An Experimental and Theoretical Study of the Piping Failure of Slope Failure Dams Heyelan Barajlarının Sızma Yenilmesi Üzerine Deneysel Ve Kuramsal Bir Çalışma

Yerbilimleri, 31 (1), 33–43 Hacettepe Üniversitesi Yerbilimleri Uygulama ve Araştırma Merkezi Dergisi Journal of the Earth Sciences Application and Research Centre of Hacettepe University

An experimental and theoretical study of the piping failure of slope failure dams Heyelan barajlarının sızma yenilmesi üzerine deneysel ve kuramsal bir çalışma

Ömer AYDAN Tokai University, Department of Marine Civil Engineering, Shizuoka, JAPAN

Geliş (received) : 01 Aralık (December) 2009 Kabul (accepted) : 26 Ocak (January) 2010

ABSTRACT The failure of slopes along rivers often results in dams of debris material. If such dams with a significant volume fail, they may cause secondary disasters downstream. The author has been involved with this problem since his reconnaissance visits to the damaged areas of Kashmir after the 2005 Azad Kashmir earthquake. This earthquake caused one of the largest dams of slope failure, which occurred near Hattian. This study reports the theoretical and physical experiments on the piping failure of such deposits that were carried out. These studies are descri- bed in this article and theoretical estimations are compared with experimental results. The comparisons imply that the experimental results generally confirm the theoretical estimations. However, there is a difference between the hydraulic gradients for initiation and for total failure due to piping, which may be attributable to the difference between the actual fluid velocity and the averaged velocity used in D’Arcy’s law.

Keywords: Earthquake, experiment, piping failure, slope failure dam, theory.

ÖZ Şev yenilmeleri çoğu kez heyelan setlerinin (barajlarının) oluşumuna neden olur. Heyelan barajlarının oldukça büyük olması halinde, bunlar barajın alt bölgelerinde ikincil doğal afetlere neden olabilirler. Yazar, 2005 Hür Kaşmir dep- reminin hasar incelemeleri sonrasında bu konuyla ilgilenmeye başlamıştır. Kaşmir depreminde yüksekliği 160 m’ye ulaşan heyelan barajı Hattian yakınlarında oluşmuştur. Yazar, bu konu ile ilgili olarak laboratuvarda değişik kum ör- nekleri ile Kaşmir depreminde Muzaffarabad yakınlarında meydana gelen büyük bir heyelandan aldığı malzeme ör- neklerini kullanarak fiziksel model deneyleri yapmıştır. Bunun yanı sıra, konunun kuramsal kısmı da incelenmiştir. Bu makalede, deneysel çalışma sonuçları sunulmuş ve kuramsal yaklaşım sonuçları ile karşılaştırılmıştır. Kuramsal so- nuçlarla deneysel sonuçların birbirleriyle uyumlu olduğu görülmekle birlikte, sızma yenilmesinin başlangıcı ile tüm- den yenilme için hidrolik eğimin farklı olduğu gözlenmiştir. Bu farklılık, büyük bir olasılıkla, gerçek akışkan hızı ile D’Arcy yasasındaki ortalama akışkan hızları arasındaki farklılıkla ilişkilendirilebilir.

Anahtar Kelimeler: Deprem, deney, sızma yenilmesi, heyelan barajları, kuram.

