Rupro, breach model used by Cemagref during Impact project

Transcription

1 PAQUIER 1 Rupro, breach model ued by Cemagref during Impact project A PAQUIER Cemagref, France andre.paquier@cemagref.fr SUMMARY For embankment dam, piping and overtopping failure are the mot frequent type of failure. A model that trongly implifie the complex phyical procee i decribed. The baic hypothei i that clear water i flowing through a breach of circular or rectangular hape and erode the wall keeping thi hape. The rate of eroion i calculated from the ediment dicharge etimated by the Meyer Peter Muller formula. The model proved to provide peak dicharge imilar to the one obtained by a tatitical analyi of the real dam failure. Such method thu provide a dicharge hydrograph that can be ued for the computation of the dam break wave through the valley downtream. Improvement are planned during Impact project, particularly to take into account heterogeneou material. 1 AIMS OF THE MODEL To elaborate emergency plan, the propagation of the dam break wave in the valley downtream the dam hould be preciely computed. The firt tep of uch a calculation i the aement of the dicharge hydrograph at the dam, which involve the modelling of the failure of the dam itelf. For embankment dam, everal type of breaching may happen but piping and overtopping are the mot common one and gather about two third of the total number of recorded failure. Such a failure i a progreive proce in which rate of eroion i the main parameter. Rate of eroion i controlled by a lot of parameter concerning the head uptream from the dam but above all the tructure of the embankment. To get the highet poible peak dicharge, implified aumption are et, which enable a rapid calculation and thu the tudy of the variation of the key parameter. Such a calculation method could alo be defined a a hydraulic tructure with evolving parameter (according to eroion proce) that may be included in a 1-D or 2-D hydrodynamic model for calculation of the whole dam-break procee. 2 DESCRIPTION OF THE MODEL 2.1 Principle of the model Rupro i baed on the main hypothei that the hydraulic characteritic of water are not modified by the high concentration of ediment, even during the beginning of the eroion proce. The embankment i uppoed to be of trapezoidal hape (Fig. 1) and of homogeneou material. Water flow through a pipe or a channel that i modelled by one mean cro ection and zero lope (Robin 1990).

2 PAQUIER 2 Figure 1. Schematiation of the longitudinal profile of the embankment in Rupro The evolution of the breach conit of two tep. During a firt tep, water tart flowing through a circular pipe (piping) or a rectangular breach (overtopping) and erode the circumference or the bottom of the breach o that it diameter or it depth i increaing with time (Fig. 2, 3). In a econd tep, after the diameter of the pipe ha reached 2/3 of the dam height and the vault of the pipe had conequently failed or after the bottom of the dam i reached, water flow in a rectangular channel the width of which i increaing due to eroion of it wall Figure 2. Evolution of the hape of the breach in cae of piping Figure 3. Evolution of the hape of the breach in cae of overtopping.

3 PAQUIER Equation olved in the model Flow characteritic within the pipe or the channel are computed from Bernoulli equation with a head lo at the entrance and a linear head lo. Thi linear head lo i computed from a Manning-Strickler coefficient K equal to 21, in which d i the median diameter of the d 1/ 6 material. The maximum value for the coefficient η of the uptream head lo i 0.5. Water level y in the pipe or channel i computed from a critical depth at the downtream end; eventually if water level downtream of the dam i higher than critical depth, the water level i raied at that level. Finally the equation to be olved i: 2 2 (1) = + S + S 2gl z y 1 η + S 2 2 4/3 2 2l S e K R S in which l i the length of the pipe or the channel, z the uptream water level, S the downtream wetted ection, S e the uptream wetted ection, S the average of the two previou wetted ection, g the gravity acceleration, R the mean hydraulic radiu. The uptream water level i calculated from the mean water level in the reervoir. Thi reervoir i decribed by it hypometry (a erie of water urface level and the correponding urface of the reervoir). At any time tep, a balance between the dicharge through the breach and the incoming dicharge due to the flood i computed. Starting from an initial water level in the reervoir, it i then poible to compute at any time thi water level. If the model i included a a hydraulic tructure in a 1-D model, thi 1-D model will directly provide the uptream and downtream water level. For piping, the initial condition conit in a mall pipe diameter o that the dicharge i very low: it may be the median diameter of the material or a little more till 10 cm. For overtopping, a minimal head i neceary to tart eroion proce: thi may be obtained by a high water level or by lowering the initial bottom of the breach. The volume of material V eroded at each time tep t i computed from the ediment dicharge Q by V = Q * t. The ediment dicharge i computed from the hydraulic variable by the Meyer Peter Müller formula (2). (2) 8 g Q 047 ρ ( ρjr 0, d( ρ ρ ) = ( ρ ρ) in which g i the gravity acceleration, ρ i the denity of water, ρ the denity of ediment, J the energy lope, R the hydraulic radiu. For piping, the volume eroded i ditributed uniformly over the cro-ection, o that the pipe remain circular wherea for rectangular breach, deepening i the only proce till the bottom of the dam i reached and then, widening occur. In thi tep, the poroity of the material i taken into account. Thu, the only parameter of the ediment that are taken into account are the denity, the diameter and the poroity. The two equation providing evolution of water level and evolution of breach are olved by a four-tep Runge-Kutta method. 3 2

