions to the numerical model, Infante et al. (2016) generated physical vulnerability for buildings.Nicodemo et al. (2020) employed the equivalent frame method to analyze the damage of a representative building in case of a slow-moving landslide by numerical modeling.However, a detailed study on the physical vulnerability of buildings using mechanical analysis is not yet available.
This study proposes a method for assessing the physical vulnerability from the perspective of mechanics and obtains its changes during the process of slow-moving landslides.We first calculate the thrust force of landslide acting on the buildings' foundation and then analyze the buildings' physical response.Multi-scenarios were applied to help in constructing the physical vulnerability curves.After the validation by utilizing an application on a typical building impacted by slow-moving landslides, a sensitivity analysis was conducted on the parameters of the building and its foundation.

Force acting on the building foundation during the landslide process
To quantitatively evaluate the building's physical vulnerability during the landslide process, it is essential to calculate the force acting on the building's foundation.In this study, landslide residual thrust force is calculated by employing the residual thrust method, which is extensively applied in China for slope stability analysis (Nie et al., 2004).A slide-mass is divided into different slices in this method and a force analysis is performed on each slice.In this way, it is possible to easily obtain the thrust of a landslide by utilizing the arbitrary shape of the sliding surface and under complex loads.The landslide residual force can be calculated by applying Eq. ( 1)-( 6).In this method the groundwater seepage should be considered under rainy conditions, which can be performed using the SEEP/W code (GEOSTUDIO).The physical vulnerability curve is estimated using landslide safety factor to express the strenght of landslide.Landslides with smaller safety factors are more unstable, resulting in greater residual thrust on the building's foundation.
For a single slice, the residual thrust force of the ith slice is given as follows: =  −1 ×  −1 +   −   /  , =   ×   , (3) = (  +   ) ×   +   ×   , (5) where   denotes the resistance force of th slice (kN/m),   denotes the driving force of th slice (kN/m),   denotes the residual thrust of th slice (kN/m),   denotes the transmitting coefficient of th slice,   denotes the weight of th slice (kN/m),   denotes the accessional vertical load of th slice (kN/m),   denotes the angle between the sliding surface and horizontal plane of the ith slice,   denotes the length of th slice (m),   denotes the cohesion of th slice (kPa),   denotes the internal friction angle of ith slice,   denotes the pore water pressure of th slice (kN/m),   denotes the horizontal seismic force of th slice, and   denotes the horizontal component of landslide thrust (shown in Fig. 2).
The transformation of landslide residual thrust force on buildings' foundation depends on the distribution of force.
According to Chinese standard (China Railway Second Survey and Design Institute, 1983) and Dai (2002), landslide thrust distribution is approximately assumed to be triangular, rectangular, or parabola shapes, based on the type of sliding mass materials.Each type of thrust distribution corresponds to a distribution function (Table 1).Note: F denotes the horizontal component of landslide residual thrust (Pi) in Eq. (3), and h denotes the vertical distance from the sliding surface to the ground surface (Fig. 2).

Inclination of buildings
The foundation of the masonry building affected by the landslide thrust can be simplified as a beam (Fig. 3).It has been observed that real structures are normally very complicated, but the simplification of the beam helps in illustrating several important features (Burland, 1974).For illustrative purposes, we only consider the case of a beam with a uniform load.Timoshenko (1984) gave the function of deflection for the uniform loaded beam of unit thickness flexing in both shear and bending as follows: where q denotes the distribution force on the foundation (kN/m), L denotes the length of the building, I denotes the moment of inertia defined by  =  3 12 , in which d denotes the depth of the foundation, and W denotes the width of the building.Also, E and G denote Young's modulus and shear modulus of the foundation materials, respectively.When =  2 , the equation for the total central deflection is the following: where the maximum deformation of the foundation is denoted by   .Meanwhile, according to Code of Deformation Measurement of Building and Structure (JGJ 8-2007), we can calculate the inclination of the building which is the ratio of the horizontal difference between observation point on the top of the building and observation point on the bottom of the building to the vertical height of the building after tilted.The formula is as follows.
Where, i ---the inclination of the building α ---the incline angle of the building ym ---the horizontal difference between the top and bottom of the building H ---the vertical height of tilted building calculated from the outdoor ground It is worth pointing out that the building in our study case is regarded as a rigid building.So, the maximum horizontal displacement of the foundation by using the simple beam mechanical model will be approximately the horizontal difference of the observation point at the top of the building relative to the observation point at the bottom.
The following is the equation for the inclination of the building: ), (10) where  denotes the inclination of the building, which is the ratio of the maximum deformation   and the vertical height of tilted building calculated from the outdoor ground H.