Ö. Aydan E-mail: [email protected] 34 Yerbilimleri

INTRODUCTION The highest slope failure dam is the Usoi slope failure dam, named after the village of Usoi, Large slope failures along rivers often result which was completely buried by the 1911 lar- in dams of debris material (Figure1). The pi- ge slope failure in Tajikistan. It has a total vo- ping failure of soil deposits is of great concern lume estimated at approximately 2 km3 with a with regard to the stability of earth and rockfill maximum height above the original valley floor dams, embankments and natural slope failure of 500 m to 700 m (i.e. Risley et al., 2006). The dams. Such failures may generally lead to ca- lake that formed behind the Usoi dam rose at tastrophic damage to downstream settlements an initial rate of approximately 75 m/y. This lake and environments. Historically, the most spec- was named after the village of Sarez, that was tacular example of piping failure is the failure drowned by the rising water. Lake Sarez is now of the Teton dam in the USA. In addition, the- over 60 km in length with a maximum depth in re are many examples of piping and overtop- excess of 500 m and a total volume of approxi- ping failure of landslide or glacier lakes in mo- mately 17 km3. The Usoi dam is the highest na- untainous areas such as the Himalayas, Andes tural dam on earth. The level and the stability and Rockies (see Singh (1996) for details) (Fi- of this dam have been continuously monitored. gures 1 and 2). There are also many slope failure dams in Tur- key. The recent Kuzulu slope failure also cau- The Ms=8 Wenchuan earthquake in 2008 caused the formation of 34 quake lakes. Among sed a small lake (see Figure 1), which was later these 34 quake-lakes, three that formed in An- breached (Ulusay et al., 2007). The gigantic pla- xian, Qingchuan and Beichuan counties were of nar rock slope failure blocked the Tortum River great scale and were caused mainly by the pla- and formed the largest landslide-dammed lake nar sliding failure of mountains (i.e. Aydan et al., in Turkey, measuring 8500 m in length, 2500 m 2 2009a). The biggest quake-lake of all was the in width and having a surfacial area of 6.77 km Tangjiashan “quake lake”, which was formed by (i.e. Duman, 2009). The slope failure occurred the collapse of a section of Tangjiashan Moun- as a rapid planar sliding failure in the Cretace- tain. Tangjiashan quake-lake was formed 2 km ous interbedded limestones with clastics. The surface of the sliding formed along the bedding from Beichuan and at its peak was 803 m long plane. The dam was estimated to have a maxi- by 612 m wide and 70-124 m high. The estima- mum height of 270m and impounded 1820km2 ted volume of water of the Tangjiashan quake- of mountainous drainage area, forming a lake lake was 250 Mm3. Luckily, nobody was killed with 538million m3 of water on the Tortum River. by the collapse of the slope failure dam. Duman (2009) claimed that the landslide could Historically, a large slope failure occurred in be more than 300 years old. Luckily, the dam the Kangding-Luding area of Sichuan, China created by this landslide has not failed for at le- in 1786. This large slope failure, caused by an ast 3 centuries. M=7.75 earthquake, created a large slope failu- In July 2003 a landslide occurred on the Pare- re dam on the Dadu River (Dai et al., 2004), and echu stream of the Satluj River in Tibet (see Fi- the sudden failure of this slope failure dam re- gure 2). The slope failure blocked the river for sulted in catastrophic downstream flooding ten about 400 m and formed a lake that eventually days after the earthquake. It was reported that breached. The lake was 2,100 m long, 1,100 m more than 100,000 people lost their lives. This wide and about 40 m deep. NASA (2005) captu- may be the most disastrous event ever caused red the formation, growth and collapse process by failure of a slope failure dam. The slope fa- of the Pareechu slope failure dam from 2003 ilure dam was about 70 m high, and it created till 2005, as seen in Figure 2. Although nobody a lake with a water volume of about 50×106 m3 was killed, by virtue of remote and in-situ moni- and an area of about 1.7 km2. The dam failed toring of the growth of the dam lake, the breac- suddenly due to a major aftershock on June 10, hed slope failure dam caused some damage in 1786. Tibet and India (Gupta and Shah, 2008). Aydan 35

Neodani, 1891 Hattian, 2005

Diexi, 1933 Donghekou, 2008

Uzungöl Kuzulu, 2007

Figure 1. Some examples of lakes resulting from slope failures (Neodani by K. Kusakabe (1891), Kuzulu by Ulusay et al. (2007) and other photographs by the author. Dates in the picture correspond to the event dates). Şekil 1. Heyelan sonucu oluşmuş gölcüklere örnekler (Fotoğraflar: Neodani (K. Kusabe, 1891), Kuzulu (Ulusay vd., 2007) diğerleri (yazar). Resimlerdeki tarihler oluş tarihini gösterir).

The author recently investigated the areas af- menon and carried out some experimental and fected by the 2005 Kashmir earthquake and theoretical studies. This article describes the the 2008 Wenchuan earthquake (Aydan et al., outcomes of these studies. 2009a, b). These earthquakes caused many rock slopes, some which resulted in landslide EXPERIMENTS dams. Some of these landslide dams are alre- ady breached while the one in Hattian still po- Two different experimental set-ups were used ses a huge catastrophic risk to the downstream in order to understand the conditions governing area. The author got interested in this pheno- the piping phenomenon. The details of the cha- 36 Yerbilimleri