4 PAQUIER 4 The end of the computation occur when the dicharge at the dam ite i zero that generally mean that the reervoir i empty. It i poible that thi end of computation occur during firt tep if the reervoir i emptying rapidly. Main reult of the computation i the dicharge hydrograph that will be propagated in the valley downtream the dam. The water level downtream the dam can alo be ued at the uptream end of the propagation model if the flow i upercritical. 2.3 Validity of the model Moreover the heterogeneity of the dam material that i often one of the caue of the pipe eroion i not taken into account. Thi point could be integrated in ome way by lowering Strickler coefficient K. Thi increae of rugoity ha, in the model, the expected reult to accelerate eroion and thu to increae the peak dicharge. However, it i clear that it i difficult to elect the uitable value for uch parameter a the diameter of the material, the Strickler coefficient. Other reaon may caue error: the hape of the breach that may differ from a circle or a rectangle trongly, the role of the longitudinal profile of the eroion channel... Neverthele, the model proved to provide peak dicharge lightly lower than the one obtained by a tatitical analyi of the real dam failure. A comparion ha been performed with the peak dicharge Q p obtained from the relation (3) etablihed by (Molinaro and Maione 1991): (3) Q p = 0.116(V/H 3 ) g 0.5 H 2.5 in which V i the reervoir volume, H the dam height and g the gravity acceleration. On the 7 dam concerned (height from 13 to 60 m, volume from 6 to 150 million of m3), the ratio between peak dicharge goe from 40 % to 100 % with an average of 64 %. Thi low value may be linked with the lope of the embankment that are generally teeper in the actually breached dam and eventually with an extra volume coming from a flood in the real cae. 3 CONCLUSIONS The model decribed (oftware Rupro) provide a dicharge hydrograph due to failure of an embankment dam by piping or overtopping. Thi hydrograph can be ued a the uptream boundary condition for a dam break wave propagation model in the downtream valley. Thi hydrograph ha a peak dicharge relatively cloe to the peak dicharge of known failure for imilar global characteritic (dam height, volume of reervoir, embankment lope). During CADAM project (Concerted Action on Dam Break Wave), compared to meaurement on phyical model, it alo proved to provide realitic reult (Broich 1999). The evolution of the peak dicharge when modifying variable uch a material ize, embankment lope, etc i in the right way. Therefore, although the model doe not decribe preciely the eroion proce, it can be ued a a bai for etablihing emergency plan. A the model provide a dicharge hydrograph, it can be integrated in a 1D or 2D propagation model a a hydraulic tructure of which the parameter change with time (Paquier 1995).

5 PAQUIER 5 REFERENCES K. BROICH (1999). Concluion from the tet cae modelling. 3rd CADAM meeting, Munich, Germany, CD Rom, Paper 11. P. MOLINARO, D. MAIONE (1991). The experience developed by ENEL in dam-break wave computation and flood rik analyi. Colloque International pour la Simulation de Onde de Submerion, Montréal, Canada. A. PAQUIER (1995). Modéliation et imulation de la propagation de l'onde de rupture de barrage (Modelling and imulating the propagation of dam-break wave). PhD thei, Univerité Jean Monnet de Saint Etienne, France. O. ROBIN (1990). Méthode implifiée de calcul d'onde de ubmerion réultant de la rupture d'un barrage.(simplified method for the computation of ubmerion wave due to dam-break). DEA thei, Univerité Claude Bernard Lyon1, France.