The dam will be founded on Schist, left and right banks will be underlain by hard Quartz Talcosic Schist and Chlorite Mica Schist respectively. The spillway will be on Quartz Talcosic Schist. Powerhouse will be constructed on Graphitic Schist. Geological map of the dam site is shown in the Figure 1. The bedrock is in hard, fresh, and intact condition (WAPDA 2017). The under-construction dam is a concrete face rockfill dam (CFRD). The main dam body will comprise of rockfill Material of different grades/qualities. A concrete slab will span the upstream face acting as a barrier to retain the reservoir due to the highly permeability of rockfill. To model the dam by both LEM and FEM, evaluation of rockfill material properties is a pre-requisite and a critical part of this study.

The size of rockfill material used in this project is large enough to necessitate the use of large scale triaxial test apparatus. However, due to non-availability of such equipment with the authors, shear strength properties of the rockfill were determined using cores obtained from the rockfill and tested using traditional triaxial apparatus. Later, the rockfill parameters were obtained by correlating the results of core-testing with the literature references. Obtained parameters serve as input for LEM and FEM Models. Rockfill samples to be tested were collected from the actual quarry site to be used for dam construction, suggested by Mohmand dam consultants in the detailed design report (NESPAK, SMEC, & ACE, 2017). The sample collection site is shown in Figure 2. Laboratory testing carried out for the study is discussed in the following section.

## Laboratory Investigations

For the current study, Petrographic Analysis is performed on rockfill sample collected at site to determine its mineral composition. Petrographic Analysis results are used to assess the suitability of the material to be used as concrete aggregate and to confirm the rock classification carried out in the field.

Due to unavailability of large-scale testing facilities for rockfill in Pakistan, shear strength parameters of the rockfill were determined through correlations available in the literature (Pinto 2007). For this, Unconfined Compressive Strength Tests were performed on the Rock Cores of the rockfill source material in accordance with the provisions of ASTM D2938–95. The tests were performed using Universal Testing Machine (UTM) to find Unconfined Compression Strength of rock cores. A minimum Length to Depth ratio of 2.5 was maintained while preparing the core sample. Load at failure was recorded and failure stress (UCS) was calculated using area of the sample.

Point Load Strength Test provides a Point Load Strength Index of the tested specimen which can be readily converted to UCS through available correlations. Point Load Tests on rockfill sample is performed in accordance with ASTM D 5731 – 08. The testing equipment consists of a Loading frame, Conical Platen and Pump handle. Rockfill sample was block shaped with different widths. Average of both sides was taken to find Mean Width and Mean depth. Maximum load was measured at the point where the sample failed, and relevant relationship was used to obtain the Point Load Strength Index. Unconfined Compressive Strength (UCS) was calculated using index-to-strength conversion factors.

Rebound hammer tests were also performed in accordance with ASTM D5873 – 00. For brevity, hammer spring was pressed by depressing the plunger until the hammer was triggered and the impact occurred. Height of hammer rebound was measured to the nearest whole number and UCS was calculated using specific equation for the material under consideration.

## Numerical Model And Parameters

Two commercially available software packages, each LEM and FEM based, are used to evaluate slope stability. FOS is computed using input parameters derived using both empirical relations and laboratory test results. The Finite Element Model was meshed with 15 nodal elements with suitable mesh refinement. Mohr-Coulomb model was used as the material model for both LEM and FEM analysis, (Figure 3).

## Loading Conditions

Analyses are performed for all anticipated loading conditions including end of construction, full supply level, minimum water level and earthquake loading. Furthermore, given that the project area falls in a tectonically active zone due to collision between the north moving Indian plate and the Eurasian plate i.e. Zone 2B (BCP 2007), post-earthquake stability was also examined using both pseudo static and dynamic analysis. The recommended ground motion value corresponding to maximum credible earthquake is 0.68 g, peak ground acceleration of 0.16g was fixed for the operation basis earthquake (OBE). Equivalent horizontal force component for pseudo static analysis (OBE) (= 2/3 of PGA i.e. 0.107 and for MCE = 1/2 of PGA i.e. 0.34) was used, while the vertical component in pseudo static analysis was kept zero. To perform dynamic time history analysis, design response spectra was developed with a PGA of 0.68 (Figure 4(a)) and the following Idriss Equation was used to develop the design spectra.