Figure 2. Growth and failure of the slope failure dam of Pareechu (Tibet) (arranged from images taken by NASA at different times). Şekil 2. Pareechu heyelan barajının büyümesi ve yı- Figure 3. Grain size distribution of experimental mate- kılması (NASA tarafından farklı zamanlarda rials. elde edilmiş görüntülerden derlenmiştir). Şekil 3. Deneylerde kullanılan malzemenin tane boyu dağılımı.

racteristics of materials, experimental set-ups, during the water head rise. Water was pumped and experimental results are given below. into the inner cylinder through a hose using an electrical pump from a reservoir. A 30 mm thick Characteristics Materials sponge layer was placed on the top of the soil column of the inner cylinder, in order to prevent Two different materials used in the experiments erosion by the pumped-in water and to attain were commercially available quartz sand (No.4) uniform water pressure head increase. In addi- and slope failure debris from Muzaffarabad in tion, an Acoustic Emission (AE) sensor was at- Kashmir. Slope failure debris material was crus- tached to the outer surface of the outer cylin- hed dolomite and constituted the fault zone (Ay- der in order to assess the time of piping failure. dan et al., 2009b). Grain size distributions and properties of experimental materials are shown Slope failure dam experiments in Figure 3 and given in Table 1, respectively. The hydraulic conductivity of the debris material Slope failure dam piping failure experiments is very similar to the permeability of the sand in were carried out by using a 100 m wide, 200 m view of the grain size distribution of the materials. high and 300 m long acrylic tank. The tank had a 105 mm wide reservoir and a 30 mm thick Experimental Set-ups sponge wall, which provided a uniform seepage into the soil and prevented erosion during water Co-centric cylindrical set-up head rise, dividing the tank into two compart- ments. The height of the earth dam was about A co-centric cylindrical set-up was used to 100-110 mm with a slope inclination of 39-43o study the conditions of the piping phenomenon and a crest width of 30-40 mm. Two pressure (Figure 4). The diameters of the outer and in- sensors were used to measure the water pres- ner acrylic cylinders were 120 mm and 75 mm, sure near the dam toe and in the water reservoir respectively. The soil column height was 80 (Figure 5). Similar to the previous set-up, it was mm and the inner cylinder was embedded to possible to measure the head difference since a depth of 35 mm from the soil surface. Two it is very difficult to prevent seepage during the pressure sensors were used to measure the water head rise. The water was pumped into water pressure near the surface of the soil in the reservoir through a hose using an electri- the inner and outer cylinders. With this set-up, cal pump from a reservoir. In addition, an AE it was possible to measure the head differen- sensor was attached to the outer surface of the ce, since it is impossible to prevent seepage tank in order to assess the time of piping failure. Aydan 37

Table 1. Properties of samples used in experiments. Çizelge 1. Deneylerde kullanılan malzemelerin özellikleri. Dry unit Void ratio Porosity Mean grain size Friction angle Hydraulic

Material weight D50 conductivity (kN/m3) (%) (%) (mm) (o) (cm/s) Sand 14.6 78.09 43.85 0.69-1.27 32-35 1.3-1.5x10-1

Debris 14.6 56.44 36.07 1.15-2.30 35-39 1.76x10-1

Experiments and Results

Co-centric cylinder tests

Co-centric cylinder tests were performed on commercially available quartz sand soil (No.4). Figures 6 and 7 show various stages of an experiment and some of measured responses during experiments, respectively. The depth of the embedment of the inner cylinder into soil, the water head differences and the hydraulic gradients at the initiation and failure of piping are summarized in Table 2. As seen in Figure 6, the initial phase of the seepage was almost uniform. Figure 4. Co-centric cylindrical experimental set-up. When the piping phenomenon started to take Şekil 4. Eş merkezli silindirik deney düzeneği. place near the outer perimeter of the cylinder a large flow started to occur. This large water flow enlarged erosion and eventually resulted in a large plume of the mixture of sand and water. Figure 7 shows the water rise of the upper reservoir, head difference and AE responses of the three model tests. The increase in head difference becomes particularly non-linear at a critical level, which corresponds to the piping initiation. The water head difference decreases monotonically following the failure of the slope failure dam. Large gradient changes of the cu- mulative AE response occur at the initiation and at the failure of the piping phenomenon. Table 2 summarizes the geometrical parameters and hydraulic gradients at the initiation and failure of the piping phenomenon for the co-centric cylindrical experiments. The ratio of the hydraulic gradient at initiation to that at the failure of the piping phenomenon ranges between 78% and 94% for the model tests.