Damage degree definition
In this study, the ratio of the building's inclination to the threshold value is represented as the damage degree.The damage degree is regarded as the output of physical vulnerability (Tarbotton et al.,2015, Kang et al.,2016).The degree of the building damage can be evaluated by utilizing some parameters, such as cracks in walls, inclination , the ratio of maintenance cost and the original value of building (Alexander, 1986;Chiocchio et al., 1997;Cooper, 2008).Finno et al. (2005) reported that when highly stiff buildings are very inclined due to ground deformation, the wall cracking phenomenon is not obvious.On the contrary, if the stiffness of the building is lower, the cracking on the wall becomes serious.This research shows that using only cracks as an indicator is not suitable for vulnerability assessment.Other indicators, such as inclination, should also be taken into consideration.Therefore, the width of the cracks is not the only indicator for building damage assesment but we should also take into account if the building has inclined.Therefore, the inclination has been chosen to represent the deformation of buildings (Huang, 2015).
Moreover, the inclination of the building is easy to measure.The standard for dangerous building appraisal (JGJ125-2016 China) provides the threshold value of the inclination of single-or multi-story buildings (Table 2).Buildings with inclination exceeding the threshold value are considered to be dangerous and uninhabitable.
By comparing the inclination of the building with the threshold value, the vulnerability (V) can be calculated as follows: The vulnerability (V) ranges from 0 to 1.0, value close to 1.0 indicates serious damage.Equation ( 11) demonstrates that the building's inclination depends on the following three parameters: size, material, and foundation depth.To ascertain the parameter with the highest significant impact on the degree of building damage, we can conduct a sensitivity analysis on these parameters by employing the principle of controlling variables.

General functions
In this study, we obtained the physical vulnerability curve by relating building vulnerability with landslide safety factor (FS).
It is important to note that FS is calculated for only the area where the building under study is located, but not for the whole landslide area.Landslide intensity is directly proportional to its stability situation.A higher intensity corresponds to a higher thrust force on the building foundation and lower landslide safety factor.Thus, we utilize the reciprocal value of FS to be the landslide intensity in this study.
The relationship between building vulnerability and the landslide intensity was fitted by employing Weibull (1951) function that produces an S-shaped curve.This type of distribution curve has been proved to be the best for physical vulnerability analysis by Dario Peduto et (2017), Kang et (2016), Papathoma-Köhle et al. (2015), and Negulescu et (2010).
Based on these findings, a modified Weibull function for calculating physical vulnerability is defined as follows: where V denotes physical vulnerability which is calculated by employing Eq. ( 11) ; Fs is calculated by employing Eq. ( 1) ; a and b are constants, which need to be determined.

Determination of constants by applying multiple scenarios
To determine the constants a and b in Eq. ( 12), we first obtain two or more scenarios, which can reflect the landslide safety factor and the building vulnerability.Using several triggering scenarios, such as rainfall, earthquake, and reservoir water level fluctuation, we can obtain several safety factors, the corresponding landslide force on building foundation, and the building vulnerability.Then, we apply the least-square method to obtain the constants based on the presupposed function in Eq. ( 12).
In this study, rainfall is the key triggering factor for the landslide.Thus, we obtain rainfall scenarios by analyzing the precipitation using different return periods.Pearson type (PT) Ⅲ distribution model (Lei et al., 2018;Radwan et al., 2019) is applied because it is useful in rainfall-induced landslides; its probability density function is defined as follows: where parameters , ,  0 , can be given by the following three statistical parameters after conversion: ( ´,   ,   ).Thus, we have where  ´ denotes the average value,   denotes the coefficient of variation, and   denotes the coefficient of skewness.
From Eq. ( 14), the PT III distribution model has three undetermined parameters:  ´,   ,   .The principle of maximum entropy, the methods of moments, and maximum likelihood estimation are employed to estimate the parameters for the PT III distribution (Singh and Singh, 1988).We plot the physical vulnerability curve after obtaining the values of these three parameters determined by different rainfall scenarios with varying return periods.
3 Application of the proposed method

