NATURAL AND HUMAN INDUCED HAZARDS Vol. II - Debris Flows and Pyroclastic Flows - Takahashi T.

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1 DEBRIS FLOWS AND PYROCLASTIC FLOWS Takahashi T. Kyoto University, Japan Keywords: debris flow, stony debris flow, immature debris flow, turbulent mudflow, hybrid debris flow, visous debris flow, granular flow, pyrolasti flow, Merapi type, main body, hot ash loud, mehanism, modeling, veloity, solids onentration, lassifiation, numerial simulation Contents 1. Definition and Fundamental Mehanism of Debris Flows. Charateristis of Stony Debris Flow and Modeling as a Dilatant Fluid 3. Charateristis of Turbulent Mudflow 4. Unified Modeling of the Inertial Debris Flows 5. Charateristis of Visous Debris Flow and Modeling as a Newtonian Fluid Flow 6. Definition of Pyrolasti Flow 7. Charateristis of Pyrolasti Flows Observed at Mt. Fugen, Unzen Volano, Japan 8. A Mehanial Model for a Merapi-Type Pyrolasti Flow 9. Two-Dimensional Numerial Simulation of the Merapi-Type Pyrolasti Flow at Unzen Volano Glossary Bibliography Biographial Sketh Summary Debris flows are lassified aording to the dominant stress: partile ontat stress, material mixing stress, and visous stress. Thereby, the respetive riteria for the ourrene of the stony debris flow, the turbulent mudflow, and the visous debris flow are demarated by Reynolds number, Bagnold number, and the relative depth of flow. Charateristis of eah debris flow, suh as veloity, solids onentration, and the mehanism to disperse the oarse partiles, are disussed. A unified theory for the inertial debris flow is given, whih explains quantitative harateristis of stony, immature, hybrid, and muddy debris flows. As for visous debris flow, a Newtonian fluid model is introdued, whih explains the veloity in the atual debris flow at Jiangjia Gully, China. After a brief review of the history of researh on pyrolasti flows, the lassifiation of pyrolasti flow is given in view of the mode of ourrene as well as the volume of the total ejeta. The high mobility of pyrolasti flow is attributed to the emission of gas from the pyrolasti material itself. Charateristis of the pyrolasti flow at Mt. Fugen, Unzen Volano, Japan, are desribed. A mehanial model that is able to explain the quantitative 1

2 harateristis of the granular flow stage that appears soon after ollapse of the lava dome and the fluidized flow stage that follows the granular flow stage in whih flow is separated into the main body and the hot ash loud is given. The basi flow equations are inorporated into the system of equations that is neessary in the numerial simulation of pyrolasti flow. The numerial simulation reprodued the pyrolasti flow at Unzen Volano. 1. Definition and Fundamental Mehanism of Debris Flows Debris flow an be defined as a highly onentrated flow of the mixture of water and sediment that surges down steep slopes or ravines in response to gravitational attration. Due to its high mobility and large density, it often brings severe disaster to the affeted ommunities. The high mobility is aused by the motion of the solid phase as partiles keep the void spae between piees large to minimize the resistane to flow. This is in ontrast to landslides, within whih the solid phase moves in a luster on a slip surfae resisting with the large fritional resistane. The apparent density of debris flow an be tons m 3 or more due to the large partile dispersing mehanism within flow. This is in ontrast to sediment-laden water floods in whih the oarse partiles are moved by the fluid dynami fores, and the partile onentration annot be more than a few perent. Thus, debris flow is a phenomenon intermediate between landslide and sediment-laden water flow in terms of solids onentration and fluidity. Debris flows appear in different behavior depending on the sediment onentration, the partile size omposition, thikness of flow, the gradient of slope down whih they surge, et. Possibly beause of suh a diversity of behavior, various nomenlatures have been used, for example, debris torrents, debris floods, mudflows, mud floods, and hyperonentrated flows. Volanologists sometimes all the debris flows originating in volani ativity "lahar." Lahar is an Indonesian word. Many large debris flows our at Indonesian volanoes due to erosion of the pyrolasti deposit. Sometimes suh a lahar is hot. All these phenomena desribed by the different names may be regarded as debris flows, and the lassifiation of debris flows in terms of mehanis of flow is disussed below. The proesses of ourrene and deposition are disussed in Debris Flow Foreast and Disaster Mitigation Measures for Debris Flows. The differene in behavior of debris flows must be the refletion of differene in the dominant stresses among others existing within the flow. If the total shearing stress, τ, and the pressure, p, in a very highly sediment-laden plain shear flow are given by the linear sum of the onstituent shearing stresses and pressures, they would be expressed as following: τ = τ + τ + τ + τ + τ + τ (1) y μ k s t