Slope failure dam piping failure experiments

In these experiments, two soil samples were Figure 5. (a) Cross section of the model, and (b) slope used. One sample was the same as that used failure dam experimental set-up. Şekil 5. (a) Modelin kesiti ve (b) heyelan barajı deney in the previous tests and it comprised quartz düzeneği. sand commercially available soil (No.4). The se- 38 Yerbilimleri

cond soil sample was from Muzaffarabad where dolomitic limestone slope failed during the earthquake and blocked the Neelum Valley for a short time, it being breached later on. Figure 8 shows various stages of a piping experiment on the Muzaffarabad debris dam model. Figu- res 9 and 10 show some of the measured responses during the experiments. Tables 3 and 4 summarize the experimental results on dam models consisting of sand No.4 and Muzaffara- bad debris material. As seen in Figure 8, the initial phase of the seepage is almost uniform. When the piping phenomenon starts to take place, a large water Figure 6. Views of piping failure at different times dur- flow starts to occur at mid height of the slope ing an experiment. failure dam. This large water flow enlarges ero- Şekil 6. Deney sırasında sızma yenilmesinin değişik zamanlardaki görüntüleri. sion and eventually results in the failure of the slope failure dam. Figures 9 and 10 show the water rise of the upper reservoir, head difference and AE responses on the model tests with the use of No.4 sand and Muzaffarabad debris. Particularly no- table is the fact that the increase in head difference tends to be non-linear at a critical level, which is indicated as the piping initiation. While the water head difference decreases monotonically for the model tests using No.4 sand, there is a sudden decrease in water head difference when the failure of the slope failure dam occurs. Tables 3 and 4 summarize the geometrical parameters and hydraulic gradients at the initiation and at the failure of the piping phenomenon. The ratio of the hydraulic gradient at initiation to that at failure ranges between 85% and 93% for the model tests using No.4 sand. On the other hand, the ratio of the hydraulic gradient at initiation to that at failure ranges between 54% and 79% for the model tests using the Muzaf- farabad debris. This difference may be attributable to a difference in the non-uniform distribution of the permeability characteristics of the model materials.

THEORETICAL BACKGROUND TO THE PIPING FAILURE PHENOMENON

Theoretical Fundamentals Figure 7. Responses measured during co-centric cylinder piping failure tests. Şekil 7. Eş-merkezli silindirik sızma yenilmesi deney- The piping failure phenomenon is as a result of lerinde ölçülen davranışlar. the dislocation of particles from the slope failu- Aydan 39

Table 2. A summary of conditions of co-centric cylindrical experiments and measured results. Çizelge 2. Eş merkezli silindrik model deney koşulları ve ölçülen sonuçlara ilişkin özet bilgi.

Embedment Water head Water head Hydraulic gradient at Test No. (l) difference at difference at failure (mm) initiation (mm) (mm) Initiation Failure

PT_S4_CYL_No1 35 88.9 94.7 2.54 2.71 PT_S4_CYL_No2 35 90.2 115.2 2.58 3.29 PT_S4_CYL_No3 30 73.0 90.7 2.43 3.02 PT_S4_CYL_No4 31 75.6 91.6 2.44 2.95

Table 3. A summary of conditions of slope failure dam experiments for No.4 sand and measured results. Çizelge 3. 4 no.lu kum heyelan barajı deney koşulları ve ölçülen sonuçlara ilişkin özet bilgi.

Base length Water head Water head Hydraulic gradient at Test No. (l) difference at difference at failure (mm) initiation (mm) (mm) Initiation Failure

PT_S4_DAM_No1 123 78.7 84.80 0.64 0.69 PT_S4_DAM_No2 123 80.8 88.2 0.66 0.72 PT_S4_DAM_No3 123 77.7 88.6 0.63 0.72

Table 4. A summary of experimental conditions for Muzaffarabad slope failure dam debris material and measured results. Çizelge 4. Muzaffarabad heyelan molozu için deneysel koşullar ve ölçülen sonuçlara ilişkin özet bilgi. Water head Base length Water head Hydraulic gradient at difference at Test No. (l) difference at failure (mm) initiation (mm) Initiation Failure (mm) PT_MD_DAM_No1 120 66.5 84.1 0.55 0.70 PT_MD_DAM_No2 120 58.6 81.5 0.49 0.68

PT_MD_DAM_No3 120 39.6 72.7 0.33 0.61

Figure 8. Various stages of the earth dam piping model test on Muzaffarabad slope debris material. Şekil 8. MuzaffarabadFigureFigureFigure moloz8. 8. 8. malzemesi üzerinde yapılan baraj sızma yenilme deneyi görüntüleri.

