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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access June 22, 2016

Modeling of landslide volume estimation

  • Abolghasem Amirahmadi , Sima Pourhashemi , Mokhtar Karami EMAIL logo and Elahe Akbari
From the journal Open Geosciences


Mass displacement of materials such as landslide is considered among problematic phenomena in Baqi Basin located at southern slopes of Binaloud, Iran; since, it destroys agricultural lands and pastures and also increases deposits at the basin exit. Therefore, it is necessary to identify areas which are sensitive to landslide and estimate the significant volume. In the present study, in order to estimate the volume of landslide, information about depth and area of slides was collected; then, considering regression assumptions, a power regression model was given which was compared with 17 suggested models in various regions in different countries. The results showed that values of estimated mass obtained from the suggested model were consistent with observed data (P value= 0.000 and R = 0.692) and some of the existing relations which implies on efficiency of the suggested model. Also, relations that were created in small-area landslides were more suitable rather than the ones created in large-area landslides for using in Baqi Basin. According to the suggested relation, average depth value of landslides was estimated 3.314 meters in Baqi Basin which was close to the observed value, 4.609 m.

1 Introduction

Instability of natural slopes is a geomorphologicgeological phenomenon that affects changing the Earth’s surface [1]. It becomes dangerous when it impresses human actions [2, 3]. Meanwhile, landslide known as a universal problem which has always brought about huge loss of lives and financial damage, is of great importance [4, 5]. Landslide is one of the major geomorphic processes that has affected evolution of landscape of mountainous regions and has caused disastrous incidents [6, 7]. Landslides must be taken into consideration for urban development, because the occurrence of landslides is a regular phenomenon, especially in the mountainous regions [8] Environmental planning consists of land evaluation and acquisition of the appropriate sites for various land uses that can be accomplished using different factors [9] The geo-environmental factors evaluated for urban land use planning [10]. The determination of the ground foundation conditions providing a useful guide for urban planning and for planning construction and technical projects [11]. The study of these phenomena is a useful tool for urban and regional planning [12]. It is considered as a bulk movement and natural hazard [13] which is very destructive in slanted lands [14]. Besides, landslides are created by many driving factors such as earthquakes, rainfall and rapid fusion of snow. They may be intensifed by topography, rock and soil type, fractures, substrate surface, humidity and human-caused reasons such as demolition of vegetation and incorrect engineering operations [1417].

As a bulk movement, landslide is defined as fast or slow movement of rocks, soil particles [18] or both of them on the slope downward which is affected by gravitation [19]. Natural and geological features of Iran are so that many landslides take place in some areas every year. In Iran, landslides cause many problems every year, such as: destruction of roads, destruction of agricultural lands and pastures, residential areas, soil erosion and transition a great deal of deposits to the watersheds [20]. It is important to be aware of number, area and volume of landslides in order to estimate sensitivity [2124], determination of landslide danger [24, 25] and long-term evaluations to estimate bulk sensitivity [23, 2631]. Area and number of landslides information is simply achieved through aerial photos, satellite images and field inspections. However, these methods are of no use for volume determination. It is a dif-ficult task that needs surface and subsurface geometrical data from the rupture slope [17]. Gathering this information which is performed as field operations is difficult and expensive and estimation of the volume of slope in steep hills is very challenging [23]. Thus, estimation of landslide volume may be only carried out by taking experimental relations that connects the volume to geometrical ruptures measurements especially the area [26, 3038]. Since, deposit delivery in a basin exit is very important in watersheds management and most of deposits are caused by landslides on side-lines of rivers; the importance of estimation of landslides volumes has to be emphasised. Some of associated studies in which the volume through landslide area was estimated are mentioned in the following references [3945].

The landslide volumes were calculated in Iran at two sides of a forest road in north of the country and investigated the effect of slide points in terms of their contribution in deposit production. It was concluded that 35 per cents of total soil displacement had been caused by landslides [46].

In a study titled as estimation of landslides volumes based on area in local scale in Mazandaran Province suggested an experimental relationship and concluded that the estimated volume for Mazandaran Province was acceptably consistent with observatory data and some of existing relations which had proved its efficiency [17]. The mathematical relations were obtained between area and mass of bulk slides in Saein Col of Nir Town [18]. They used

existing relations for their investigations and concluded that under any circumstances, there is a meaningful relationship between the volume and area of the slid bulk and new relations are a beginning to calibrate magnitude of slides. A reference [47] investigated the slide area and overburden volume of Khaleneje Tunnel falling bulk based on geophysical measurements. The effective volume of instable falling bulk was estimated to be 3400000 m3 that proved the possibility of landslide in the vicinity of the second tunnel of Khalenje in near future [47]. Hence, considering the significance of deposit volume caused by bulk erosion and also expensive and time-consuming field operations.