3 p = p + ps + ph () where τ y is the yield strength of the interstitial fluid (slurry), τ μ the visous stress due to deformation of the mixture of slurry and the oarse partiles, τ the shear stress due to inelasti partile ollision, τ k the kineti stress due to plunging of partiles from a layer into other layers, τ s the stati Mohr-Coulomb shear stress due to enduring ontat motion between the partiles, τ t the turbulent mixing stress, p the pressure due to partile ollision, p s the stati pressure due to enduring fritional ontat between the partiles, and p h the isotropi pressure in the interstitial fluid. If ( τ y + τ μ ), ( τ + τ s) and ( τ k + τ t) are written as τ υ, τ g and τ m, respetively, τ υ is onsidered to represent the shear stress due to visoplastiity of the material, τ g is that due to ontat of partiles and τ m is that due to mixing of the material. As an extreme ase, if the total shear is shared only by τ υ, flow is the visous type debris flow. If the total shear is shared only by τ g, flow is either the stony inertial type debris flow or the quasistati shearing motion. The latter ours when the mean oarse partile onentration in the material is more than the threshold value of about 0.5, whereby τ g is almost shared only by τ s. If the total shear is shared only by τ m, that is, the turbulent mudflow type debris flow, and the marosale turbulene inorporated with water and sediment prevails almost in the entire depth of flow. The atual debris flows appear within the wide spetrum of these extreme ases. Many previous experimental and theoretial explorations of the onstitutive relations of granular flows onfirm the following forms: τ ( ) = σdp f1 C γ (3) τ ( ) k = σdp f C γ (4) τ f ( C) μ = μ 3 γ (5) where σ is the partile density, d p is the oarse partile diameter, γ is the shear rate, μ is the visosity of the interstitial fluid that inorporates with fine partiles, and f 1 (C) f (C), and f 3 (C) are the funtions of the oarse partile onentration C, respetively. The shear stress due to the marosale turbulene is given by τ = ρ γ (6) t l a where ρ a is the apparent density of the material, and l is the mixing length. The ratio τ / τ approahes 1 when the ratios τ m / τ and τ μ / τ beome small. In the ase of maroturbulent flow the kineti stress τ k is onsidered to be inluded in τ m, and if C is larger than about 0.3, τ k is far smaller than τ, so that from the Eqs. (3) and (6) 3

4 τm τt ρa l 1 = (7) τ τ σ d f ( C) p 1 The largest value of the ratio ( l/ d p ) will be represented by the relative depth of flow, ( H / d p ), in whih H is the depth of flow, and ( ρa / σ )/ f1( C) beomes small with inreasing C. Therefore, ( τ m / τ ) beomes small when the relative depth is small or the oarse partile onentration is large. If τ y is negleted, as is usually justified in atual debris flow, τ τ is given as υ / 1/3 τ υ μ μ f3( C) 1 f3 ( C) C* = = dp f1( C) Ba f1( C) C τ τ τ σ γ where B a is alled Bagnold number, and C * is the oarse partile onentration when paked. The ratio ( τυ / τ ) beomes small when Bagnold number beomes large. Thus, the inertial stony type debris flow appears when the relative depth is small, the oarse partile onentration is large, and the Bagnold number is large. This ondition is satisfied when the omprising partiles are large, the ontent of fine partiles is small, and the partile onentration is large. The oarse partile onentration must, however, be smaller than the threshold value of about 0.5. The ratio ( τ / τ ) is given as t μ τ ρ l γ ρ UH 1 = = (9) τ μ f ( C) μ f ( C) f ( C) t a a ~ Re μ where R e is the Reynolds number. The funtion f 3 ( C ) inreases with inreasing onentration. Therefore, the turbulent mudflow type debris flow will appear when Reynolds number and the relative depth are large, but the oarse partile onentration must not be too large. This ondition is satisfied when the omprising partiles are relatively small and the solids onentration is not so large. 1 1/ The visous type debris flow will our when both Reynolds and Bagnold numbers are small and the oarse partile onentration is large. This ondition is satisfied when the onentration of the fine ohesive partiles in the interstitial fluid is large, the oarse partile onentration is also large, and the diameter of the oarse partiles is not very large. (8) Summarizing the mentioned disussions, the domains of the existene of the respetive kinds of debris flows whose oarse partile onentrations are between about 0.5 and 0.5 are given within the ternary diagram as shown in Figure 1. Hybrid debris flow in the figure means the intermediate type of the typial types of debris flows. 4