40 Yerbilimleri Figure 9

Figure 10.

FigureFigure 9 9. Responses measured during an experiment FigureFigure 10 10. Responses measured during an experi-

on a dam model using sand No.4. ment on a dam model using Muzaffarabad Şekil 9. 4 no.lu kum kullanılarak yapılan baraj modeli debris material. deneylerinde ölçülen davranışlar. Şekil 10. Muzaffarabad moloz malzemesi kullanıla- rak yapılan baraj modeli deneylerinde ölçü- Figure 10. len davranışlar.

re dam under the action of seepage forces. The (5) drag stress (seepage stress) on a per unit soil p pgh

mass under a seepage field gradient is given in where, g is gravitational acceleration. With the p = ρgh (5) the following form (i.e. Biot, 1941, 1962). use of Equation 5, Equation (4) becomes

Figure 10 where, g is gravitational acceleration. With the use of Equation 5, Equation (4) becomes ∂ η ξ= − ρ h (6a) = − (1) sf g ξsf vr ∂x k ∂h ξ = −ρg (6a) sf ∂x Where; and are permeability (areal), vis- If the fluid is water, this equation may be writ- k,η vr cosity and average relative velocity of fluid with ten in terms of unit weight of water as follows. respect to solid skeleton. The average relative If the fluid is water, this equation may be written in terms of unit weight of water as velocity of fluid is generally expressed through follows. ∂ ξ= − γ h (6b) D’Arcy’s law as follows: sf w ∂x ∂h ξ = −γ (6b) Equationsf w ∂6x is the relation which appears com- k (2) vr = − ⋅ p monly in many soil mechanics textbooks. η Equation 6 is the relation which appears commonly in many soil mechanics textbooks. Formulation of the Co-centric Cylindrical where p is fluid pressure. Inserting Equation (2) Piping Experiment into (1) yields the following relation. FormulationLet us consider of the two Co-centric co-centric Cylindrical cylinders Pipingwhich Experiment are used for piping failure tests (see Figure k vξr sf==− −∇⋅p (3) 4). Furthermore, let us assume that the water η Lethead us is consider increased two during co-centric experiments. cylinders whichThe for are- used for piping failure tests (see Figurece exerted 4). Furthermore,at the base of let the us inner assume cylinder that ca the- water head is increased during In one dimensional form, one may write the fol- experiments.uses the movement The force of exerted the soil at columnthe base inof the the ininner- cylinder causes the uplift of the lowing soilner columnand outer in the cylinders. inner and Under outer cylinders.this circumstan Under -this circumstance, one may write the followingce, one may relation: write the following relation: ∂ ξ = − p (4) sf ∂ hA xA = x w i sub o 0 (7) (7)

Let us assume that pressure is given in terms of where γ sub = γ sat − γ w . fluid density ( ) and fluid head (h) as follows: where γ= γ − γ = ρ sub sat w and x l

Since γ sat is equivalent toγ sat = (1− n)γ g + nγ w , γ sub may be given in the following

form

(G −1) γ = (1− n)(γ − γ ) or γ = g γ (8) sub g w sub 1+ e w

where, γ g is unit weight of solid grains. Porosity (n) and void ratio (e) are related to p = ρgh (5)

where, g is gravitational acceleration. With the use of Equation 5, Equation (4) becomes

each other in the following form ∂h ξ sf = −ρg (6a) ∂x each eother in the following form n = (9) 1+ e Thus, thee following identity holds from Equations 7 and 8 at the time of piping failure. If the fluid is water, this equation may be written n in terms of unit weight of water as (9) = e follows. 1+ ΔThus,h G the− following1 A identity holds from Equations 7 and 8 at the time of piping failure. = s o γ (10) x e A w Δ 1+ i ∂h h G A Δ s −1 o ξ sf = −γ w = γ (6b) (10) ∂x x 1 e A w FormulationΔ + ofi the Dam Piping Experiment

