Quantitative Risk Assessment of Cut-Slope Projects under Construction Zhihong Li1; Hongwei Huang2; Farrokh Nadim3; and Yadong Xue4 Abstract: In some cut-slope projects landslide is a common problem during construction due to unfavorable geomorphological and geomechanical conditions. It is necessary to do a quantitative assessment of the risk posed by landslide before determining the budget or tender price. This paper outlines a general procedure for doing this, followed by an example to demonstrate the approach in comparison to a known failure. Finite-element analyses identify the most dangerous landslide scenario among all construction steps. The slope failure probability is then estimated using reliability theory based on the most dangerous construction step. After identifying the potential failure surface and estimating the volume of the sliding mass, the runnout behavior of sliding mass is simulated to delimit the extent of likely impacted area. Then, the exposed elements at risk and their vulnerabilities are identified and analyzed. The landslide risk is assessed quantitatively for three types of consequences: casualties, economic loss, and time overrun. Compared with actual consequences, the estimation results were in acceptable agreement with the case study. The paper demonstrates that it is feasible to analyze the risk associated with landslides during construction of cut-slopes. DOI: 10.1061/共ASCE兲GT.1943-5606.0000381 CE Database subject headings: Quantitative analysis; Assessment; Risk management; Landslides; Construction management. Author keywords: Quantitative analysis; Assessment; Risk management; Landslides; Construction.
Introduction Under the conditions of unfavorable topography and geology, the construction of cut-slopes may pose a significant risk to the project. Unfortunately, failure of engineered slopes during construction, leading to huge economic loss, time overrun, and even loss of human life are common occurrences. For example, along the section from Shaoguan to Wengcheng of the Beijing-Zhuhai Highway, there were so many landslides and collapses that the owner had to perform a reinvestigation and reconstruct with a new design. This resulted in about 1 year delay and 0.3 billion Chinese Yuan 共about $42 million兲 economic loss in the project. Another example is the cost of slope stabilization in the BaojiGuangyuan section of the Baoji-Chengdu Railway, which totaled over 0.47 billion CNY 共about $67 million兲, 60% more than the planned cost. It is therefore necessary to do a quantitative assessment of the risk posed by landslide before determining the budget or tender price for cut-slope projects. 1
Ph.D. Candidate, Dept. of Geotechnical Engineering, Tongji Univ., 1239 Siping Rd., Shanghai, China; formerly, Research Guest at International Centre for Geohazard/Norwegian Geotechnical Institute, Sognsveien 72, Oslo, Norway. 2 Professor, Dept. of Geotechnical Engineering, Tongji Univ., 1239 Siping Rd., Shanghai, China 共corresponding author兲. E-mail: huanghw@ tongji.edu.cn 3 Director, International Centre of Geohazards, Norwegian Geotechnical Institute, Sognsveien 72, Oslo, Norway. 4 Associate Professor, Dept. of Geotechnical Engineering, Tongji Univ., 1239 Siping Rd., Shanghai, China. Note. This manuscript was submitted on March 19, 2009; approved on April 26, 2010; published online on May 6, 2010. Discussion period open until May 1, 2011; separate discussions must be submitted for individual papers. This paper is part of the Journal of Geotechnical and Geoenvironmental Engineering, Vol. 136, No. 12, December 1, 2010. ©ASCE, ISSN 1090-0241/2010/12-1644–1654/$25.00.
Quantitative risk assessment 共QRA兲 is a method of quantifying the degree of risk through a systematic examination of the factors contributing to slope stability and affecting the severity of consequences. For probabilistic analysis, some advance has been made, including classical reliability methods and Monte Carlo simulation 共e.g., El-Ramly et al. 2002兲, together with the modeling of spatial variation of groundmass properties 共e.g., Nadim et al. 2005兲. For consequences quantification, Wong et al. 共1997兲 have developed a generalized, quantitative landslide consequence model for use in QRA of man-made slopes. With the improved capability of numerical modeling of debris runout, it is possible to carry out more refined assessment of consequence 共Ko and Kwan 2006兲. Since the mid-1990s, some notable application cases have been performed in assessing and managing landslide risk, notably in Hong Kong 共Wong et al. 1997; Ho and Ko 2009兲 and Australia 关Australian Geomechanics Society 共AGS兲 2000兴. This paper outlines a general procedure for quantitative risk assessment of cut-slope projects under construction in aspects of casualties, economic loss, and time overrun. Then the methodology is demonstrated for a landslide along the Shuifu-Maliuwan Highway in Yunnan Province of China.
General Procedure This present study proposes a general procedure of quantitative risk assessment for cut-slope projects under construction. The process mainly comprises four components: hazard identification, probabilistic analysis, consequences analysis, and risk calculation. Fig. 1 shows the process in a flowchart form. In simple form, the process involves answering the following questions: • Which construction step is the most dangerous? • What is the failure probability of the cut-slope at this construction step?