The main objective of the present study is to examine the relation between volume and landslide area to fnd an experimental model for estimating volume at Baqi Basin which then can be applied for similar basin.

An effort is made to incorporate for the first time planning parameters as natural hazard assessment map such as landslide in conjunction with other geomorphological parameters, beside the commonly used factors.

2 The studied region

Neyshabour Baqi Basin is placed in the main catchment area of Central Desert (one of the six basins of Khorasan Province) in Iran. It expands from 59” 38 ’58° to 13” 44’ 58° longitudes and from 09” 31’ 58° to 30” 38’ 36° latitudes; in southern slops of Binaloud Mountains in Iran (Figure 1).

Figure 1 Location of the studied area.
Figure 1

Location of the studied area.

Baqi Basin is in north of Neyshabour, placed in Sarvelayat Division. Villages of Bojno Olia and Sofla, Ghorune and Baqi are placed in the studied region. The studied region limits from west to Barmahan Village, from south to Bar Village and from southwest to Tangeh Olia Village. Total area of basin is 6367 hectares and its average altitude is 2209 metres with maximum of 2880 m and minimum of 1720 m. Lowlands contain deposits of floodwater plains in two sides of the rivers.

3 Materials and methods

In this research, in order to provide landslide information, some questionnaires were used which were made by Landslide Investigations Group, Basins Studies and Assessment Office, Department of Watershed Management. The questionnaires contained information such as geographical location, length, width and type of landslides. Field operations were carried out to identifiy and record the existing landslides and also to calculate depth of slides. Figure 2 illustrates distribution of landslides in Baqi Basin.

Figure 2 Landslides distribution in Baqi Basin.
Figure 2

Landslides distribution in Baqi Basin.

Statistical specifications of data were calculated by SPSS 18 after being controlled in terms of correctness and quality in Microsoft Excel Software.

In order to suggest an experimental relation to estimate the volume of recorded landslides, the only ones were chosen that had complete area and volume information. Thus, data of 44 observed landslides including longitude, latitude and area was given to SPSS Software to set a relationship between area (AL) and volume (VL). In order to model the experimental relation of AL & VL, considering existing statistical relations, general form of this model was used:


Finally, in order to estimate the volume of landslide by area information considering regression assumptions, a power regression model was obtained. In this relation, the observed mass is given by multiplication of slide area and depth which was obtained from Remote Sensing calculations and GIS.

Various experimental power relations have been employed for landslide volume calculations by researchers at locations in different countries. To evaluate these relations in the study area, the numbers of landslides and the associated area with calculated volume are given in Table 1. These relations were applied for 44 observed landslides areas in the basin. The Volume values calculated by these relations were compared with the volume of observational landslide of the basin.

Table 1

Experimental relations for calculation of landslide volume by means of area.

NumberMaximum ALMinimum ALEquationSource
2071.9 × 1052.3 × 100VL = 0.1479AL1.368Simonett (1967)
292 × 1022.1 × 100VL = 0.234AL1.11Rice (1969)
536 × 1072 × 105VL = 0.242AL1.250Abele (1974)
305 × 1023 × 101VL = 0.0329AL1.385Innes (1983)
453.9 × 1064 × 104VL = 0.769AL1.250Whitehouse (1983) [51]
10191.6 × 1045 × 101VL = 1.826AL0.898Larsen and Sanchez (1998)
6155.2 × 1042 × 102VL = 1.0359AL0.880Martin et al. (2002)
1241/2 × 1057 × 102VL = 0.1549AL1.0905Guthrie and Evans (2004)
23-> 1 × 106VL = 0.00004AL1.307Korup (2005b)
653.9 × 10103 × 105VL = 12.273AL1.047Haflidason et al. (2005)
1602 × 1085 × 105VL = 4.655AL1.292Tenbrink (2006)
513 × 1031 × 101VL = 0.39AL1.131Imaizumi and Sidle (2007)
5391 × 1091 × 101VL = 0.0844AL1.4324Guzzetti et al. (2008)
114 × 1035 × 101VL = 0.19AL1.19Imaizumi et al. (2008)
371.5 × 1031.1 × 101VL = 0.328AL1.104Rice and Foggin (1971)
6771 × 1092 × 100VL = 0.074AL1.450Guzzetti (2009) [50]
4421.085 × 1061.23 × 102VL = 0.0974AL1.176Omidvar and Kavian (2011)

