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Estimating Probability of Failure Due to Internal Erosion with Event Tree

Analysis

Ehsan Goodarzi

PhD Student of Department of Biological and Agricultural Engineering, Faculty of Engineering, Universiti Putra Malaysia, 43300, Serdang, Selangor, Malaysia

E-mail: ehsan.g@hotmail.com

Lee Teang Shui

Professor of Department of Biological and Agricultural Engineering, Faculty of Engineering, Universiti Putra Malaysia, 43400, Serdang, Selangor, Malaysia

Mina Ziaei

Master Student of Department of Biological and Agricultural Engineering, Faculty of Engineering, Universiti Putra Malaysia, 43300, Serdang, Selangor,

Malaysia

Ali Haghizadeh

PhD Student of Department of Biological and Agricultural Engineering, Faculty of Engineering, Universiti Putra Malaysia, 43300, Serdang, Selangor, Malaysia

ABSTRACT Safety of existing dams has been one of the most important worry of hydrosystem engineers and identification of serious accidents which may cause dam failure, is very crucial. In the present study, the probability of dam failure due to internal erosion was estimated under two conditions as; outward flow toward the slough with a full reservoir, and inward flow toward the reservoir with an empty reservoir for Doroudzan earth-fill dam. The applied tool to estimate risk of dam failure was an event tree analysis similar to that outlined in USBR (1997). The results have been demonstrated that annual probability of piping failure is 2.25 × 10 and the weighted probability of failure for inward and outward flow are 1.68 ×10 and 5.625 × 10 , respectively. KEYWORDS: Internal erosion, risk, inward flow, outward flow, event tree analysis

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INTRODUCTION There are about 800000 dams in the world built for different purposes such as control of

flood, water supply to support irrigation, drinking, industrial needs, and electricity generation. Safety of existing dams has been one of the most important worry of hydrosystem engineers and prediction of serious accidents, which may cause dam failure, is a major task for them. Although, the knowledge about hydrosystem has been improved and resistance of dam structure has been raised, but the probability of malfunction of some parts of dam (spillway, diversion tunnel) or failure of whole of dam is not zero and an accident may occur as a result of variation of hydrologic and hydraulic conditions, or the weakness of operation.

Risk and reliability are two major concepts in hydrosystem engineering. Reliability can be defined as probability of non-failures. So, by increasing the probability of system failure the reliability of system will be decline. When the reliability of a system decreases, public attentions and the concern about the safety of system will be increased. The reliability in the hydrosystem also can be defined as capability of a system to complete its tasks under some definite condition for a specific time period. Estimation of the reliability of a system needs many statistical tools because it is often reported in terms of a probability, and it is necessary to have sufficient knowledge about the probability theory and statistics rules.

Evaluation load forces and resistance of system are the main parts of risk and reliability analysis in the hydrosystem engineering where the reliability of a system can be evaluated by studying the interaction of load and resistance. When a system is reliable, resistance or capacity of system is more than the load forces due to different kinds of external events. Finally, we can say, risk is the probability of failure to attain the proposed object. Evaluating reliability is a complex and important issue in hydrosystem engineering particularly when there is a terrible consequence after structural failure. Risk and reliability are main parts of decision making process, because it is not possible to have complete information about the parameters and variables and definitely they are subject to uncertainty. Hence, the main goal of decision theories is finding a systematic way to make best and rational decision as well as decrease the effect of uncertainty.

INTERNAL EROSION DEFINITION The process of moving fines throughout the foundation or core of the dam is called internal

erosion and it is one of the main causes of dam breaking. Internal erosion is dangerous because there is no external evidence during the episode and a dam may fail only some hours after evidence of internal erosion. Internal erosion can be developed from the beginning of water storage in the reservoir or during dam life. Fines and soil particles are carried from the embankment or foundation when a water leak (seeps) through the dam body tends to make a pipe in the body of dam. Figure 1 shows a schematic picture of pipe in the dam body.