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Consequences analysis Probabilistic analysis Hazard Identification Identifying the critical scenario among the construction steps Using the code PLAXIS to find out the most dangerous construction step
Landslide probability estimation at the most dangerous construction step Based on reliability theory Using the code FLAC 3D to get the factor of safety, and using small program made by the authors to count the number of failure samples
Identifying the landslide magnitude Estimating the potential impacted area Identifying the exposed elements in the impacted area Estimating the extra time due to landslide Using FLAC 3D to estimate the landslide volume and the probable position of sliding surface Using PFC 3D to estimate the runout behavior of sliding mass Identifying the exposed elements (e.g the number of workers and corresponding temporal and spatial probability) in the impacted area
Risk calculation Risk= failure probability × spatial probability × temporal probability × elements at risk
Fig. 1. Flowchart of QRA for cut-slope projects under construction 共the sentences in italics indicate the methods adopted in demonstration example兲
Hazard Identification The stability of a cut-slope varies significantly during the construction time because of the excavation and protection schemes implemented. Furthermore, the probable sliding volume and impacted areas are different for different steps of cutting and slope protection. Therefore, the elements at landslide risk are not static as the slope failure probability and corresponding consequences change in various stages of construction. Fig. 2 shows an example of risk variation as a function of construction time or construction steps. Generally, the purpose of construction activity is to make the slope much safer and more reliable. Meanwhile, the engineers must ensure the constructed slope will have a good reliability during a long operation period. Therefore, the reliability is usually greater near the project completion than during initial phases of the project, and the most dangerous scenario is often one of the intermediate construction steps. In the risk assessment process, the critical landslide scenarios should be identified for different construction steps to identify the scenario that poses the highest risk to the project. At every construction step the landslide occurrence probability and corresponding consequences should be analyzed. For simplicity, only the factor of safety based on average strength parameters was
used in this study to assess the stability situation and triggering of landslide. The estimated volume of sliding sediments was then used to assess the consequences.
Probabilistic Analysis of Slope Instability There are a variety of methods of estimating probability from the disparate sets of information that may be assembled. Soeters and van Westen 共1996兲 and van Westen et al. 共1997兲 divided these methods into inventory, heuristic, statistical, and deterministic approaches. The Australian Geomechanics Society 共AGS兲 共2000兲 outlined the methods as five types: observation and experience, inventories, triggering, cause and effect, and deterministic/ probabilistic. Fell et al. 共2008兲 summarized the methods as: historical records, sequences of aerial photographs and/or satellite images, silent witnesses, correlation with landslide triggering events, proxy data, proxy data, and subjective assessment. In practice, assessing the frequency or probability of the landslides will usually require using different and complementary methods. Without historic data, the probability is often very subjective and approximate because of the complex interaction between the mechanical behavior of geomaterials and triggering factors 共Fell et al. 2008兲. It can be seen that most of the frequency or probability analysis methods are based on experience, subjective judgment and/or historical records. However, for many slopes such as those encountered in highway construction in mountainous regions, historical data may be lacking, incomplete or inaccurate. Furthermore, empirical methods typically work for specific areas from which the original data were taken, but may be misleading for other areas.
CS ithe ith construction step
risk
• What is the magnitude if landslide occurs? • What kinds of and how many elements can be shocked? • How long time the construction resumption will take and what is the economic loss and casualties? As the cutting of the slope will create a new free face, redistribute the stresses at the toe of the slope, and disturb the equilibrium of the primary geological environment, engineered slopes are mainly influenced by the construction activity. Therefore, the critical landslide scenario should be identified first among the construction steps. Based on the critical scenario, which represents the landslide risk of the cut-slope project, the failure probability is analyzed. Meanwhile, the most important considerations in a construction project may be the safety of construction workers, money, and time. Therefore, in this study, the landslide consequences were analyzed for these three aspects, i.e., casualties, economic loss, and time overrun. In order to quantifying these consequences, the landslide magnitude and its runout behavior should be simulated and estimated. Once the impacted area is identified, the elements shocked by landslide can be listed. Together with the vulnerability coefficients of exposed elements, the consequence can be calculated and the risk can be obtained.
CS 1 CS 2
CS n
construction time
Fig. 2. Schematic figure for risk changes with construction time
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In order to progress from a qualitative to a quantitative approach, the use of reliability theory is appropriate when the historical records are scarce. For individual slopes, the probability of failure can usually be considered as simply the probability corresponding to a safety factor less than unity. In conventional methods, the performance function of a slope is usually formulated using the simplified limit equilibrium method, such as the ordinary method of slices, simplified Bishop’s method, or simplified Janbu’s method 共Dai et al. 2002兲. The shortcoming of this approach is that the critical slip surface is generally determined or assumed based on deterministic analysis and then probabilistic analysis is performed on this predetermined critical slip surface. In fact, the resulting value of failure probability from the method above is not necessarily the maximum value. The critical probabilistic failure surface is a function of both the value of the parameters at the critical condition and the critical shear surface. The maximum instability probability occurs on some critical probabilistic surface that does not, in general, coincide with the critical deterministic surface 共Hassan and Wolff 1999兲. Some researchers 共e.g., Bergado and Anderson 1985; Chowdhury and Xu 1994兲 have performed parametric studies considering different specified surfaces not necessarily associated with the minimum factor of safety or minimum reliability index. In this study the uncertainties of soil and rock strength parameters were accounted for by the Monte Carlo simulation method. The factor of safety was then calculated using the strength reduction method. For every group of strength parameters, the slip surface can be searched and identified automatically and the factor of safety can be calculated. Also, in the calculation process, installation of anchors and cables can also be modeled according to the real construction situation. The researched slope referred is a cut-slope project, therefore, the cutting and protecting activities may influence the stability strongly. So the human constructed activities were analyzed in detail and the rainfall infiltration was not considered in this study. The landslide hazard, or occurrence probability, corresponds to failure probabilities obtained for different construction steps.