Formulation of the Dam Piping Experiment Equation 6 is the relation which appears commonlyNext, in many a special soil formmechanics of the textbooks. slope failure earth dam was considered, as illustrated in

Figure 5. The force equilibrium per unit width for this particular case may be written as: Next, a special form of the slope failure earth dam was considered, as illustrated in

Figure 5. The force equilibrium per unit width for this particular case may be written as: Formulation of the Co-centric Cylindrical Pipingγ ΔExperimenth2 γ Δhl w − sub = 0 (11) 2 2 γ Δh2 γ Δhl w − sub = 0 (11) Let us consider two co-centric cylinders which are 2 used for2 piping failure tests (see Figure 4). Furthermore, let us assume that thewhere water h and headl are water is increased head and base during length. With the use of Equations 8 and 11, one canwhere easily h and obtain l are the water following head and relation base length. for the With piping the failure.use of Equations 8 and 11, one experiments. The force exerted at the base of the inner cylinder causes the uplift of the can easily obtain the following relation for the piping failure. soil column in the inner and outer cylinders. Under this circumstance, one may write the Δ h G −1 s (12) following relation: h= G γ w lΔ 1+s −e 1 = γ w (12) l 1+ e hA xA = 0 w i sub o Equation 12 is well-known as the critical (7) hydraulic gradient of Terzaghi (1929, 1943). Equation 12 is well-known as the critical hydraulic gradient of Terzaghi (1929, 1943). As noted from the relations above, the size distribution and permeability of the dam As noted from the relations above, the size distribution and permeability of the dam where γ = γ − γ . material do not play any role in the resistance against piping failure. Another alternative sub sat w material do not play any role in the resistance against piping failure. Another alternative formulation may be based on the utilization of Stoke’s law. The drag force acting on a Aydan formulation may be based on the utilization of Stoke’s41 law. The drag force acting on a particle with an average diameter D can then be given in the following form: particle with an average diameter D can then be given in the following form: Since γ sat is equivalent toγ sat = (1− n)γ g + nγ w , γ sub may be given in the following