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Figure 1: Schematic view of piping process in Embankment dam

The piping failure is defined as breaking dam due to water penetrating throughout the embankment of dam, transportation soil particles of dam materials, and continuously widening the pipe (Foster Fell, 1999a).

Sherard and Dunnigan (1985) investigated the effect of filters on the process of internal erosion in embankment dam. The results showed that if the modern criteria applied for design of filter, the internal erosion process will certainly not continue. Johansson et al. (1995) studied the most important parameters of internal erosion. According to their work, the results showed that the process of internal erosion causes increasing porosity because of carrying soil particles and fines. The most important factors which were disused in their paper were; hydraulic conductivity, seepage flow, density, seismic velocity, temperature, di-electricity, and resistivity. USBR (1997) applied an event tree to estimate the risk and reliability of embankment dam due to internal erosion. The event-tree included the following steps:

1. Initiation of concentrated leak throughout the embankment of dam,

2. Continuation of internal erosion process throughout unfiltered exit,

3. Progression of internal erosion, ability to support a roof,

4. Progression of internal erosion, inability to limit flows,

5. Progression of internal erosion, erodible soils.

6. Unsuccessful early intervention,

7. Initiation of breach, and

8. Unsuccessful heroic intervention.

Foster and Fell (1999, 2000) studied the process of piping throughout foundation, embankment of dam, and identified three main issues in the procedure as; the soil capability to support pipe roof, expansion existing hole, and limitation of flow by Crack filling of upstream

Vol. 15 [2010], Bund. J 938 filter of the core. Malkawi and Al-Sheriadeh (1999) considered about probable sources of seepage flow and measurement of seepage by excitation-response analysis. Bureau of Reclamation (2001) assessed a risk and reliability for an embankment dam in the North Dakota. In this study, two potential failure modes were considered:

1. Assessing seepage and piping throughout foundation, and

2. Assessing seepage and piping throughout embankment of dam. Fell et al. (2003) presented a new approach to estimate the time of internal erosion development and piping in embankment dams.

Robert and Torres (2008) presented considerations to develop monitoring systems for internal erosion (IE) detection in embankment dams. The need for, and location of, instrumentation systems within a dam must be evaluated by a risk analysis, which develops potential failure modes and detailed information on the concerns leading to those failure modes. Important considerations included: 1) characteristics of the embankment materials that may be sensitive to IE, 2) detection of seepage concentrations in sections parallel to the embankment profile, 3) in areas of concentrated seepage flows, detailed information of the ground water characteristics should be obtained using state of the art instrumentation, 4) proper monitoring procedures for the seepage collected by drain system, and 5) design of data collection systems to obtain continuous readings for long term monitoring. References of where these specialized instruments have been placed and successfully monitored are included.

The literature has been shown internal erosion can fail dam and causes disaster events for downstream area. Hence in this study, the event-tree method was applied to estimate the probability of failure due to internal erosion for Doroudzan earth-fill dam, in Iran.

EVENT TREE ANALYSIS Event tree includes visual illustration of the possible outcomes of system which is made of an

initial event and several branches which in each branch shows an event in the model. By increasing the number of event, the branches of tree will be increased and the model will be more complicated. When all elements of system continuously work, the event tree technique can be applied for reliability analysis of system.

The main advantage of event tree is ability of modeling the mechanism of breach of a system such as dam or reservoir from beginning to failure. Evaluation of conditional probabilities by event tree has limitations in that there are not many objectives to estimate it and the experts need more subjective judgment. The probability of failure and damage of a particular system for discrete random variables can be calculated by applying a simple event tree. In Figure 2 different parts of an event tree which are including start point, branches and sub-branches of the tree are shown. Morgan and Henrion (1990) found that discrete-probability decision trees are applicable method between the decision makers in risk and uncertainty analysis.