Consequences Analysis When assessing the landslide consequences, it is important to estimate the area that the slide mass will impact. The probable impacted area depends on the slope geometry, natural characteristic of slope forming materials, failure mechanisms, modes of movement, characteristics of downhill path, etc. 关Australian Geomechanics Society 共AGS兲 2000兴. Once the most hazardous scenario has been identified, the impacted area can be assessed. Therefore the necessary steps to allow the definition of consequences are as follows 共Amatruda et al. 2004a兲: • Identification of elements at risk in the impacted area; • Evaluation of the value of elements at risks; • Vulnerability evaluation; and • Consequences analysis. The assessment of landslide debris mobility is fundamental in the evaluation of the consequences of slope failure and quantification of landslide risk 共Ho and Ko 2009兲. Runout prediction methods of a landslide can be grouped into three broad categories: empirical methods, analytical methods, and numerical methods 共Dai et al. 2002兲. Empirical methods, which should only be used for preliminary estimates, are based on simple correlations between the volume of the mass involved in the movement and the geometrical parameters of slope. Analytical methods describe
no occurrence 1-p landslide occurrence p
p
no loss of life p1 time interval 1 p2 time interval 2 p3 time interval 3
slight injury severe injury
No.
death or missing
Fig. 3. Event tree approach for analyzing casualties
the physical behavior of debris movement based on lumped mass methods in which the debris mass is lumped at a single point. Therefore, analytical methods cannot account for lateral confinement and spreading of the flow and the resulting changes in flow depth. Numerical methods, which mainly comprise computational fluid dynamics models and discrete element methods, can simulate the runout distance, damage corridor width, debris depth, etc., more accurately. Their limitation is that the required calculation parameters are difficult to obtain. Amatruda et al. 共2004b兲 used two methodologies, PFC3D in cooperation with FLAC3D and the dynamic analysis model DAN 共Hungr 1995兲 integrated with ROTOMAP 共Geo and Soft International 1999,2003兲, to analyze the landslide debris mobility for the Oselitzenbach landslide in Austria. FLAC3D, which is a three-dimensional 共3D兲 finite-difference program, was used to estimate the approximate volume of sliding mass. PFC3D, which can model the movement and interaction of spherical particles by the distinct element method, was applied to estimate the runout behavior of sliding debris. The comparison showed that the PFC-Ball Wall model had the similar results as the DAN Code model in travel distance, runout width and affected area. The combined use of FLAC3D and PFC3D-Ball Wall model presented an effective approach for runout analysis when the pore pressure is not a main triggering factor to landslides. In this paper, numerical simulation method was used for runout estimation. The methodology of consequence analysis is shown in Fig. 1 in italics. First, FLAC3D was used for modeling the three-dimensional failure surface and estimating the sliding volume. Then the code PFC3D was used to simulate the runout behavior of landslide and determine the probable impacted area. Once the affected area is established, the elements exposed to the landslide threat can be identified, their vulnerabilities analyzed, and the consequences estimated. The consequences analyzes focused on the scenario that gives the highest risk. Casualties The probability of casualties can be analyzed using event tree analysis, as shown in Fig. 3, where p is the occurrence probability of landslide. The probabilities p1, p2, and p3 are the temporal probabilities of each shift interval in one day. Estimation of the human impact of landslide should also account for the spatial distribution of constructor workers at any given time interval. According to terminology recommended by the Technical Committee on Risk Assessment and Management under International Society for Soil Mechanics and Geotechnical Engineering, vulnerability, expressed on a scale of 0 to1, is defined as the level of potential damage or degree of loss for a given element affected by a hazard 关Wong et al. 1997; Australian Geomechanics Society 共AGS兲 2000; Nadim and Kvalstad 2007兴. Finlay et al. 共1999兲 provided some data on vulnerability derived from Hong Kong’s statistical information, with a subset of the data presented in Table 1. The casualties are obviously related to the number of construction workers on-site when the landslide occurs. For one construc-
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Table 1. Summary of Hong Kong Vulnerability Ranges and Recommended Values for Impact of Landslides on Humans in Open Space Vulnerability of person Case
Range in data
If struck by a rockfall If buried by debris If not buried
0.1–0.7 0.8–1.0 0.1–0.5
Recommended value Persons in open space 0.5 1.0 0.1
tion step, the number of construction workers on-site can be assumed to change on one-day cycles. The vulnerabilities of persons can be estimated based on the landslide magnitude and the distance between the individual and the center of sliding mass. According to the impacted area and the relative position of construction workers to the sliding mass, the vulnerability can be estimated.
Economic Loss Construction Equipment On construction-sites, excavation equipment, such as scrapers and trucks, are always used. The equipment is vulnerable to damage by landslides. The degree of damage can be divided into three levels for simplified risk calculation. The economic loss can be estimated as the product of the net present value of the equipment and the recommended vulnerability coefficients listed in Table 2. The data in Table 2 are based on the experiences from construction sites in China and subjective judgment. The probability of damage to construction equipment in the area affected by the landslide is also a temporal and spatial probability problem. Like the risk of casualties, it can be calculated using event tree analysis. Existing Structures The slope protecting structures, such as bolts, cables, framed beams, and antislide piles, are vulnerable to landslides. Once a landslide occurs, the economic loss for the slope protecting structures affected by landslide will be almost the total cost for these structures. Most of these structures cannot be repaired or reused even though the damage degree might be far less than 100%. Therefore the loss calculations are based on the total cost for rebuilding these structures.
Comments May be injured but unlikely to cause death Death by asphyxia almost certain High chance of survival
Cost of Construction Resumption The economic loss because of landslide not only includes the loss of exposed elements at risk but also the construction resumption cost. The cost for clearing debris and the loss due to time overrun are the most important factors in this cost. If the magnitude of the landslide is large, the cost for clearing the debris could be very high. In the risk analysis, once the approximate sliding volume is evaluated, the cost for clearing the debris can be estimated based on the local unit price of cutting and transportation expense. In practice, the volume of debris cannot be predicted accurately. In the analyses, the slide volume obtained from 3D numerical simulation was considered as the most likely value. The probable cost range can be expressed in a probabilistic format. Meanwhile, the loss due to construction time overrun should not be neglected in the cost estimation. The economic loss because of time overrun includes direct and indirect losses. The indirect loss mainly includes the economic loss resulting from social or environmental problems because of time extension. The direct loss is mainly time-dependent costs, such as wages, equipment cost, management fee, etc., because of extra time. Meanwhile, for a long delay in construction activities, the loss due to inflation and loan interests should be considered. Therefore, the economic loss because of extra time can be expressed as the sum of the loss due to increased time-dependent cost, loss because of postponed operation and loss because of inflation and loan interests 共Yang and Cao 2003兲. In this study, only the direct loss due to time-dependent costs, including wages, equipment rental, and management fee was considered; indirect losses were not included due to lack of data.