dF 3 D v (13) Since is equivalent to , dF== 3ππDηηvr (13) (13) form γ sat γ sat = (1− n)γ g + nγ w r γ may be given in the following form sub where η is fluid viscosity. The effective weight whereofwhere a spherical ηηisis fluidfluid particle viscosity.viscosity. can TheThe be effective writteneffective as weight weight follows: of of a sphericala spherical particle particle can canbe written be written as as (G −1) ()G −1g follows:follows: γ sub = (1− n)(γ g − γ w ) or or γ sub = s γ w (8) γsub = γw (8) 1+ 1e + e πDD33 dWdW'='=(1(1−−nn)()(γγ − γ ) (14) (14) (14) ss w 6 where, is unit weight of solid grains. Porosity (n) and void ratio (6e) are related to where, γ gis unit weight of solid grains. Poro- γ g sity (n) and void ratio (e) are related to each ot- Equating Equations 13 and 14 together with the her in the following form use of Equations 2 and 5, one can easily obtain Equating Equations Equations 13 13 and and 14 14together together with with the usethe of use Equations of Equations 2 and 5,2 andone can5, one easily can easily each other in the following form theEquating following Equations relation: 13 and 14 together with the use of Equations 2 and 5, one can easily e obtain thethe following following relation: relation: n = (9) obtain the following relation: + h GG 11 DD2 2 1 ee Δ h Gs s−−1 D 2 n Δ == s − γγw w (15) (15) (15) = l = 1 1 ee γ w 18 18k k (9) (15) 1 e l 1++ e 18k Thus, +the following identity holds from Equati- + onsThus, 7 andthe following8 at the time identity of piping holds failure. from Equations 7 and 8 at the time of piping failure. TheThe permeability permeability coefficient coefficient k may k maybe related be related to to mean grain size D (i.e. TheThe permeability permeability coefficient coefficient k k may may be be related related to to mean mean grain grain size size D D (i.e. (i.e. Kozeny-Karmanmean grain size relation, D (i.e. Kozeny-Karman Aydan et al., 1997), relation, as follows: G A Kozeny-Karman relation, Aydan et al., 1997), as follows: ∆Δhh Gss −−11 Aoo Kozeny-Karman relation, Aydan et al., 1997), as follows: = γ (10) Aydan et al., 1997), as follows: (10) = γww ∆Δxx 11++ee AAi i 1 k = D 2 (16) 11 22 kk ==A DD (16) (16) (16) Formulation of the Dam Piping Experiment AA Formulation of the Dam Piping Experiment Next, a special form of the slope failure earth Inserting Equation 16 into Equation 15 yields the following expression: Inserting Equation 16 into Equation 15 yields dam was considered, as illustrated in Figure 5. InsertingInserting Equation 1616 intointo Equation Equation 15 15 yields yields the the following following expression: expression: Next, a special form of the slope failure earth dam the was following considered, expression: as illustrated in The force equilibrium per unit width for this par- h G 1 A Figure 5. The force equilibrium per unit width for thisΔ particulars − case may be written as: ticular case may be written as: = γ w (17) Δlhh G1Gs e−1 18A Δ +s − (17) == γ w (17) (17) 2 ll 11+ e 18 γ Δh γ Δhl + w − sub = 0 (11) (11) 2 2 There are many suggestions for the value of A. The appropriate one should be used takinThereThere the are are ground many many suggestions conditionssuggestions into for for the cons the valueideration. value of of A .A However,. The appropriate the value one of A should generally be used There are many suggestions for the value of A. The appropriate one should be used where h and l are water head and base length. rangesThetakin appropriate between the ground 12 one and conditions should 20. be into used cons takingideration. the However, the value of A generally Withwhere the h useand ofl areEquations water head 8 and and 11, base one canlength. ea- Withtakin groundthe use the conditionsof groundEquations into conditions 8 consideration. and 11, into one cons However,ideration. However, the value of A generally ranges between 12 and 20. silycan obtaineasily obtainthe following the following relation relation for the forpiping the pipingrangesthe failure. value between of A generally 12 and 20.ranges between 12 and COMPARISONS AND DISCUSSIONS failure. 20. COMPARISONS AND DISCUSSIONS h G Δ s −1 COMPARISONSFigureCOMPARISONS 11 compares AND AND the DISCUSSIONS computational DISCUSSIONS results with the experimental results for the ∆ =G −1 γ w (12) lh 1s e (12) = + γ w co-centric cylindrical set-up. Theoretical predictions were based on Equation 10 with l 1+ e Figure 11 11 compares compares the the computational computational results results with the experimental results for the Figure 11 compares the computational results with the experimental results for the thewithco-centric use the ground experimental cylindrical material set-up.resultswith the for Theoretical properties the co-centric gi predictionsven in Table were 1. Thebased experimental on Equation values 10 with Equation 12 is well-known as the critical hydraulicco-centricfor cylindricalgradient the initiation of set-up. cylindrical Terzaghi and Theoretical failure (1929, set-up. of 1943). predictions Theoretical the piping phenomenonwere predictions are were higher based than on those Equation of the 10 with Equation 12 is well-known as the critical hydra- the use ground material with the properties given in Table 1. The experimental values ulicAs noted gradient from of theTerzaghi relations (1929, above, 1943). the As size no - distributionthetheoreticalbased use and onground estimations.Equation permeability material 10 Furthermore, with ofwith thethe the damuse properties there ground is a ma slightgi-ven scattering. in Table 1.The Thedifference experimental may be values terialfor the with initiation the properties and failure given of in theTable piping 1. The phenomenon are higher than those of the tedmaterial from thedo notrelations play any above, role thein the size resist distributiance -againstattributed piping failure.to the frictional Another resistancealternative between soil and cylinder walls as well as to the on and permeability of the dam material do not forexperimentaltheoretical the initiation estimations. values and for failure Furthermore,the initiation of the and there piping failure is a phenomenon slight scattering. are The higher difference than those may ofbe the formulation may be based on the utilization of Stoke’sdifference law. The between drag theforce actual acting and onaveraged a velocities of fluid. play any role in the resistance against piping theoreticalofattributed the piping toestimations. thephenomenon frictional Furthermore, resistanceare higher between thanthere tho is soil-a slight and cylinderscattering. walls The as difference well as to maythe be failure.particle Another with an alternativeaverage diameter formulation D can may then be be givenattributedse in of the the following theoreticalto the frictional form: estimations. resistance Furthermore, between soil and cylinder walls as well as to the theredifference is a slightbetween scattering. the actual The and difference averaged mayvelocities of fluid. based on the utilization of Stoke’s law. The drag Figure 12 compares the computational results with experimental results for the force acting on a particle with an average dia- differencebe attributed between to the thefrictional actual resistance and averaged betwe velocities- of fluid. dF 3 D v co-centric cylindrical set-up. Equations (13) 12 and 17 were used for theoretical estimations meter= Dπ canη thenr be given in the following form: enFigure soil and 12 cylinder compares walls the as computational well as to the results dif- with experimental results for the with the use of ground materials with the properties given in Table 1. The experimental