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However, event tree analysis has some important disadvantages such as the inability of estimating the error in outcomes, use discrete random variables, and increasing computational effort by increasing the number of random variables. The above disadvantages are big weaknesses to estimate risk and reliability of complex system like dams which involve many continuous random variables such as precipitation depth, inflow to reservoir, overtopping depth, and wind set-up and wave run-up. Discretely these random variables would lead to a very large event tree.

CASE STUDY (DOROUDZAN EARTH-FILL DAM) The Doroudzan dam is one of the most important dams in the south of Iran, Fars province.

The basin of multipurpose earth fill dam is situated near the North West of Shiraz on Kor River and in the Bakhtegan lake catchment area. The Kor river watershed is between the 51∘43’ and 52∘ 54’ east longitudes and 30∘ 08’ and 31∘ 00’ latitudes. The Highest point elevation of the watershed is 3749 meter from the mean sea level and located at the west north of the watershed. The total volume and dead storage of the reservoir are 993 and 133 𝑀𝐶𝑀, respectively. Some basic information of Doroudzan dam has been shown in Table 1. Doroudzan dam design was done in 1963 to 1966 and dam construction started in 1970 and was completed in 1974. Doroudzan supplies the necessary water for 112,000 hectares agricultural lands and providing domestic and industrials needs of Shiraz (as capital of Fars province), Marvdasht, and Zarghan.

Table 1: Doroudzan dam information Dam Description Type Earth-fill

Height 57 𝑚 Crest length 710 𝑚 Crest width 10 𝑚

Crest elevation 1683.5 Max width at base 450 𝑚

Fill volume 4.8 𝑀𝐶𝑀 Foundation Limestone rock

Slope of upstream 3𝐻: 1𝑉 Slope of downstream 3𝐻: 1𝑉

Figure 2: Different parts of an event tree

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The most important artifacts located downstream of the Doroudzan dam are the Pasargadae and Persepolis monuments which are remains from 515 BC. These structures are one of the most famous monuments in the world that are annually visited by people from all over the world. Therefore, any problems for the Doroudzan dam will undoubtedly immerse theses two ancient and valuable heritage.

Doroudzan reservoir dam, constructed of homogeneous materials, has a central drain for the internal seepage of the dam. The dam drains are connected to three longitudinal drainages, each of them 10 meters width, by which water is conveyed to the dam’s stony downstream toe. Generally, drainage system of the dam sidewall and foundation are as following:

1. Vertical drain width is 2.5 meters;

2. Vertical drain maximum elevation is 1670 meters,

3. Three horizontal drains,

4. Horizontal between drains 106 meters,

5. Width of drains 10 meters,

6. Thickness of drains 3 meters,

7. Eleven relief well in the shoal.

In total, 29 double-pipe hydraulic piezometer of USBR type have been installed in the dam body of which there are 13 units in the sidewall and 16 units in the foundation of the dam (Figure 3).

Figure 3: The schematic section of dam with different piezometer

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Due to incomplete and inadequate data of the piezometer installed in the dam sidewall, the drain line of the dam sidewall cannot be explained accurately. However, based on the good quality of the output drain of the relief wells, it can be concluded that the dam drainage system including the vertical filters and horizontal drainages operate well.

According to the available technical reports, the impermeable materials of the shell, upstream the embankment included 45% to 90% fine grain material (less than 200 sieve) and 10% to 26% clay (smaller than 0.002 mm). The plasticity index between 20 to 30 percent and the effective friction angle is about 26 degrees. In addition, permeability coefficient of materials above the shell in the horizontal direction is equal to 10-4 to 10-5 𝑐𝑚 𝑠⁄ . Downstream shell materials with lower permeability materials made of silt-clay with 10 to 14 percent silt, plasticity index of 10 to 20 percent effective and internal friction angle 28 degrees.