At last, a statistical improved model for Baqi Basin was also compared with relations of Table 1. Comparison was made through coefficient of determination (R2), percentiles statistics values, maximum, minimum and average and the Root Mean Square Errors (RMSE).

3.1 Coefficient of DeterminationR2

R2 was used to choose the best relation and compare it with other relations.


Where, o is the average of observed volumes; p is the average calculated volume; oi is the observed volume value, pi is the calculated volume and n is number of the variables [17]. The closer R2 value to 1 indicates more correlation of actual (observed) and calculated data [48]. In order to use R2, the observed value of landslides area was placed in the relation and the associated volume was calculated; then, each value was compared with observed value of volume and the explanation coefficient was evaluated.

3.2 Percentile statistics values, maximum, minimum and average

After calculation of volume values for all recorded landslides in the studied region by means of various experimental relations and the suggested relation for Baqi Basin, statistics of 25%, 50% and 75% of total slides volumes, minimum, maximum and average of estimated volumes were calculated.

3.3 Root Mean Square Error (RMSE)

RMSE indicates efficiency of a model. It can be calculated as the second root of mean square of subtraction of calculated and observed values. Slide area was placed in each experimental relation, the slide volume was calculated; and then, according to Equation 2, the model with the least RMSE value was chosen as the best one.


Where n is number of variables, oi is the observed landslide volume, pi is the estimated landslide volume by each relation [49].

3.4 Estimating the Depth of Landslide

3.4.1 Estimating the depth of landslides observed in the area for estimating the model

Field and surveying methods have been used to estimate the depth observed in the landslides of the region, because some regions are impassable, so it was impossible conducting field studies. Therefore there has been used of remote sensing and ASTER satellite images as well as the pair of left and right satellite images in these images and Digital Elevation Model, 2003 and digital elevation model from topographical maps with scale of 1:50000 (prepared from aerial photographs, 1956). Because landslides have been occurred in this area during these years and at 70s, the observational depth was calculated by reducing both layers of 2003 and 1956 DEM from each other.

3.4.2 Estimating the Mean Depth of Landslides in the area for evaluating the model

After evaluating the given model, this model was used for estimating the mean size of landslides. Then the mean depth of landslides in the area were calculated and compared with mean depth of observational data and depths obtained from different models.

4 Results

4.1 Statistical Specifications of Geometrical Data in Landslides

After collecting the data required from surveys, first their accuracy and quality were controlled and then their statistical properties were calculated and provided in Table 2. According to the results of this table, landslides in the Baghi area are in a relatively wide range of area, size and depth, such that their area (AL) was in the range between 1.5 × 104 m2AL ≤ 2 × 106 m2 . The observational volume or size of landslides (VL) was in the range between 1 × 103 m3VL ≤ 8.4 × 106 m3 and their depth (DL) was in the range of 0.1 m ≤ DL ≤ 13.85 m. This wide range may increase the standard deviation (SD) followed by variation coefficient for each parameter.

Table 2

Descriptive statistics related to range of geometric parameters, volume and depth of landslides in the Baghi Area.

Data typeNoMeanMinMaxSDVarSkewnessStretch
Area44280852.27 m215000 m22000000 m2332420.6251.105E1116.4463.517
Depth444.06939 m0.1 m13.858 m2.8796548.2922.0191.315
Volume441260190.00 m310000 m38400000 m31941738.3873.770E126.6392.618

According to above models, by estimating the volume based on results of this study for descriptive statistics of range of data, volume and depth of landslides (Table 2), increased variation coefficient, skewness and stretch of data, it maybe indicate the abnormality of data. It must be however noted that the size of landslides occurred in the nature are different and a landslide can even cover 1 square meter or a few cubic meters to several km2 or km3 of an area or a volume of a soil in a region, such that the range of area as indicated in the study of reference [50] was between 2 m2 to 1 × 109 m2 and or maximum area of landslides studied in[43] obtained to 3.9 ×10110 m2 and in such cases this range of changes may increase the mentioned coefficients. Therefore higher variation coefficient, skewness and stretch may not be a reason for reduced statistical quality of data used in this study.