Time Overrun The construction time for a project is often modeled as a random variable. The  or triangle distributions are often used because
Table 2. Vulnerability of Construction Equipment Level
Descriptor
Description
Case If the equipment is buried for a long time, and is struck or crushed by a big rockfall with large deformation. If the equipment is buried for a long time, and some components are destroyed. If the equipment is just struck by a small rockfall.
I
Major damage
The equipment is extensively damaged, and it cannot be used or requires major overhaul for use.
II
Medium damage
III
Minor damage
The equipment is moderately damaged, and it can be used after some components are repaired. The damage to the equipment is limited.
Recommended vulnerability 0.7
0.3 0.05
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sufficient data are rarely available to justify a distribution with complex parameters 共Nasir et al. 2003兲. The characteristic values for these distributions are usually based on expert opinions taking into consideration the scale of the probable landslide. In the analyses presented here, the extra time because of landslide was assumed to consist mainly of the extra time for clearing the debris and reconstruction. The time overrun because of clearing debris is closely related to the landslide magnitude. However, it is also strongly influenced by management factors and technical skill of the construction team. If the team has emergency plans beforehand, decisions can be taken swiftly and the accident can be dealt with rapidly and efficiently. Thus, the extra time for clearing the debris can be minimized. Otherwise the time overrun may sharply increase. The extra time for reconstruction, such as redesign and rebuilding of the protective structures can be estimated based on the conventional schedule estimation methods.
Risk Calculation Quantitative risk assessment involves integration of the probability and consequences analysis. For human impact, the risk can be calculated from R共HI兲 = P共L兲 ⫻ P共T兩L兲 ⫻
兺 关P共S兩L兲 ⫻ V共S兩L兲兴
共1兲
where R共HI兲 = average individual risk in different time intervals; P共L兲 = occurrence probability of the landslide event; P共T 兩 L兲 = temporal probability that landslide occurs in different time intervals; P共S 兩 L兲 = probability of spatial impact; and V共S 兩 L兲 = individual vulnerability given the spatial impact. For nonstationary property 共e.g., trucks, backhoe loaders兲, the risk calculation formula can be R共NSD兲 = P共L兲 ⫻ P共T兩L兲 ⫻
兺 关P共S兩L兲 ⫻ V共S兩L兲 ⫻ E兴
共2兲
where R共NSD兲 = damage risk of nonstationary property and E = total net value of damaged elements. For stationary property 共e.g., buildings or exist structures兲, it can be R共SD兲 = P共L兲 ⫻
兺 关P共S兩L兲 ⫻ V共S兩L兲 ⫻ E兴
共3兲
The value of V共S 兩 L兲 in this study is considered to be 1.0 because most of protecting structures cannot be repaired or reused even though the damage degree might be far less than 100%. For collective risk, casualty estimation is taken as an example. In this study, the impact area shocked by landslide is divided into three zones including fatality or missing zone, severe injury zone, and slight injury zone. The probable number of fatalities, severe injury, and slight injury can be expressed as binomial distribution 共Ronald and Raymond 1993兲. And the probability that k workers are impacted can be expressed as
冉冊
n k 共n兲 p共k兲 · p 共1 − pi兲n−k i =p k i 共n兲
i = 1,2,3
共4兲
where p = probability that there are n construction workers onsite; p1, p2, and p3 = probabilities of one construction worker locating in fatality or missing zone, severe injury zone, and slight injury zone respectively; and k = number of impacted workers. If the spatial probabilities of locating in these three zones are estimated according the construction activity at the critical landslide scenario, the number and corresponding probability can be calculated according to Eq. 共4兲 easily. For some nonstationary properties, the process is similar to casualties estimation.
(a)
(b)
Fig. 4. Situation of landslide: 共a兲 the landslide; 共b兲 the barrier lake
Demonstration Example General Situation of the Project and the Landslide The Shuifu-Maliuwan Highway is located in the area adjacent to the Yungui Plateau and Liangshan Mountain, in northeast of Yunnan Province in China. The area is characterized by high mountains, steep gorges with heavy erosion, rapid rivers, and saw-cuts, and there are many cut-slopes along this highway. The studied slope is located in canyon terrain cut by the Guanhe River. On the construction site, the bedrock partially outcrops. The stratum layer mainly consists of loose accumulation, which is distributed over a width of more than 200 m. The main component is medium-weakly weathered hard limestone. The detritus content is from 30 to 50%. The diameter of detritus ranges widely, and the greatest value is about 1.5 m. The content of mudstone and siltstone is quite low, which is less than 5%. The particle size is only from 1 to 2 cm. The maximum thickness is about 10m. There is no seepage found in this slope and it is not likely that the undergroundwater had any inference with slope excavation. The landslide occurred in the section from K121+ 490 to K121+ 670 at about 5:00 a.m. on June 27, 2006. Fig. 4 shows the situation of landslide. The biggest thickness of the debris was estimated to be 10 m. The sliding surface was approximately a straight line. According to the sliding geometry, the maximum width along the highway embankment is more than 200 m. The horizontal area is about 10, 400 m2. The total volume is assessed roughly at some 230, 000 m3. The furthest travel distance was about 150 m. The landslide dam, which was formed with 200-m width, raised the water level by over 10 m. Fortunately, the landslide occurred at a time when there were not many construction workers at the site. Still, the landslide resulted in two deaths, four missing, and two severe injuries, as well as several slightly injured. The protecting structures were completely destroyed. Two trucks were buried or hit by debris or rockfall. One of the piles for bridge near the slope was broken.