RESULTS Depending on the operation of the reservoir, seepage may happen in two ways: 1) toward the

reservoir, and 2) towards the slough. The seepage will be started from the slough toward the reservoir, if the adjacent slough is more than water elevation in reservoir. While when the reservoir is full, the seepage started from the reservoir toward the slough. Note that, because of differences in head between the reservoir and the adjacent slough during those stages of normal operations, when the reservoir is empty (inward flow) the probability of occurring internal erosion is higher than when the reservoir is full (outward flow) (USBR, 1997).

The event-tree has been used to compute the probability of failure due to internal erosion included the following steps:

1. Initiation of concentrated leak through the embankment,

2. Continuation of internal erosion process through unfiltered exit,

3. Progression of internal erosion- ability to support a roof,

4. Progression of internal erosion- inability to limit flows,

5. Progression of internal erosion- erodible soils,

6. Imitation breach.

Factors affecting the likelihood or unlikelihood of each of the above steps were considered in assigning probabilities based on verbal descriptions. The verbal descriptions used are tabulated in Table 2.

Throughout this study, the dam failure risk due to internal erosion during normal operations was estimated under two water flow conditions;

1. Outward flow toward the slough with a full reservoir,

2. Inward flow toward the reservoir with an empty reservoir.

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Table 2: Verbal descriptors of probability (USBR, 1997) Descriptor Probability

Virtually Certain 0.999 Very Likely 0.99

Likely 0.9 Neutral 0.5

Unlikely 0.1 Very Unlikely 0.01

Virtually Impossible 0.001

For the inward flow condition, the likely and unlikely factors and the assigned probabilities of the event-tree for an entire year of normal operations are discussed in the Tables 3 through 9 as below.

According to the technical reports available for Doroudzan dam, foundation materials in the former river channel is alluvial sediments and the highest layer is a layer of permeable sand and clay. There is a clay layer 28 meters deep, thickness of 8 meters, which control leakage of the dam. Therefore, possibility of foundation leakage is not calculated. Hence, regarding to Table 3, Unlikely condition with 0.1 probabilities for initiation of concentrated leak through embankment is considered.

Descriptor Description Probability

Likely Silty and embankment can crack and shear due to settlement of underlying peat during construction.

0.9

Unlikely Exit gradients determined form seepage analyses are

less than would likely cause sand boils or piping. 0.1

Due to incomplete access and inadequate results of the piezometer installed in the dam sidewall, the drain line of the dam sidewall cannot be explained accurately. However, based on the good quality of the output drain of the relief wells, it can be concluded that the dam drainage system including the vertical and horizontal filters operate well (Table 4). Therefore, it can be assumed that leakage probability is low and has been assigned 0.1 (unlikely).

Table 4: Continuation of internal erosion process through unfiltered exit (USBR, 1997)

Descriptor Description Probability Likely There is no drain under the reservoir side embankment

to reduce seepage forces, or

There is no filter zone located ‘’downstream’’ of the reservoir side embankment fill.

0.9

Unlikely In areas likely to crack filter fabric will be installed between the existing levee and new embankment fill.

Integrity of filter fabric will be dependent on the amount of deformation.

0.1

Table 3: Initiation of concentrated leak through embankment (USBR, 1997)

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As mentioned above, Doroudzan dam is highly impervious due to clay layers and the probability to form roof is low. Therefore, according to Table 5, the assigned probability for ability to support a roof is 0.1.

Descriptor Description Probability

Likely If erosion were to reach fibrous peat foundation, it

would support a roof.

0.9

Unlikely New embankment material would not support a roof. 0.1

During 1998 till 2001, in the careful inspections of the dam crest, cracks on the crest and left abutment of the dam was observed. Indeed, with continuous inspections and measurements of the shape and approximate depth, significant changes in the dimensions of the cracks between intakes especially in the high elevations were observed. Investigations have shown that lack of insulation in the left abutment has caused a permanent flow between reservoir and shoal which has appeared as the available springs in the left abutment. This process with a permanent movement between the sidewall and the left abutment and lack of filter and suitable conditions for controlling the flow can cause piping or low rate erosion. In fact, there is a permanent flow between sidewall and abutment that can move particles of the sidewall toward downstream. The new condition is not the same as the design condition and criteria, and soil stability would be changed in this area, which can cause low reliability coefficient of stability of the downstream repose. Regarding to above, the probability value for inability to limit flows has been chosen 0.5 (Table 6).