Because all calculations and results of this study are based on data observed in the region, therefore one can see the importance of observational data more. This can be clear more for a part of data with lower frequency or not being seen in the observational data; because using a part of with frequent data – in this study areas between 1× 105 m2 < AL < 5×106 m2, one can extract the relationships between volume and area for a part with lower data.

4.2 Calculating the Depth of Observational Landslides (44 samples) by Remote Sensing and GIS

Because there are no observational data for depth, we decided to calculate the observational depth of landslides by remote sensing and GIS. In addition, to ensure the reliability of data, by selecting 8 sites for landslide out of 44 landslides occurred in the region and field studies, the accuracy of calculation depth were estimated (Table 3). On the other hand, to determine the accuracy and reliability of calculation data, correlation between estimated depth and observational field depth (Table 4 and Figure 3) obtained by confidence of 99%, R2: 0.84 and correlation rate of 0.92, we can confide to depth data calculated by remote sensing and GIS.

Figure 3 Diagram of correlation coefficient between field and estimated depth.
Figure 3

Diagram of correlation coefficient between field and estimated depth.

Table 3

The estimative and field depth.

Slide NoDepth estimated (m)Field depth (m)
Table 4

Correlation between field and estimated depth.

.915[**]1Pearson Correlation
.001Sig. (2-tailed)Field
1.915[**]Pearson Correlation
.001Sig. (2-tailed)Estimated

4.3 Developing a Statistic Model for Baghi Area

Figure 5 indicates No. 44 of landslide with complete data of area (AL) and volume (VL), in a diagram with Log-Log UTM coordinates. According to Figure 5, the frequency of slides is higher in the area range between 100000 m2 to 1000000 m2 and volumetric range between 500000 m2 to 5000000 m3. The model exhibits lack of fit for small very values of area and volume. Physical review of Figure 4 indicates an exponential relation in different values between AL and VL; with axis indicated in log UTM coordinates. Exponential regression fitness on the data of observational area and volume finally resulted in creation of Equation (3).

Figure 4 Diagram of exponential regression ftness on area and volume data.
Figure 4

Diagram of exponential regression ftness on area and volume data.

Figure 5 Experimental equation obtained between area and volume for landslides present in the area.
Figure 5

Experimental equation obtained between area and volume for landslides present in the area.


Where; AL is the area (m2); VL is the volume (m3). This exponential model can be used for estimating the size of mass movements of slide type, with known interrupted range area.

Studying the diagram obtained for calculating the size of landslides indicate that despites showing data in log-log UTM coordinates, there can be more seen the observational data far from the given fitness line related to regression equation.

4.4 Evaluating the Model Provided

To evaluate the calculation values of size of landslide by related equation, these values were compared to volumetric estimations by other equations (Table 1). Figure 6 indicates the results of such comparison in the frame of a calculating the statistics values of 25, 50 and 75%, min, max and total mean of data estimated by different experimental equations as well as equation provided for Baghi area.

Figure 6 Comparing the statistics of 25%, 50%, 75%, min, max, mea of volumes estimated by different equations and equations provided in Baghi area.
Figure 6

Comparing the statistics of 25%, 50%, 75%, min, max, mea of volumes estimated by different equations and equations provided in Baghi area.

Table 5

Exponential Regression Data.

Dependent Variable: Volume
EquationModel SummaryParameter Estimates
R SquareFdf1df2SigConstantb1
dimension1 Power.69292.034141.0002.4821.024
The independent variable is Area

After calculating the size of landslides in the Baghi area, the diagram for range of area determined (Table 1) were drawn by different equations (Figure 7).

Figure 7 Diagram of different experimental equations as well as diagram obtained by this study.
Figure 7

Diagram of different experimental equations as well as diagram obtained by this study.

According to Figures 6 and 7, it can confirm that equations like references [30, 33, 39] were relatively in good conformity to diagram of this study (equation 3); however, models developed by[35, 41, 42], have relatively lower estimation than developed equation. In the above area range, of course, there were also developed some models like [31, 36, 37, 50] with relatively higher estimations than equations provided here. As indicated in Figure 4, for equation developed by [37, 43] for very great landslides (Table 1), the minimum predicted volume by such equations was 91.289279 m3 and 1157256.40 m3; while minimum observed volume in the province was 10000 m3 and minimum volume calculated by related equation was 15000m3 and was almost reliable estimation. As mentioned above, such limitation for maximum data can be also seen in the equations like [35, 41, 42].