Geological settings and deformation of landslide
The Manjiapo landslide (110°10′0.32″E,29°25′3.69″N),located in Sangzhi County, Zhangjiajie, China was selected as the case study (Fig. 5).The area is mountainous and hilly with elevation ranging from 154 m to 1890 m a.s.l.The climate is humid subtropical, and the estimated average annual rainfall is about 1400 mm.
The landslide covers an area of about 6.6 × 10 4 m 2 with an average thickness of 6.9 m and an estimated volume of 45.5 × 10 4 m 3 .It demonstrates strip shape in a plan with a longitudinal dimension of about 560 m and the average width of approximately 176 m along the northwest (NW)-southeast (SE) direction.The elevation of the main crack is about 370 m a.s.l.
The toe of the landslide is located at 272 m elevation along the stream.
The topography demonstrates a multi-step shape, the height of which ranges from 1 to 3 m.The middle and upper parts of the landslide are relatively gentle with a slope gradient of about 8°，while the lower part is steeper ( 12° slope).The sliding direction of the landslide includes two parts: the upper part orients at 335°, and the lower part at 313°.
The main materials of the landslide comprise loose debris from silty clay and siltstone, in which the latter only distributes in the middle and upper sections of the landslide (Fig. 6).The bedrock is argillaceous siltstone with a slope angle of approximately 10°.The shear-strength parameters of the slip soil of the landslide, shown in Table 3, are obtained from the detailed landslide report 2017 of the Hunan Institute of Xiangxi Geological Engineering Survey.The shear-strength parameters are based on 6 groups of undisturbed soil samples and their laboratory tests.and 7a,b).Numerous tension cracks in the upper part had a visible depth of 2-5 cm, with a length of 1 600 to 6 600 cm and a width of about 15 cm .In the middle part of the landslide, staggered extrusion deformation can be observed locally apart from numerous tension cracks.
Moreover, the surface deformation caused the rise of groundwater in the silty clay layer.As a result, the shear strength of the soil mass decreased and the sliding zone was formed.It was revealed by boreholes dug during fieldwork in 2017.On the lower part of the landslide, cracks and some uplift deformation were observed on the roads (Fig. 7c).
Rainfall appeared to be the most important triggering factor of the slow-moving Manjiapo landslide.The cracks and the macroscopic deformation on the landslide were monitored since 2016.Analysis of the monitoring data shows that only heavy rainfall could reactivate the landslide.Analysis of the borehole data shows that the groundwater table is stable in the dry season.
The landslide did not show any displacement in the absence of extreme rainfall.For example, the cracks on the landslide did not expand, and there were only a few new cracks.

Damaged buildings on the landslide
Field investigation, carried out in July 2017, shows that 15 houses were affected by the landslide, of which 5 were constructed using brick-wood and 10 brick-concrete (Fig. 8).The buildings located in the middle part of the landslide were the most severely damaged.Due to landslide deformation, the walls of these buildings were cracked and inclined.We selected a damaged building for a detail study.Severe cracks appeared on the walls, and finally, the building was abandoned.
The selected building for study is a story masonry building with a length of 25 m and a width of 9 m.The building has six rooms, and each room was damaged as a result of continuous rain from June 28th to 30 th in 2016.Large-scale ground collapse occurred in rooms C，D, and E (Fig. 9).Meanwhile, the walls of these rooms developed numerous diagonal cracks with width varying from 2 to 8 cm.The walls were heavily tilted, with inclination varying from 0.7% to 1.0% (Fig. 10a,b,c).Remark: The elastic modulus value is called the code for the design of masonry building (GB50003-2011).Thus, an isotropic elastic material is defined as follows:   ⁄ = 2(1 + ν), where ν denotes the Poisson's ratio for ν = 0.3, and   ⁄ = 2.6 (Burland, 1977).H denotes the vertical height of tilted building calculated from the outdoor ground.

Rainfall data analysis
Landslides are induced by extreme or short-term sustained intense precipitation (Chen et al., 2014； Qiong et al., 2018； Huang et al., 2014).Furthermore, 3-day rainfall proved to be the most relevant parameter of landslide occurrences in the study area (Lin et al., 2018 ).Precipitation data of Sangzhi County for the period 1995 to 2016 were collected from the sitehttp://www.cma.gov.cn/.The data was analyzed for extreme rainfall and scenario determination (Fig. 11).