$$\text{ln}Y= [{{\alpha }}_{0} +{e}^{({\alpha }1 + {\alpha }2 \text{M}) \text{J}}+[ {{\beta }}_{0}- {e}^{({\beta }\text{l} + {\beta }2 \text{M})\text{ln}(R+20)}+\text{O}.2\text{F}+ {\epsilon }]$$

1

where, Y is ground motion parameter, M is earthquake magnitude, R is the closest distance to the source in Km, F is style of faulting factor (i.e. F =0 for a strike slip fault; F =1 for a reverse fault and F =0.5 for an oblique source), ε is standard error term (natural logarithm) and αo, α1, α2, β0, βl, β2 are Constants.

The design response spectrum was matched with sample time history of Loma Prieta Earthquake recorded at Lexington Dam California on 18th October 1989 (Figure 4(b)) to generate design time history using Seismomatch software (Figure 4(c)). Lexington dam was selected because of its similar geological features with Mohmand Dam. Notably, major input parameters, which affect the slope stability, are angle of internal friction (\(\varphi\)), undrained cohesion (c) (Irfan et al. 2013), and modulus of elasticity (E) (Bhandary 2019).

## Friction Angle

Barton (2013) compared shear strength of the Rockfill material with the shear strength of the intact rock, jointed rock, filled discontinuities and fractured rock. He derived an Equation for the Rockfill material shown below.

Where, *𝝉* = Shear Stress, *𝝈**𝒏* = Normal Stress, *R* = Roughness, *S* = Unconfined Compression Strength, **Φ** b = Basic Friction Angle.

*R* is the value of roughness which was calculated using visual observation of rockfill sample (7 mm mean value), **Φ** b is the Basic Friction Angle (300) provided by Barton (2013), S is the value of Unconfined Compression Strength (UCS) calculated through Laboratory testing (35 MPa). Shear Stress was plotted against Normal Stress to find out the Friction angle. (Figure 5).

Empirically, Friction Angle was calculated using International Commission on Large Dams (ICOLD 2016). For brevity, it suggests that the Friction angle for rockfill varies from 450 (lowest density, poorly graded weak particles) to as high as 600 for high density well graded particles. For Slope Stability Analysis using critical conditions, a conservative estimate of friction angle was taken as 45°.

## Modulus of Elasticity

Material Modulus of Elasticity thus affects the Factor of Safety (FOS) in FEM. Pinto’s (2007) method was used to calculate Modulus of Elasticity from Valley shape factor, which is defined as the area of Concrete face slab (measured normal to the face) divided by the square of maximum dam height. i.e. (A/H2). Face slab area of Mohmand Dam is 151,470 m2 and height of main dam is 213 m. Valley shape factor (A/ H2) comes out to be 3.33. From this valley shape factor, Modulus of Elasticity from Pinto’s chart is calculated as 70 MPa that is referred to as the Construction Modulus (Ecr). This will change to a new value when the dam is filled, called Filling Modulus. To calculate the filling modulus, Marque and Pinto (1998) method is used. In this method, a Modular Ratio is calculated using Valley Shape Factor. Modular ratio is defined as the ratio of Filling Modulus to Construction Modulus.

Using the graph between shear stress and normal stress (Figure 5), the friction angle is calculated to a value of 41.5o. Further to that, the friction angle is calculated empirically using ICOLD 2016 manual with a recommended value of 45o. The value of friction angle obtained empirically was overestimated (7.8 %) than the one obtained through laboratory testing. The probable reason for increased values of friction angle through empirical equations (ICOLD 2016) may be related to the fact that the given equations are generalized and did not truly represent the specific dam material being used (rockfill). In contrast, the laboratory tests were performed on samples collected from the actual site, suggesting more reliable results. In essence, the values of A/ H2, modular ratio, and filling modulus have been computed as 3.33, 2.65, and 185.5 MPa (i.e. 2.65 x 70 MPa).