The Effect of Faults on the Behaviour of the Earth Dam – Case Study of the Ourkiss Dam


 The analysis of the failure due to the effect of the propagation of normal and reversed faults with different angles of inclination and by sliding through the Ourkiss dam isstudied numerically. Mainly at the end of construction and at the highest water level, for this purpose the non-linear finite difference method is used considering four fault angles of inclination, activated at the center of the base of the embankment.The results of the study show that the shear stress values increase with the increase of the vertical base displacement imposed in both conditions of the dam state, and this for both normal and overturned faults.


Introduction
The phenomenon of propagation of fault rupture by sliding has been studied by many authors. Bray & al [4,5] concluded that the behaviour of fault propagation is in uenced by soil characteristics. It causes signi cant damage to the structure.Numerical simulations and physical modelling have been carried out on the phenomenon of fault fracture propagation through uniform horizontal soil layers (Bray JD & al, 1990 [5]; Bonilla [18]).The study of fault propagation and its impact on the response of the underlying bedrock in the case of earth dams has been the subject of several studies. Fault displacements were rst observed by Louderback(1937) [19]. This subject has been detailed by (Wieland,M& al, 2008 [29]; Sherard, J.L, Cluff, L.S, 1974 [25] Swiger, W.F, 1978 [26]; Allen, C.R, Cluff, L.S ,2000 [2]. Cheney, J.A, & al (1984) [7] analyzed fault failure in models of silt embankments using centrifugation tests.In order to study the in uence of material properties, geometry and kinematic conditions on the response of the saturated clay back ll due to a Lazarte fault, 1996 [16] carried out a physical model test with experimental studies and 3D numerical analyses. Mejia &coll (2005) [21] numerically studied the combined effects of earthquakes and fault displacement of the foundation of the Aviemore Dam in New Zetland. Solhmirzaei& al (2012) [27] numerically model the propagation of the failure of an active dipping fault through clayey soil. Soroush& al (2015) [28] numerically studied two homogeneous and zoned embankment dams when faults occur in their underlying bedrock under steady-state in ltration conditions.Khoshini& al (2014) [15] and MortazaviZanjani& al (2016) [22] carried out nite element analyses on zoned homogeneous earth dams in an attempt to de ne fault propagation and consequently the stability of the Ejlali dam & al (2015) [9] analysed the propagation paths of the fault rupture through a zoned embankment dam. Hazeghian&Soroush (2015) [11],(2017) [12]have shown that the inclinations of fault failures are in agreement with Roscoe's theory (Roscoe, 1970). Hazeghian & Soroush (2018) [13] have carried out numerical parametric analyses examining the effect of soil surface geometry on the propagation of slip faults through granular soil. Finally, Eeleni& al (2019) [10] focused their work on the effects of normal fault propagation on a motorway embankment based on a single-layer soil.

Presentation Of The Ourkiss Dam
The Ourkiss Dam is an embankment dam built with clayey materials and alluvium with a watertight geomembrane screen on the upstream face of the dike and on the sides of the dam. It is located 14 km

3.1) Geometry and boundary conditions
The numerical analysis of the propagation of the active fault fracture through the Ourkiss dam lled and at the end of construction was studied using FLAC 2D [14] in plane deformation mode with a Mohr-Coulomb elastoplastic criterion. The research focuses mainly on the quasi-static dislocation and normal and reverse propagation of the fault with various submergence angles α (30°-45°-60°-75°), with the fault tip located in the center of the overlying embankment at the base of the dam.
To simulate the movement of the fault, a displacement with angles of inclination α is applied to the left (upstream) part while the right part is xed [28] gure 2.

3.2) Loading application:
The basic vertical displacement (h) necessary for the propagation of the fracture through the structure for uniform horizontal layers of non-cohesive material is 2 to 6% of the height of the overlying layer is imposed according to [5,8,18]. Bray & al [5] base displacements of 10 to 16% of the height are required for horizontal layers of saturated clay materials [23].
However, the materials commonly used in back ll are stiffer than saturated clay materials. Preliminary analyses in this study reveal that smaller base displacements are su cient for the development of a fracture across the trapezoidal geometry of the embankments [23]. Mortazavi Zanjani and Soroush (2014, 2016) suggested a vertical base displacement of 2% and 4% of the size of the dam for normal (NF) and reverse (RF) faults respectively in order for the failure to reach the ground surface. On the basis of these studies, we have chosen equivalent vertical displacements as shown in Table 1.   [23] we see that they are close to the surface and shallow in a trapezoidal geometry Figure 16. While for α = 45° the gures (10-11-12-13-14-15) show that the rupture line in our case propagates towards the crest and the downstream side. On the other hand, the break line in the case of the MortazaviZanjani M, Soroush A, Khoshini M [20] study propagates out of the core towards the upstream and downstream sides at the base of the dam and this is due to the effect of the core stiffness.
About the reverse fault α = 60 ° and α = 75 °, the gures (10-11-12-13-14-15) show that the primary ruptures (P) through the Ourkiss dam, deviate from the fault projection lines upstream, for both conditions (EOC) and (HWL). These results are consistent with the work of Zanjani and Soroush (2013) [23]. For the case where h=1.5m, we nd that under both EOC and HLW conditions and for α = 60°, the P ruptures across the dam deviate from the fault projection lines towards the downstream side.

Comparison Of Shear Stress Increments
In order to demonstrate the importance of the distribution of shear stress increments (SSI) as a function of the state of the two dam conditions (EOC and HWL) and the type of fault (RF and NF), a graphical presentation is shown in the gure below.
According to Figure 17 (a and b) (h=0.68 m and h=1.36 m), it can be seen that in the case of the presence of a reverse fault, the increases in shear stress are greater than those of a normal fault. For the case when α=30° representing the HLW angle, the increases in shear stress for a normal fault become signi cant.
It appears from Figure 18 (a and b) (h=1. 5m) that at the end of construction (EOC) the shear stress increments for a normal fault are greater than for an reverse fault for α=45° and α=60° as opposed to α=30° and α=75°. It should also be noted that the shear stress increments for a reverse fault become important for the condition of the dam in case of higher water level. In the case of the presence of a normal fault the shear stress increments are more important than in the case of a reverse fault, independently of the values of the angles of inclination α.
According to Figure 19 (a and b) (h=1m) it can be seen that for both dam conditions, end of construction and higher water level, the shear stress increases for a normal fault are greater than for a reverse fault and these values are devoid with increasing angles of inclination α.

Conclusions
Numerical analyses of the propagation of normal and reversed shear cracks in the Ourkiss Dam in the nite element state (EOC) and the upper water level state (HWL) were performed. Four angles of inclination were applied to the center of the base of the dam, resulting in the following remarks and conclusions: The shear stress values increase with the increase of the vertical base displacement for both conditions (EOC and HWL) and this for both the normal fault and the reversed fault.
The core stiffness has an in uence on the direction of crack propagation in the fault.
In the case of a reversed fault, the shear stresses take higher values compared to a normal fault and this for both dam conditions (EOC and HWL), independently of the inclination values α under the effect of the two basic vertical displacement values 4% and 2% of the dam size for the normal (NF) and reversed (RF) faults respectively. The tip of the fault is located in the center of the overlying embankment           Propagation of the reverse fault rupture in a clay embankment) [23] and a zoned dam) [22].

Figure 18
Variation of shear stress increments (SSI) as a function of α and h (h=1.36m and h=0.68m) Figure 19 Variation of shear stress increments (SSI) as a function of α and h (h=1.5) Figure 20 Variation of shear stress increments (SSI) as a function of α and h (h=1 m)