Probabilistic Analysis of Slope Instability Hazard Identification In order to identify the most dangerous construction step, the construction process of cutting and protecting the slope was simulated using the finite-element code 共PLAXIS 2007兲. In the simplified analysis, the factor of safety which was calculated based on strength reduction method under the condition of average strength parameters, was used to evaluate the stability state of the slope. The section area of the sliding mass, which can be representative of the debris volume, was used to assess the consequences. The calculations comprised total 10 steps 共or cases兲 as
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Table 3. Calculation Cases for the Cutting and Protecting Case Case Case Case Case
Probabilistic Analysis
Description 1 2 3 4
Case 5 Case 6 Case 7 Case 8 Case 9 Case 10
Initial gravity stress calculation Calculating the safety factor at natural state Excavating the first layer Safety factor calculation under the condition of Case 3 Excavating the second layer and installing the anchors for first layer Safety factor calculation under the condition of Case 5 Excavating the third layer and installing the anchors for second layer Safety factor calculation under the condition of Case 7 Installing the anchors for third layer Safety factor calculation under the condition of Case 9
listed in Table 3. The average cohesion of the loose deposit body and its average internal friction angle were estimated to be 45 kPa and 30°, respectively, according to the geological investigation report. According to the simulation results 共as shown in Fig. 5兲, the factor of safety at the natural state is 1.16, which implies the slope is safe under the condition with average strength parameters. The factor of safety increases under Case 4, because the cutting unloads the slope. However, the critical slip surface under Case 4 is basically identical to that at the natural state. From Case 6 to Case 10, the critical slip surface changes markedly; this causes the volume of the probable sliding mass to vary. Considering the probable volume of landslide, the quantity of vulnerable elements, and the factor of safety, the state at Case 8 is considered as the most critical scenario. The landslide scenario corresponding to this case was analyzed in detail.
With cutting and protecting, the probability also the consequence changes with time or construction steps. So the probability and consequence analysis should be performed for every construction step. It will be a time and effort consuming and but maybe low efficiency work. Based on the research above 共hazard identification兲, Case 8 is considered as the most hazardous construction step. Therefore, the failure probability of Case 8 is analyzed in detail. The uncertainty and variability of soil and rock parameters were simulated by the Monte-Carlo method. The factor of safety was obtained using strength reduction method. The calculation process allows anchors to be installed according to the real construction situation. The failure probability can be estimated by counting the portion of simulations where the computed factor of safety is less than 1.0. According to the test data from the geological investigation report, a probability density function can be fitted over the frequency diagram of strength parameter, which is a modified histogram whose ordinate has been scaled, so that the area under the histogram is unity. In practice, normal distribution is very popular and often selected to express the uncertainty of soil and rock 共Matsuo and Kuroda 1974; Tobutt 1982兲. The mean value represents the best estimate of the random variable, and the standard deviation, or coefficient of variation, represents the uncertainty. According to the geological investigation report, the mean value of cohesion, c, is 45 kPa, and its coefficient of variation 共COV, ratio of standard deviation to mean value兲 is estimated to be 6.7%. The average interval friction angle, , is 30°, and its CoV is 10%. The average density is 1 , 800 kg/ m3, and its corresponding COV is estimated to be 11%. The analysis was done for the case where c − parameters are correlated. The value of c − correlation coefficient was assumed to be ⫺0.5. Using the code Riscue 共Huseby and Terramar 2008兲, 1,000 groups of strength parameters were generated for the Monte-Carlo simulations. The FLAC3D code was used to calculate the factor of safety at Case 8. In order to decrease the calculation effort, a typical calculation profile was selected and a simple three dimensional
loose deposit body
bedrock
(a)
(b)
(c)
(e)
(f)
(d)
Fig. 5. Factors of safety and shear strain contours at critical states under different cases 共FoS: factor of safety兲: 共a兲 the numerical model; 共b兲 FoS= 1.16 at natural state; 共c兲 FoS= 1.21 under Case 4; 共d兲 FoS= 1.28 under Case 6; 共e兲 FoS= 1.10 under Case 8; and 共f兲 FoS= 1.28 under Case 10 JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING © ASCE / DECEMBER 2010 / 1649
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0.16 0.14 0.12
Probability
0.10 0.08 0.06 0.04 0.02
1.78
1.66
1.55
1.44
1.34
1.24
1.15
1.09
1.06
1.03
1.00
0.96
0.93
0.88
0.00
Factors of safety
Fig. 6. Histogram of simulated factors of safety Fig. 8. Final state of runout calculation
Consequences Analysis To assess the consequences, the volume of the landslide mass that will impact the elements at risk should be estimated. Here, the landslide volume was estimated on the basis of the threedimensional failure surface obtained with FLAC3D 共ITASCA 2002兲. The simulation was performed based on average parameters. This is shown in Fig. 7. The 3D model was set up according to the most hazardous construction step in Case 8. The surface of largest shear strain ratio from the result based on the average strength parameters can be considered as the approximate critical slip surface. The volume which is involved in this landslide mass is estimated to be about 180, 000 m3. The runout behavior of the landslide mass was then analyzed using particle flow code PFC3D 共ITASCA 2005兲 and it was done in deterministic method. The input parameters included density, contact stiffness, friction coefficient, contact-bond strength, and parallel-bond strength, etc. In this example, the parameters were estimated based on the geological investigation report and experience judgment. Because the parameters for runout analysis are often hard to determine accurately, the parameters are somewhat subjective. According to the approximate position of the slip surface, a ball wall model was set up. The protecting structures were not modeled in the calculation. Fig. 8 shows the final state of the runout calculation. In order to visualize the travel distance of the debris, balls with different colors represent different displacement ranges. The longest travel distance is about 135 m. According to the results, the impacted length along highway route is over 250 m. A landslide dam is formed on the river. Its greatest width is
Fig. 7. 3D model and sliding mass volume estimation
over 250 m and the average depth is more than 10 m. The landslide dam is a serious secondary hazard, which needs more attention. The direct impacted area is about 250 m ⫻ 100 m near the slope. The elements at risk include mainly construction workers, equipment, existing structures, and the secondary threat of the landslide dam blocking the Guanhe River.
