Introduction

For last 50 years, engineers imposed seismic coefficients to their static load calculations

in order to stimulate earthquake effects onto dam body. Those conventional methods do not

assess deformations of dam body which may significantly affect slope stability. However, with

the advancement of computational technology, ordinary computers have enabled to solve

earthquake problems under recorded ground motion spectrums taking into consideration various

effects such as permanent deformations for each time interval and more importantly soil

liquefaction phenomena.

As a part of earthquake design, QUAKE/W has been applied under two parent analyses namely

Steady- Seepage and In-Situ Static which serve as initial conditions of dynamic analysis.

During earthquake analysis, corresponding deformations for each time interval at integration

points are recorded under 3 different peak acceleration values from 0.2g to 0.4g in order to

utilize them in slope stability analyses.

In the end, Newmark`s algorithm which takes into account inertial forces of soil blocks (mass

times acceleration) have been conducted for both upstream and downstream part of the dam in

order to calculate factor of safeties for slopes.

Objective

The main purpose of the analysis is to observe dynamic behavior of the dam body under strong

ground motion that could be happen in 3rd earthquake zone and to obtain factor of safety values

of slopes. Also, there is a possibility that there may be presence of excess pore-water pressures

which in turn may lead to liquefaction.

Problem Configuration

Below figure shows the problem configuration. In short, it is a rock filled dam with symmetric

side slopes of 1:1.6 and has a height of 19m. Also, foundation of the dam is assumed to be rock

strata with shear modulus of 35 mPa and has a depth of 10m initially. Full supply level is at 21.5

m above from the origin.

Figure 1 Problem Configuration

Earthquake Characteristics

A strong motion record from Bala (67 km south-east of the city of Ankara) occurred at

2009/01/11 01:51:40 (GMT) with a peak acceleration of 0.1g has been taken as base data during

analyses. Sampling intervals are divided into 0.02 second intervals in order to obtain more

accurate results. Since the dam body belongs to 3rd earthquake zone, anticipated ultimate

acceleration value is between 0.2 and 0.3g. For that reason, upper-cap of the acceleration value is

taken as 0.3g to be on the safe side and original spectrum amplified 3 times accordingly.

Following figure represents spectra that is used for dynamic analyses with a duration of 10

seconds.

Figure 2 E.Q Record Amplified 3 Times

In-Situ Stresses and Pore Pressure Results

As a first step of dynamic analysis, QUAKE/W requires results of insitu stress state conditions

that exist before the earthquake hits. Two main material properties are needed to be implemented

into program, unit weight and Poisson`s ratio ν which has vital importance since it influences K0-

coefficient of earth pressure at rest. Also, ground is prevented to move both in x and y direction.

However, edges of the foundation part can displace vertically. In below figure, pore pressure

contours and boundary conditions are drawn to compare results with dynamic analysis.

Figure 3 Insitu PWP Conditions

Dynamic Analysis

When the insitu stress conditions are obtained, now earthquake record could be applied to the

dam body. Equivalent Linear Dynamic analysis type is conducted on that problem. Firstly,

boundary conditions of the problem changed. Now the dam body is allowed to swing laterally

but it is fixed at the ground. Therefore, these adjustments have enabled to dam body deform

laterally under strong ground motion. In addition, history points at where the displacements are

saved are located at crest and lowest elevation of the foundation.

After analysis conducted under maximum acceleration of 0.3g, increase in the pore water

pressure at bottom level of the dam has been observed. That phenomenon may cause liquefaction

problems and consequently weaken shear strength of the clay core and filter zone. Below figure

shows increase in the pore water pressure by 50 kPa comparing to static analysis and deflected

shape of the body at the end of 10 second earthquake.

Figure 4 After Dynamic Analysis

Slope Stability Analyses

Once the displacement results at history points are recorded, final step is to conduct slope

stability analysis at the both side of the dam to check whether a global failure will occur under a

ground motion. Bunch of earthquake records are applied to the body with a maximum

acceleration of 0.2, 0.3 and 0.4g. Although Turkish Earthquake Code suggests that 0.2g with a

return period of 475 years and has 10% probability of exceedance is a sufficient ultimate

acceleration for design purposes in 3rd earthquake zone, it has been realized that designing an

earthquake resistant dam is really complicated and challenging job, an earthquake with 0.3g peak

acceleration has become our main design ground motion to count for unnamed effects that we

are not master at on that level. Therefore, following Factor of Safety vs. Time plots and probable

failure surface profiles are obtained under 0.3g for both upstream and downstream parts where

the all factor of safety values are larger than 1. It can be notified that occurrence time of positive

maximum acceleration and minimum factor of safety value are nearly coincident for upstream

part. That fact may be an indicator of accuracy of dynamic analysis results.

Figure 5 Factor of Safety vs. Time- 0.3g- Upstream Part

Figure 6 Factor of Safety vs. Time- 0.3g- Downstream Part

Figure 7 Slip Critical Surface- Upstream Side

Figure 8 Slip Critical Surface- Downstream Side

Effect of Foundation Depth to the Slope Stabilities

In order to see how an input parameter impacts the results of slope stability, very same dam body

is modeled with 5 and 15m deep foundation. At first, we anticipated that if the foundation level

goes into deeper elevations, slope stability values may increase accordingly. However, results

have revealed that deep foundation forces dam body to swing more and consequently new taller

body ended up with amplified lateral displacements at the crest which is the location of history

points. As a result, slope stabilities drop down on upstream part of the dam. Following figures

reflect effect of foundation depth.

Figure 9 Factor of Safety vs. Time - 5m Deep Foundation- Upstream

Figure 10 Factor of Safety vs. Time - 15m Deep Foundation - Upstream