Extreme rainfall scenarios and landslide residual thrust calculation
The extreme rainfall distribution curve is depicted in Fig. 12 that is constructed by employing PT Ⅲ distribution model and the rainfall data collected for the period 1995-2016.Using this curve, we can obtain the amount of 3-day cumulative precipitation corresponding to each return period.The SEEP/W code (GEOSTUDIO) was applied to analyze the groundwater seepage of Manjiapo landslide to obtain the amount of 3-day cumulative precipitation corresponding to each return period by using PT (Pearson type) Ⅲ distribution model(Fig.12).The average amount of 3-day cumulative precipitation is input to the software in turn, and the groundwater under the rainfall scenarios is simulated.
The saturated volumetric water content is 0.4 by cutting the ring method.The saturated permeability coefficient is obtained by back analysis.We choose the saturated volumetric water content and the permeability coefficient by the variablecontrolling approach.Three groups of input values are: 0.4, 0.1; 0.4, 0.2; 0.4, 0.3.The results of the residual thrust and the corresponding safety factor are presented in Table 6.These values were obtained by the landslide residual force calculation method (section 2.1) for the geological profile (Fig. 6).In the dry season (scenario a), the landslide performs residual thrust of 142 kN/m and safety factor for the area where the case study building is located of 0.853, while the these values can change significantly in rainy season (scenario b, c and d).For an example, the residual thrust can be increased by at least 15 times and the safety factor can be reduced by nearly half in the rainy season with a 50year rainfall.This indicates an important influence of rainfall on landslide stability and the building's safety.Here, Fsb denotes the factor of safety for the area where the building is located.

Results of scenario-based vulnerability curve of the building
As described earlier in section 3.1 and demonstrated in the geological profile (Fig. 6), the sliding mass material is silty clay and bedrocks.Therefore, the thrust distribution form can be considered as rectangular based on Table 1.By applying the results of the horizontal component of landslide residual thrust (using the method in section 2.1) and the soil depth where the building is located (Table 3), the pushing force on the foundation was calculated by the corresponding thrust distribution function.
Table 6 illustrates the results of pushing force on the foundation, inclination, and the building vulnerability based on different scenarios.The result indicates that the building's vulnerability is very low (V = 0.053) in the dry season, with a pushing force of 28 kN/m on the building's foundation.However, in rainy seasons, the building can experience severe damage with the vulnerability of 0.798 (10-year rainfall) or even 0.985 (50-year rainfall).
Using the four sets of scenario data (Table 6), we constructed the physical vulnerability function and the constants in Eq.
12 were determined by employing the Weibull function.
Based on the Chinese standard of Specification of Risk Assessment for Geological Hazard (DZ/T 0286-2015), there are three stability states of landslide according to the range the safety factor (Fs) of landslide.Please see more details in the following table 7. The value of Fst is defined based on the slope safety level and slope type.Meanwhile the slope safety level is defined based on the potential economic loss and element at risk.According to the field investigation, there are 116 residents in the affected area of the Manjiapo landslide, and the road passes through the middle part of the landslide.In case of geologic hazard, it will threaten the lives and property of 116 residents and damage more than 67,000 square meters of the land.At the same time, the road will be damaged, threatening the safety of the pedestrians and passing vehicles.The potential economic loss will be more than CNY 5 million.Based on the table 9 , the safety level of the Manjiapo landslide is judged to be second level.Note: If one of the conditions is met, it will be judged to be the corresponding slope safety level.
So, when the safety factory of the Manjiapo Landslide is greater than 1.30, the landslide is stable and the landslide intensity is very low.In addition, the resistance ability of the building can prevent the building from being destroyed by the low intensity of the landslide (Du, 2013).In summary, the physical vulnerability of the building on Manjiapo landslide is very low when the safety factory is greater than 1.30.It provides that the physical vulnerability of the building on Manjiapo landslide is 0 when the reciprocal value of the safety factor is 0.5.The physical vulnerability of the case study building on Manjiapo landslide is demonstrated in Fig. 13.
We can observe that the physical vulnerability is very low when the landslide is stable with a safety factor greater than 1.0.When the safety factor is lower than 1.0, the physical vulnerability rapidly increases.Vulnerability approximates 1.0 when the reciprocal value of the safety factor is 2.5.By utilizing this curve, we can obtain the possible physical vulnerability of the building if the safety factor of the landslide is known.Therefore, we need to demonstrate that the safety factor is for the local area where the case study building is located, but not for the whole landslide.
and displacement on the main scarp.
(3) Cracks on the crown of landslide.
the cracks on the buildings.( 4) Small cracks on the crown of landslide.
and vegetation on the landslide.
(3) No scratch and obvious displacement on the main scarp.