Casualties due to Landslide In order to estimate the casualties, the horizontal distance, h, from an individual construction worker to the center of sliding mass is used. According to the mechanism and intensity of the landslide event, the vulnerability values specifying the damage degree of persons at risk can be assessed as a function of h, based on the reference values given in the literature 共Finlay et al. 1999兲. The human impact here is classified into three levels including fatalities or missing with h from 0 to 80 m, severe injury with h from 80 to 110m, and slightly injury with h from 110 to 150m. The persons beyond 150m are considered safe. The vulnerability ranges are, respectively, 1.0–0.8, 0.8–0.2, and 0.2–0.0 for the three groups. The number of construction workers on-site with different time intervals is assumed to be as shown in Fig. 9. There could be 20–25, 14–18, and 8–12 construction workers, respectively, during 6:00 a.m. to 6:00 p.m., 6:00 p.m. to 12:00 a.m., and 12:00 a.m. to 6:00 a.m. at Case 8. As listed in Table 4, the recommended values of vulnerability coefficients are 1.0, 0.5, and 0.1, respectively. According to the construction activities at criti-
No. of construction workers on site
model with thickness of 5 m, which is the spacing distance of anchors, was set up. The histogram of the simulated safety factors is shown in Fig. 6. Out of 1,000 simulations, 51 cases had a factor of safety less than 1.0. This implies a failure probability of 0.051 at the most dangerous construction step 共Case 8兲 is 5.1%.
25 20 15 10 5 00:00
06:00
18:00
00:00
time
Fig. 9. Example of the distribution of number of construction workers on-site as function of time of day
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Table 4. Risk Calculation for Casualties Number of workers on-site Time interval
Range
Temporal probability P共T 兩 L兲
Distance, h 共m兲
Spatial probability, P共S 兩 L兲
Vulnerability, V共S 兩 L兲
Individual risk, P共L兲 · P共T 兩 L兲 · V共S 兩 L兲
Average individual risk, R共HI兲
06:00–18:00
20–25
12/ 24= 0.5
14–18
6 / 24= 0.25
00:00–06:00
8–12
6 / 24= 0.25
0.7 0.2 0.1 0.7 0.2 0.1 0.7 0.2 0.1
1.0 0.5 0.1 1.0 0.5 0.1 1.0 0.5 0.1
0.0255 0.01275 0.00255 0.01275 0.006375 0.001275 0.01275 0.006375 0.001275
0.020655
18:00–00:00
0–80 80–110 110–150 0–80 80–110 110–150 0–80 80–110 110–150
cal construction step 共Case 8兲, the spatial probabilities of one worker locating in fatalities or missing zone, severe injury zone and slightly injury zone are respectively estimated to be 0.7, 0.2, and 0.1 based on subjective judgment and experiences. Since the slope failure probability is known, the individual risk can be obtained. The construction workers working from 6:00 a.m. to 6:00 p.m., whose horizontal distance to the center of sliding mass is in range of 0 to 80 m, are most vulnerable to landslide hazard. Their individual risk is 0.0255 共failure probability of 0.051 ⫻ temporal probability of 0.5⫻ vulnerability of 1.0兲. The average individual risk of time interval from 6:00 a.m. to 6:00 p.m. is 0.020 655 according to Eq. 共1兲. With the information provided in Table 4 and Eq. 共4兲, the casualties can be estimated as shown in Fig. 10. Here, the number of construction workers on-site is assumed to have uniform distribution. For example, the number of workers during 12:00 a.m. to 6:00 a.m. is from 8 to 12, so the probabilities of 8, 9, 10, 11, and 12 are all 1/5. It shows the probable number of fatalities or missing, severe injury, and slight injury, and their corresponding probabilities and cumulative probabilities if the landslide occurs, For example, the probability of 15 fatalities is 0.085 and the probability of fatalities less than and equal to 10 is 0.345.