4.5 Statistical comparing the Developed Model with Other Models

Each different model as introduced in Table 1 were used for 44 landslides present in the Baghi area and data predicted by each equation were comparing to observational data by standard coefficient and Chi-Square Errors (RMSE) (Table 6).

Table 6

Results for studying the values of standard coefficient and RMSE between observed and predicted data by different relations.

Experimental equationsThis studyGuz (2009)Sim (1967)Inn (1983)Guth (2004)Kor (2005)Ima. (2007)Guz. (2008)Ima (2008)
Standard coefficient0.6460.5740.590.5870.6380.4760.6330.5770.623
RMSE1.245 ×10615.757 ×1069.165 ×1061.785 ×1062.097 ×10610.730 ×1061.500 ×10613.794 ×1061.443 ×106
Experimental equationsRic. (1971)Abe (1974)Whi. (1983)Lar. (1998)Mar (2002)Haf. (2005)Ric. (1969)Ten. (2006)Omi. (2011)
Standard coefficient0.6370.6020.6130.6550.6560.6440.6360.6050626
RMSE1.805 ×1065.798 ×1068.942 ×1062.129 ×1062.221 ×1068.241 ×1061.910 ×106116.148 ×1063.118 ×106

Results for standard coefficient indicated that there is a significant correlation in the confidence level of 99% between predicted values by all these equations with observational volume. Because standard coefficient can accurately indicate the accuracy of different equations, therefore RMSE was also used. As indicated in Table 4, besides equation developed by this study, according to [38] has a lower RMSE value than other equations followed by [30, 34, 39], having predictions relatively close to the observational data.

4.6 Calculating the mean depth of landslides in the area

According to the similarity between equation obtained for determining the size of landslides in the Baghi area (Equation 3) with equations developed internationally (Table 1) as well as relative conformity of these equations with equations obtained, it seems that this developed model include an acceptable model for predicting the volume of landslides. Therefore, the volumetric mean for 44 landslides with given data have been estimated by using the equation developed by this study equal to 922658.42 m3. According to mean area for these landslides, the mean depth for landslides in Baghi area was estimated about 3.314 m. Because mean depth for these 44 landslides was also estimated about 4.06 m, therefore it can be seen a slight difference between observed depth and depth calculated by this equation.

These calculations were also conducted for different relations and mean depth was calculated based on mean volume predicted by any equation (Figure 8). As indicated in Figure 8, the equations with higher predictions for mean total volume of slides, they seemed to have higher depth as well. For equations with lower predictions however, the calculated depth is lower than observed depth.

Figure 8 Values for depth of landslides by using different equations.
Figure 8

Values for depth of landslides by using different equations.

5 Conclusions

Results from this study indicated that the equation developed for Baghi area are in good conformity to some equations developed by others internationally. Because these equations presented in study areas with different local and physiographical conditions than Baghi area as well as for different ranges of areas, therefore, this conformity indicates that the relation between volume and area of landslide is basically geometrical and independent from local and physiographical conditions. In final conclusion, according to statistical accuracy of model provided and its conformity to some other models as well as benefiting from results of this model from data obtained through whole area, this model can be considered as a desirable model for Baghi area and for calculating the size of landslides in the northeastern part of Iran; and because of lack of such models in the country, this study can be used as an introduction for developing the models estimating the volume and other morphometric parameters for landslide. By developing this model, when calculating the area of a landslide, one can find its volume and depth. By providing this model indeed, one can save the cost and time for calculating the volume and depth of landslide. Because equations with higher priority have some predictions with higher and lower mean than observational data and because even lower difference between means when a study area is wide with higher landslides, may cause high changes in the total volume of region, therefore it can be concluded that it is necessary to develop a unique equation for each region, if there are data for volume and area of landslides. Therefore it is recommended to design and develop such models for regions susceptible to landslide through the country having such data.


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Received: 2015-1-27
Accepted: 2016-2-15
Published Online: 2016-6-22
Published in Print: 2016-6-1

© A. Amirahmadi et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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