Influence of building characteristics on vulnerability and the sensitivity analysis
To obtain the influence of building characteristics on vulnerability, we conducted sensitivity analysis.We know that numerous 375 parameters of the building were included in the building inclination and vulnerability calculation e.g.length, width, depth of foundation, and E/G ratio .We conducted sensitivity analysis by changing the values of each parameter in step while keeping others constant and estimated the possible physical vulnerabilities of the building.The results are shown in Fig. 14.As demonstrated in Fig. 14, we observe that the physical vulnerability is directly proportional to the building length， E/G ratio and is inversely proportional to the other parameters: building width, and foundation depth.It also shows that the higher the ratio of building length and width, the more vulnerable to damage the building is.Besides, buildings with deeper foundation and higher E/G ratio have higer resistance.
The results of the sensitivity analysis of the building parameters are demonstrated in Fig. 15.The red line that represents length has the steepest slope among all the lines, indicating that the length of the building has the most significant influence on the physical vulnerability of building.We can simultaneously obtain the second major factor that is the width of the building, while the third one is the foundation depth.
We tested four types of buildings with different lengths: 15 m, 20 m, 25 m, and 30 m (Fig. 16(a)).When Fsb is greater than 1.0, the building physical vulnerability with any length is very low, that is, almost no damage.In addition, the building demonstrated a different performance when Fsb is less than 1.0.The building physical vulnerability with length 15 m was slightly increased when the landslide stability was getting worse.However, the building physical vulnerability with length 30 m rapidly increased when Fsb was less than 1.0.This indicates that the buildings on the location where the target building stands have a limit length of 30 m.When the length of the building was greater than 30 m, the building faced severe damage if Fsb was less than 1.0.
To further test the detailed influences of the building parameters, we select the top two parameters based on the above results of sensitivity analysis: building length and width.Two sets of physical vulnerability curves are depicted in Fig. 16, and the corresponding functions of building physical vulnerability at the three scenarios are presented in Table 10. of the buildings with different building width is not significant when the Fsb is greater than 1.0.Meanwhile, the building with 405 building width 9.0 is susceptible to the changes of Fsb.A rapid increase of building damage with such building width occurs when the Fsb is less than 1.0.When the building width is close to the building length, the vulnerability of the building is low under the same value of Fsb.

Discussion
We developed a scenario-based mechanical method for analyzing the physical vulnerability of buildings on slow-moving landslides.The method enabled us to analyze the physical vulnerability from a mechanical view on soil-structure interaction, which can help us to better understand the building damage on the slow-moving landslides and is useful for physical vulnerability assessment of masonry buildings loacated on slow-moving landslides.By inputing the geometry parameter (length and width of the buliding) and the safety factor of the area where buildings located, the potential vulnereability can be obtained by using the vulnerability functions we provided in this study.
The results of the application correspond to the fact from the field investigation.As described in section 3.2, the building damage occurred due to rainfall from June 28th to 30th, 2016.the calculated physical vulnerability is observed to be 0.762 (Table 5), which is close to the real damage measured in the field varied from 0.7 to 1.0 (Fig. 10a,b,and c).Herein, the influence of building parameters (length, width, height, foundation depth, etc.) on physical vulnerability corresponds to other previously conducted studies (Li et al., 2010;Du et al., 2013;Corominas et al., 2014).This is consistent with the study conducted by Corominas et al. (2014) that the typology of buildings is a key factor in the quantification of physical vulnerability.
The vulnerability funcitons from this study is suitable for the masonry buidings which are locoated on slow-moving landslides and are perpendicular to the slope direction.The case study building is oriented along the contour lines or nearly perpendicular to the direction of the slope or the landslide.If the building was oriented parallel to slope direction, the damage would not have been so severe.It is revealed by the results obtained from the sensitivity analysis of building parameters in the assessment of vulnerability.In the case of buildings perpendicular to slope direction, the larger the building length, the more serious is the building's damage with the same force of landslide.The case study building (25 m long) showed much damage, it almost collapsed when the landslide occurred.Our study shows that the building length perpendicular to the sliding direction of the landslide should not be too large.We note that 30 m is the threshold value for the length of masonry buildings.Physical vulnerability will be decreased if the building width is increased and the length is decreased considerably (Fig 14 a and b).In this case the orientation of the building will be changed in such a way that the longest axis of the building is in the same direction of the slope.Therefore, we suggest that it is important to consider the building length-width ratio as well as the orientation of the buildings in land-use planning for the development of settlements on sloping areas.
Since the output of physical vulnerability is related to the safety factor for the area where the building is located, it is possible to evaluate the physical vulnerability of buildings prone to slow-moving landslides at a regional scale.For instance, the distribution of FS can now be obtained from several studies (Muntohar et al 2009, Takara K et al 2010, Salciarini et al 2006and Sorbino et al 2010).If we employ the physical vulnerability curves or the curves from this study, the risk can be quantified for the potential losses of buildings based on the Fs analysis for landslides at regional scale.But the application of physical vulnerability assessment at the regional scale should be tested first before implementing regional land use planning activities.
The research is based on detailed filed investigation, monitoring, and analysis in such specific landslides and case building.
Concerning the limitation of this study, it is important to mention that the results are applicable for the similar geological background areas prone to slow-moving landslides or similar landslide displacement process.The quantitative relationship between the physical vulnerability of buildings and landslide displacement process is very weakly studied around the world.
It needs more concentration of studies.Moreover, the physical vulnerability assessment was carried out for the building which is located inside the landslide area for which soil pressure on the foundation is suitable.Our study does not include the estimation of vulnerability for the buildings which are located acrossing the boundary of the landslide, the result of which may be a bit different.Also, we did not consider the friction between the foundation and soil, and also uncertainty analysis was not performed.In future studies, more relative mechanical models are required.Similarly, random distribution of soil parameters for landslide FS calculation, such as shear strength, can be considered for generating fragility curves based on this study.
Currently, intensive researches on slow-moving landslides vulnerability in the Three-gorges Reservoir (Zizheng G et al 2020) is strengthened, where the authors are applying our approach for more case studies.This approach will be verified and modified through continuing studies.