Economic Loss For potentially affected construction equipment, the damaged degree can be divided into three levels, as shown in Table 2. The loss can be estimated as the product of the average net present
0.20 0.15 0.10 0.05 0.00 0
2
4 6 8 10 12 14 16 18 20 22 24 26 Number of impacted construction workers
(a)
Cumulative probability
Probability
fatalities or missing severe injury slightly injury
0.0103275
value and the vulnerability coefficients. The probability of the construction equipment being in the area affected by the landslide event is also a temporal and spatial probability problem. The estimation method is similar to casualty estimation. For this project, the construction equipment on-site includes mainly backhoe loaders and trucks. If the landslide occurs, the possible loss for construction equipment is shown in Table 5. Taking account of the number of damaged equipment according to Eq. 共4兲, the probable loss range of backhoe loaders is from 0.3 to 1.4 million CNY. The average loss is about 1.1 million CNY as shown in Fig. 11共a兲. The probable loss range of trucks is from 15 to 840 thousand CNY as shown in Fig. 11共b兲. The average loss is around 275 thousand CNY. The probability of loss less than 240 thousand CNY is 0.66. As a whole, the average economic loss of construction equipment is 1.4 million CNY, corresponding to an average risk of 71,000 共1.4 million⫻ 0.051兲 CNY. The economic loss for the existing structures in the impacted area was calculated on the basis of the cost for building these structures. The structures built previous to this construction step include bolts, cables, framed beams, and catchwater ditch. The main built structures and construction cost in or near the affected area are listed in Table 6. The total economic loss for previously built structures is estimated to about 10.85 million CNY. According to the three dimensional simulation, the total volume of landslide mass is approximately 180, 000 m3. From the results of PFC3D simulation, some of the debris traveled a long distance or rushed into the Guanhe River. At last the debris which is needed to be removed is estimated from 110, 000 m3 to 130, 000 m3. The local average unit price of cutting and trans-
0.30 0.25
0.0103275
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
fatalities or missing severe injury slightly injury
0
2
4 6 8 10 12 14 16 18 20 22 24 26 Number of impacted construction workers
(b)
Fig. 10. Casualties if landslide occurs: 共a兲 probability; 共b兲 cumulative probability JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING © ASCE / DECEMBER 2010 / 1651
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Table 5. Information on Probable Damaged Construction Equipment On-Site Number 共probability兲
Horizontal distance 共m兲
Spatial probability, P共S 兩 L兲
Damage level
Recommended vulnerability, V共S 兩 L兲
Backhoe loaders
1共0.3兲 2共0.7兲
Trucks
1共0.6兲 2共0.3兲 3共0.05兲 4共0.05兲
0–80 80–110 110–150 0–80
0.9 0.1 0 0.8
I II III I
0.7 0.3 0.05 0.7
80–110 110–150
0.1 0.1
II III
0.3 0.05
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
Cumulative probability
Cumulative probability
Equipment
0
200
400
600
800
1000
1200
1400
Economic loss, V共S 兩 L兲 ⫻ E 共103 CNY兲
1,000
700 300 50 210
300
90 15
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0
1600
Average value E 共103 CNY兲
100
200
300
400
500
600
700
800
900
1000
Economic loss for trucks (×103 CNY)
3
Economic loss for backhoe loaders (×10 CNY)
(a)
(b)
Fig. 11. Probable economic loss for equipment: 共a兲 probable economic loss for backhoe loaders; 共b兲 probable economic loss for trucks
porting expense is about 10 CNY/ m3. In the risk calculations, the debris volume was assumed to have a triangular distribution with the most likely value of 120, 000 m3. Using the code RISCUE 共Huseby and Terramar 2008兲, one group of data of debris volume with triangular distribution can be obtained. Timing the unit price, the loss of clearing debris can be estimated. The average economic loss for clearing the debris is around 1.2 million CNY, corresponding to an average risk of 61.4 thousand 共1.2 million⫻ 0.051兲 CNY. The economic loss due to time delay can be expressed as a probability curve. Here, the time-dependent cost including wages, management fee, and rent for equipment is calculated. The loss resulting from postponed operation and inflation or loan interest rise was not considered due to lack of data. The extra time can be estimated from the analysis presented in the next section, and ranges from 136 to 157 days. The number of construction workers ranges from 42 to 55. The average wage for one person per day
varies from 70 to 80 CNY. These latter two parameters are assumed to have uniform distributions. The average management fee is 2,000 CNY per day, and the rent cost for one backhoe loaders is 2,000 CNY per day. Finally, the economic loss because of time overrun is estimated to be between 3 and 4 million CNY as shown in Fig. 12. The average economic loss because of time overrun is about 3.5 million CNY, corresponding to an average risk of 0.18 million 共3.5⫻ 0.051兲 CNY. Four groups of data including loss of affected construction equipment, damaged structures, removing debris, and time delay were obtained. The total economic loss can be expressed as the sum of all these losses. Fig. 13 shows the cumulative probability of the probable economic loss if the landslide occurs. It can be seen that the probable loss ranges from 15.5 million CNY to 18.2 million CNY. The probability of the loss less than 17.0 million CNY is 0.5, and the probability of the total loss being less than 17.4 million CNY is 0.9. The total average economic loss may be
Table 6. Main Construction Quantity in or near Sliding Mass Number 1
2
Earlier built structures
Unit Quantity
⌽32 steel bar Vertical beam Transverse beam Concrete C25 Anchor cable frame beams Anchor cable 3⌽15.24 Vertical beam 共0.5⫻ 0.6 m兲 Steel Vertical beam Transverse beam 共0.4⫻ 0.5 m兲 Transverse beam Concrete C25 Watercatch ditch Mortar flag stone 共M7.5兲 Anchor frame beams
Anchor Beam 共0.4⫻ 0.5 m兲
Steel
3 Total Note: Most of the data are from the design and budget documents; part is estimated based on experience.
m ton ton m3 m ton ton m3 m3
4,480 30 30 300 22,000 170 80 1,600 1,850
Unit price 共CNY兲
Subtotal 共CNY兲
120 5,400 5,400 350 350 5,400 5,400 350 150
537,600 162,000 162,000 105,000 7,700,000 918,000 432,000 560,000 277,500 10,854,100
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1.0 0.9
Cumulative probability
Cumulative probability
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
2900
3050
3200
3350
3500
3650
3800
3950
0.0
4100
15.4
3
Economic loss because of time overruns (×10 CNY)
Fig. 12. Economic loss because of time overrun
16.9 million CNY if the landslide occurs, corresponding to an average risk of 0.86 million 共16.9⫻ 0.051兲 CNY.