Table 6: Progression of internal erosion: Inability to limit flows (USBR, 1997)

Descriptor Description Probability Neutral

0.5

Neutral In areas likely to crack higher potential flows through cracks will be limited by filter fabric.

0.5

As the specifications of material selected from loan sources are different from the primary designed specifications and criteria, they are very fine and especially downstream materials are silt and clay that are erodible, the probability has been chosen 0.9 (Table 7).

Table 7: Progression of internal erosion: Erodible soils (USBR, 1997)

Descriptor Description Probability Likely Existing levee materials are variable and include peat

clay, and silty sand. Silty sands are erodible.

0.9

Unlikely

0.1

Regarding to large dimensions of the dam and the cracks on the crest, the erosion control is very hard, hence the probability is 0.5 (Table 8).

Table 5: Progression of internal erosion: Ability to support a roof (USBR, 1997)

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Table 8: Unsuccessful early intervention (USBR, 1997)

Descriptor Description Probability Neutral Long embankment will be more difficult to monitor.

0.5

Neutral Leakage generally accessible on reservoir-side slope, Early phases of erosion process can be controlled,

Assume monitoring will be conducted during and after construction,

Assume embankments instrumented, During construction equipment and materials will be

readily available.

0.5

The probability of breach initiates regarding to the material of dam has been considered 0.1 (Table 9).

Table 9: Breach initiates (USBR, 1997)

Descriptor Description Probability Likely Silty sand in portions of the existing levee is highly

erodible.

0.9

Unlikely 0.1

The estimated probability of failure for an entire year due to internal erosion caused by inward flow is equal to the product of the individual probabilities in Tables 3 to 9. Therefore the estimated probability of failure due to internal erosion by inward flow during one year of normal operations due to either excessive seepage or cracking is 2.25 × 10 percent. The process of calculation probabilities and event-tree of the internal erosion for the Doroudzan dam is mentioned below.

Figure 4: Internal erosion event-tree in Doroudzan dam

Probability of failure du𝑃 = 0.1The probability of failu

the inward and outward flowthe portion of the year undreservoir is full or outward is assumed to be 10% of thathe reservoir almost is less tthis matter.

The calculated annual p10.

Figure

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due to internal erosion was calculated as; × 0.1 × 0.1 × 0.5 × 0.9 × 0.5 × 0.1 = 2.25 × 10ilure due to internal erosion during normal operationslow conditions were calculated by weighting the abovnder two conditions as; 1) reservoir is empty or inw

rd flow. For this study, the probability of failure due to that for the inward flow. As is shown in Figure 5, eles than the normal elevation of water and so 10% is app

probability of failure due to internal erosion has bee

re 5: Water elevation-year graph for Doroudzan dam

ons considering both ove probabilities by

inward flow, and 2) e to an outward flow elevation of water in appropriate value for

been shown in Table

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Table 10: Probability of failure due to internal erosion during normal operations

Flow condition Portion of year Annual probability of

failure (%) Weighted probability of

failure (%) Inward flow

0.75 2.25 × 10 1.68 × 10

Outward flow 0.25 2.25 × 10 0.5625 × 10

Annual probability of failure for outward flow (%): 2.25 × 10 × 10% = 2.25 × 10 (%)

Weighted probability of failure (%) for inward flow: %75 × 2.25 × 10 = 1.68 × 10 (%)

Weighted probability of failure (%) for outward flow: %25 × 2.25 × 10 = 5.625 × 10 (%)

CONCLUSION The paper demonstrated the process of estimating risk of internal erosion for Doroudzan

earth-fill dam in south area of Iran. The annual probability of failure of outward flow, weighted probability of failure of inward flow, and weighted probability of failure of outward flow have been computed. The results have shown risk of piping for inward flow 1.68 × 10 (%) is more than risk of outward flow 5.625 × 10 (%). So it confirmed that when the reservoir is empty (inward flow) the probability of occurring internal erosion is higher than when the reservoir is full (outward flow).