5 Figure 1. Existene domains of various types of debris flow. Charateristis of Stony Debris Flow and Modeling As a Dilatant Fluid Figure shows a stony debris flow passing through a hannel onsolidating struture in Kamikamihori Gully, Japan. Generally, stony debris flow surges down the gully setting up a bore-like front, whih swells with gathering big boulders. The size of partiles in the front is the largest and partile size dereases toward the rear; water ontent in the front is low and the rear part ontains more water. The partile size in the whole debris flow material distributes from a few meters to the lay size, but the ontent of fine partiles smaller than 0.1 mm is normally less than a few perent. The big stones on the surfae that often seem to float, proeed faster than the translation veloity of the forefront. Those stones tumble down to the gully bed, arriving at the tip of the snout, the smaller partiles are then aught under the snout. Thus, the biggest stones aumulate at the front. Debris flows build a fan at the mouth of the gully. This is steeper than the usual alluvial fan and onsists of poorly sorted mixture of partiles. An individual debris flow forms a lobe deposit on the fan. The lobe that is omposed of numerous boulders has a semiylindrial shape, just as if flow is suddenly frozen, and this type lobe deposits on the upper part of the fan where the slope angle is more than three degrees. In this kind of deposit, the there is often inverse grading (i.e., from top to bottom, the partile size dereases). The deposit that is rih in sand size partiles forms flatter lobe and it reahes the lower part of the fan. Sometimes, a debris flow overflows from the inised hannel on a fan and makes the natural levees with big boulders along the hannel. 5

6 Figure. A stony debris flow passing through a gully onsolidating struture at Kamikamihori, Kamikohi, Japan Figure by H. Suwa For the first approximation of the motion of stony inertial debris flow, let us assume that τ balanes with the external driving fore due to gravity, and use the Bagnold s onstitutive relation in Eq. (3). Then, we obtain the following equation: 1/3 C* du H ( sin ) p 1 sin [( ) z a ασ d = g C C dz θ σ ρ + ρ ]dz (10) where u is the veloity at the height z measured from the bottom of flow, g the aeleration due to gravity, θ the hannel gradient, ρ the density of the interstitial fluid (water), and ( a sin α ) is a onstant. A oneptual fluid within whih the shearing stress is proportional to the square of the shear rate is a kind of dilatant fluid. Therefore, Eq. (10) means that debris flow is modeled as a dilatant fluid flow. If a homogeneous distribution of solids throughout the entire depth is assumed, Eq. (10) is easily integrated to give the vertial veloity distribution and finally the formula of resistane to flow as 1/ 1/3 U 1 ρ C* = C (1 C) 1 H u* 5dp asinα + σ C (11) 1/ where U is the ross-setional mean veloity, and u* = ( ghsin θ ). The previous experimental data show that asinα is approximately 0.0, and Eq. (11) well predits the 6

7 mean veloity of the stony debris flow if H / dp 30. Substitution of the larger H / d p value than 30 into Eq. (11) gives unreasonably fast veloity, beause in suh a large relative depth the debris flow is no more the stony type but the turbulent mudflow type. Another balane of fore equation in terms of pressure that is transmitted diretly from partile to partile must also be satisfied as 1/3 * ( os ασ C du H ) 1 = os θ ( σ ρ ) p z a d g C C dz dz (1) Integration of Eq. (1) also results in a resistane law formula. This result and Eq. (11) must be the same one, and this ondition requires the following relationship: ρ tanθ C = ( σ ρ)(tanα tan θ) The previous experiments on the stony debris flow show that the equilibrium ondition, in whih neither erosion nor deposition on an erodible bed ours, is satisfied if C is equal to C, tan C = ρ θ ( σ ρ)(tanφ tan θ) where tanφ is the internal frition oeffiient of the stable solids layer, whih must be approximately equal to tanα in a highly onentrated debris flow. This would be the reason why Eq. (11) is valid. Eq. (14) alulates small onentration when the hannel inlination is small. However, to disperse the partiles throughout the entire flow layer by the ation of interpartile ollisions, it needs omparatively high onentrations. Atually, under a onentration less than the limit value of about 0.5, the partiles are no longer dispersed throughout the entire depth, but are onentrated in the lower part of the flow. Above this partile mixture layer a water layer appears. This kind of flow is named "immature debris flow." In immature debris flow, the partile onentration in the mixture layer is held almost onstant of about 0.5, but the thikness of the layer inreases with inrease in hannel inlination. Thus, immature debris flow an appear in the hannel slope range from about 13 to about 3. (13) (14) Aording to the authors experiments the equilibrium transport onentration, Cs, for immature debris flow is given by 7