Conclusions
We propose a method for constructing physical vulnerability curves and functions by utilizing the analysis of the horizontal force of landslide acting on the foundation and the physical response of the building.The proposed method was applied to slow-moving landslides in China, for which a severely damaged building was considered as the case study structure.
The proposed method mainly comprises calculating the landslide safety factor and horizontal load on foundations based on different scenarios (extreme rainfall with different return periods); the physical response of foundation and the inclination of the building was also analyzed.Finally, the physical vulnerability curves were generated by applying the Weibull function.
Good consistency between the estimated physical vulnerability and on-field damage evidence was observed in the case study building.The sensitivity analysis of the building characteristics revealed that building length and foundation depth are the main determining factors in the physical vulnerability in the slow-moving landslides.The larger the building length, the higher is the vulnerability.Apart from the length, the orientation of the building seems to be equally important.Thus the building length, especially if it is oriented perpendicular to the sliding direction of the landslide, should not be too large.We hope that this study can be a useful supplement for the physical vulnerability estimation of buildings in the area prone to slowmoving landslides.

Fig. 1 .
Fig. 1.Computing model of residual thrust method with a broken-line slip surface (Ministry of Housing and Urban-Rural Development of PRC, 2013).

Fig. 2 .
Fig. 2. A schematic diagram of landslide thrust action on a building.

Fig. 3 .
Fig. 3.The simple beam with its foundation affected by landslide thrust.

Fig 4 .
Fig 4. The inclination of the building

Fig. 8 .Fig. 9 .Fig. 10 .
Fig. 8.A typical example of a damaged building in the landslide area (Unmanned Air Vehicle image obtained during field investigation ).

Fig. 11 .
Fig. 11.Annual and maximum daily rainfall in the study area during the period of 1995-2016.

Fig. 13 .
Fig. 13.The physical vulnerability curve for masonry buildings impacted by the slow-moving landslides.

Table 3 . Shear-strength parameters of Manjiapo landslide slip soils (data source: Hunan Institute of Xiangxi Geological Engineering Survey, China).
Manjiapo landslide has a history of 10-year displacement.According to the residents, the landslide occurred in August 2008, which resulted in a few ground fissures.Due to heavy rain during 28th to 30th June in 2016 induced severe displacement of the landslide.Field investigation carried out in July 2017 revealed that the displacement mainly occurred in the middle and upper parts of the landslide(Figs.5c

Table 5 . Permeability coefficient back analysis of the rainfall event in March 2018, by comparing the root mean square errors (RMSE) of three hydrological gauges (installed by the authors in December 2017, see Fig.5) on the Manjiapo landslide
Then, the groundwater is simulated and validated for the rainfall event in March 2018.The root mean square error (RMSE) is utilized to check the accuracy.Lower RMSE means smaller error and better prediction.The results of the RMSE are shown in the following table.The saturated volumetric water content is 0.4 and the most suitable permeability coefficient is 0.3 m/d.

Table 7 . The range of safety factor (Fs) of landslide and its state (referred to Ministry of Land and Resources of the PRC, 2015)
Fst denotes the design safety factor.