Figurevaluesco-centric for 12 the cylindrical compares initiation set-up. and the failure computationalEquations of the 12piping and results 17phenomenon were with used experimentalare for lower theoretical than resultsthose estimations of for the where η is fluid viscosity. The effective weight of a spherical particle can be written as co-centricthewith theoretical the use cylindrical of estimations. ground set-up. materials The Equationsspecific with theweight 12properties andof material 17 givenwere varied usedin Table between for 1.theoretical The 2.3 experimental and estimations2.6, follows: withasvalues the the specific for use the ofweight initiation ground of the materialsand Muzaffarabad failure with of ththe dee brispipingproperties is about phenomenon given2.3. The in estimationsTableare lower 1. The thanbased experimental those on of D 3 dW n π valuesthe theoretical for the initiationestimations. and The failure specific of weightthe piping of material phenomenon varied arebetween lower 2.3 than and those 2.6, of '= (1− )(γ s − γ w ) (14) 6 theas thetheoretical specific weightestimations. of the TheMuzaffarabad specific weight debris isof about material 2.3. variedThe estimations between based2.3 and on 2.6,

as the specific weight of the Muzaffarabad debris is about 2.3. The estimations based on

42 YerbilimleriFigure 11.

Figure 4: Relation between critical hydraulic gradient and void ratio

Figure 11. Figure 11. Comparison of co-centric cylindrical mod- FigureFigure 12. 12. Comparison of slope failure dam model el experimental results with theoretical esti- experimental results with theoretical esti-

mations. mations. Şekil 11. Eş merkezli silindirik model deneysel so- Şekil 12. Heyelan barajları model deneysel sonuçla- nuçlarının kuramsal sonuçlarla karşılaştırıl- rının kuramsal sonuçlarla karşılaştırılması. ması.

ference between the actual and averaged velo- well as in seepage properties. This problem has

cities of fluid. been well known for a long time. Nevertheless,

it is still difficult to assess the overall stability of Figure 12 compares the computational results slope failure dams due to their complex geo- with experimental results for the co-centric metry and the distribution of their particles. Ex- cylindrical set-up. Equations 12 and 17 were periments on commercial sand as well as on used for theoretical estimations with the use natural slope failure debris indicated that the- Figureof ground 4: Relation materialsbetween critical with hydraulic the gradient properties and void ratio given oretical relations may be applied to predict pi- in Table 1. The experimental values for the initi- ping failure conditions. Nevertheless, there is a ation and failure of the piping phenomenon are difference between the hydraulic gradients for lower than those of the theoretical estimations. Figure 12. initiation and total failure due to piping. The ini- The specific weight of material varied between tiation of piping failure starts at lower hydraulic 2.3 and 2.6, as the specific weight of the Mu- gradients. This may be attributable to a diffe- zaffarabad debris is about 2.3. The estimations rence between the actual fluid velocity and the based on Equation 12 are considerably higher averaged velocity used in D’Arcy’s law. than the experimental values. However, Equa- tion 17 yields better estimations for experimen- When, upon complete inundation, slope failure tal results. Furthermore, there is a slight scat- dams are stable, the breach of such dams may tering. The scattering may be attributed to the occur by overtopping. This is a more complex slight differences in ground material in each ex- phenomenon on which some experimental and periment. theoretical studies have been undertaken. Ne- vertheless, further studies of this problem are CONCLUSIONS necessary. The well-publicized breach of the Tangjiashan slope failure dam, which was ca- Piping failure of earth or rock fill dams, as well used by the 2008 Wenchuan earthquake, sho- as slope failure dams, is quite important for the wed the importance of this problem. safety of settlements downstream as well as for the protection of property. Although dams are REFERENCES constructed with great attention to this problem, slope failure dams are a result of natural Aydan, Ö., Üçpırtı, H., and Ulusay, R., 1997. disasters and the resulting mass is very comp- Theoretical formulation of Darcy’s law lex in geometrical distribution of particles as for fluid flow through porous and/or jo- Aydan 43

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