8 C s = 6.7C (15) The transport onentration is defined by qs / q, where q s is the sediment disharge per unit width, and q is the disharge of water plus sediment per unit width. It must be noted that Eq. (15) is valid in the range about 0.0 < Cs < C orresponding to the above mentioned hannel slope range. The empirial formula of the resistane to flow obtained by the author s experiments is U H = 0.4 (16) u d * p Although Eqs. (14) and (15) suggest that the equilibrium sediment onentration in the mature and immature debris flows are determined uniquely orresponding to the hannel inlination, the atual existene fields of the mature and the immature debris flows overlap eah other. The proess of deposition of a mature debris flow is an inertial phenomenon, and depending on the longitudinal profile of the ravine, the boulder rih front of the mature debris flow sometimes arrives to a mildly inlined area whose slope angle well falls in the domain of immature debris flow. In suh a ase, the suessive flow that overpasses the deposit made by stopping of the debris flow front beomes immature debris flow. 3. Charateristis of Turbulent Mudflow At the ative volani area the frequent ash-falls and/or pyrolasti flows over the mountain slope, and this over hinders the infiltration of rain into the ground. Thus, even a weak rainfall produes the surfae water flow ontaining highly onentrated pyrolasti partiles whose size distributes from about that of silt to a few millimeters. Suh muddy flow onentrates on the gully system and erodes the hannel to develop to a debris flow. This type debris flow is usually very muh turbulent, and although it ontains many big boulders they do not gather around the front ontrary to a stony debris flow, the boulders are transported by the fluid dynami fore rather than due to partile olliding effet. The typial turbulent mudflows ourred at Mt. Unzen, Kyushu, Japan, originating from the deposit of a large number of pyrolasti flows. More than 114 debris flows ourred in the Mizunashi River during the ativity of the volano from 1991 to 1995, resulting in the deposition of more than m 3 of debris and destroying about 1000 buildings on the fan area. Many debris flows passed through the reah steeper than.9 and deposited in the reah whose slope is between.0 and ~1.5. 8

9 Bibliography Cheng C., ed. (1997). Debris-Flow Hazards Mitigation: Mehanis, Predition, and Assessment. 817 pp. Amerian Soiety of Civil Engineers. [This onferene proeedings ontains a variety of findings onerned with debris flows in the 1990s.] Costa J.E. and Wiezorek G.F., eds. (1987). Debris Flows/Avalanhes: Proess, Reognition, and Mitigation. 39 pp. The Geologial Soiety of Ameria. [This gives wide reviews of findings onerning debris flows in the 1980s.] Coussot P. (1997). Mudflow Rheology and Dynamis. 55 pp. Rotterdam: Balkema. [This artile gives a different viewpoint on visous mudflow.] Gidaspow D. (1994). Multiphase Flow and Fluidization. 467 pp. London: Aademi Press. [This book introdues the onstitutive equations for granular flow and mehanis of fluidization.] 33

10 Nakada S., Eihelberger J.C., and Shimizu H., eds. (1999). Unzen eruption: magma asent and dome growth. Journal of Volanology and Geothermal Researh 89, [This speial issue gives the major findings on the Unzen eruption.] Takahashi T. (1991). Debris Flow. 165 pp. Rotterdam: Balkema. [This is the first omprehensive book desribing the mehanism of the stony type debris flow.] Takahashi T. and Tsujimoto H. (000). A mehanial model for Merapi type pyrolasti flow. Journal of Volanology and Geothermal Researh, in press. [This gives a little more detailed and strit disussions than other artiles.] Biographial Sketh Tamotsu Takahashi Date and Plae of Birth: Otober 0, 1939, Kyoto Japan Nationality: Japanese Permanent Address: 6-6, Kitaoji 3, Otsu, Shiga , Japan Aademi Degrees: 1963 B. Eng. (Civil Engineering, Kyoto University) 1965 Ms. Eng. (Civil Engineering, Kyoto University) 197 Dr. Eng. Kyoto University Professional Appointments: Instrutor, Disaster Prevention Researh Institute, Kyoto University Leturer, Department of Civil Engineering, Kyoto University Assoiate Professor, Disaster Prevention Res. Inst., Kyoto University 198-present Professor, Disaster Prevention Res. Inst., Kyoto University Diretor of Hodaka Sedimentation Observatory, Dis. Prev. Res. Inst. Diretor, Disaster Prevention Researh Institute, Kyoto University Member of the University Counil of Kyoto University 34