Time Overrun
15.8
16.2
16.6
17.0
17.4
17.8
18.2
6
Total economic loss (×10 CNY)
Fig. 13. Total economic loss and corresponding cumulative probability
6 months. Because there were no preplans to handle emergency accidents like this, the actual loss was higher than the estimated range in this study.
Conclusions
Comparison of Simulation Results and the Actual Consequences The results from the numerical simulations were very close to the actual situation. Table 7 shows the comparison of model predictions and actual consequences. The probabilities of fatalities less than and equal to 5, 10, 15, 20, 25 are, respectively, 0.05, 0.34, 0.73, 0.99, and 1.00. The probability of 15 fatalities is greatest, which is 0.085. The estimated range of economic loss is between 15.52 and 18.21 million CNY, and the probability of loss less than 17.2 million CNY is 0.72. Loss equal to 17.1 million CNY is greatest possible, and its probability is about 0.11. Similarly, the probability of time overrun less than and equal to 155 days is 0.99. The average time overrun is about 146 days. According to official data after this accident, the economic loss for this landslide was over 20 million CNY and the time extension was about
The risk associated with landslide in cut slopes is very high during the construction time, especially for sites with unfavorable topographical and geological conditions. Therefore, it is necessary to do a quantitative assessment of the risk posed by landslide before determining the budget or tender price for cut-slope projects. In this study, a methodology for doing this was outlined. The most hazardous scenario was identified among all construction steps based on numerical simulation of the construction process. The failure probability was then estimated using the reliability theory. According to the probable sliding mass and the impacted area obtained from 3D numerical models, the elements at risk were identified for the most hazardous construction step. The temporal probability and spatial distribution of movable exposed elements at risk were estimated according to the actual project situation. Through analyzing the vulnerabilities, casualties, and economic loss were estimated probabilistically. In addition, the probable extra time for clearing the debris and the extra time for construction resumption were estimated based on experience and construction plan. The method was tested on a large cut-slope project in which a landslide did occur. In comparison with the actual situation, this method proved to be effective and reasonably accurate. However, the predicted time extension and the economic loss for time-dependent cost were significantly less than the actual values. In general, the time overrun is difficult to estimate, because it is influenced by both the
Probability
As analyzed above, the time overrun mainly consists of the extra time for clearing debris and reconstruction. As mentioned earlier, the volume of debris which needs to be cleared is estimated to be 110, 000 m3 to 130, 000 m3. The average practical productivity to clear waste cut ranges from 1600 m3 to 2000 m3 / day for one backhoe loader. Because of the limitation of site conditions, only 1 or 2 backhoe loaders can be used to remove the debris. It is assumed that the temporal probability of one or two backhoe loaders is 0.8 and 0.2, respectively. Based on these assumptions, the number of days needed for clearing the debris was simulated using the Monte Carlo method. If the construction team made emergency preplans, they can handle this task efficiently. Fig. 14 shows the estimated time extension for the project. The extra time for clearing debris ranges from 46 to 67 days. The extra time for reconstruction, such as redesign and rebuilding the protecting structure, can be estimated based on the conventional schedule estimation method. In this study, according to construction plan without landslide, the construction time is estimated to be 90 days from start to this construction step. This number is applied as the reconstruction time. Therefore, the total time extension ranges from 136 to 157 days. The average extra time for clearing the debris and completing redesign is around 146 days. The average risk for extra time is 7.4 共146 ⫻ 0.051兲 days.
0.20 0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 40
43
46
49
52
55
58
61
64
67
70
73
Extra time for clearing debris (days)
Fig. 14. Extra time for clearing debris
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Table 7. Comparison of Estimated and Actual Consequences For injury or loss of life Probability 共n = number of construction workers兲
Range Fatalities or missing Severe injury Slightly injury
0.05共n ⱕ 5兲 0.33共n ⱕ 2兲 0.73共n ⱕ 2兲
0–25
0.34共n ⱕ 10兲 0.70共n ⱕ 4兲 0.96共n ⱕ 4兲
0.73共n ⱕ 15兲 0.92共n ⱕ 6兲 0.99共n ⱕ 6兲
0.99共n ⱕ 20兲 0.99共n ⱕ 8兲 1.00共n ⱕ 8兲
Actual consequences 1.00共n ⱕ 25兲 1.00共n ⱕ 10兲 1.00共n ⱕ 10兲
6共2 + 4兲 2 Several
For economic loss CNY 共in millions兲
Range 15.52–18.21
0.01共c ⱕ 16.0兲
Probability 共c = economic loss兲 0.24共c ⱕ 16.6兲 0.72共c ⱕ 17.2兲 0.99共c ⱕ 17.8兲
1.00共c ⱕ 18.2兲
Actual consequences Over 20
Range 136–157
0.03共t ⱕ 139兲
Probability 共t = probable extra time兲 0.29共t ⱕ 143兲 0.62共t ⱕ 147兲 0.88共t ⱕ 151兲
0.99共t ⱕ 155兲
Actual consequences About 6 months
For time overrun Days
landslide magnitude and human factors. Finally, it must be noted that because of scarcity of data, experience, and subjective judgments are required in this type of study.
Acknowledgments This research was sponsored by National Natural-Science Foundation of China 共Grant No. 40772179兲 and Western Science and Technology Project of Ministry of Communications 共Grant No. 2006318799107兲. Grateful appreciation is expressed for these supports. This paper was written while the first writer was a guest researcher at the International Centre for Geohazards 共ICG兲 in Oslo, Norway. The support provided by ICG during this period is gratefully acknowledged.
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