This investigation demonstrated initial water level is the most important factor in dam safety analysis. Changing water level can has affects on the probability of overflowing, probability of seepage occurring in the reservoir, and supplying water to downstream (agricultural, domestic, and industrial needs). So, the elevation of water in the reservoir must adjusted by operator properly to make a tradeoff among all conditions.

In general, regarding to the cracks on the crest and left abutment of the dam, existing permanent flow between reservoir and shoal, incomplete access and inadequate results of the piezometer installed in the dam sidewall, and the computed values of risk for Doroudzan dam, it is necessary to have continues inspections for desired dam.

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REFERENCES 1. Johansson, S (1997) “Seepage Monitoring in Embankment Dams”.

Unpublished doctoral dissertation, Department of Civil and Environmental Engineering Royal Institute of Technology, Stockholm, Sweden.

2. Fell, R., & Wan, C. F (2005) “methods for Estimating the Probability of Failure of Embankment Dams by Internal Erosion and Piping in the Foundation and from Embankment to Foundation”. The University of New South Wales.

3. Fell, R., Wan, C. F., Cyganiewicz, J., & Foster, M (2003) “Time for Development of Internal Erosion and Piping in Embankment Dams”. Journal of Geotechnical and Geoenvironmental Engineering, 129(4), 307.

4. Foster, M. A., and Fell, R (2000) Use of Event Trees to Estimate the Probability of Failure of Embankment Dams by Internal Erosion and Piping. Proc., 20th Int. Congress on Large Dams, Beijing, International Commission on Large Dams (ICOLD), Paris, Question 76, 1, 237–260.

5. Foster, M. A., Fell, R., and Spannagle, M (1998) “Analysis of Embankment Dam Incidents”. UNICIV Rep. No. R-374, September 1998, Univ. of New South Wales, Sydney, Australia.

6. Foster, M. A., Fell, R., and Spannagle, M (2000b) “A Method for Estimating the Relative Likelihood of Failure of Embankment Dams by Internal Erosion and Piping”. Can. Geotech. J., 37(5), 1025–1061.

7. Hill, P., Bowles, D., Nathan, R., & Herweynen, R (2001) “On The Art of Event Tree Modeling for Portflio Risk Analysis”. NZSOLD/ANCOLD 2001 Conference on Dams, (pp. 1-10).

8. Malkawi, A. H., & Al-Sheriadeh, M (1999) “Evaluation and Rehabilation of Dam Seepage Problems”. A Case Study: Kafrein Dam. Journal of Engineering Geology, 56, 335-345.

9. Robert, L., & Torres, P (2008) “Considerations for Detection of Internal Erosion in Embankment Dams”. Biennial Geotechnical Seminar. Denver.

10. Sherard, J. L., and Dunnigan, L. P (1985) “Filters and Leakage Control in Embankment Dams”. Proc., Symposium on Seepage and Leakage from Dams and Impoundments, R. L. Volpe and W. E. Kelly, eds., Geotechnical Engineering Division, ASCE National Convention, Denver, May 5, 1–30.

11. U.S. Department of the Interior Bureau of Reclamation (1983) “Safety Evaluation of Existing Dams”, a Water Resources Technical Publication, Denver, Colorado.

12. U.S. Department of the Interior Bureau of Reclamation (1986) “Guidelines to decision analysis. Denver”, CO.

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13. U.S. Department of the Interior Bureau of Reclamation (1997) “Probability of Failure Due to Internal Erosion”.

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