Seismic Slope Safety. Seismic Slope Safety. Seismic ground motion. Ground Motion 4/5/2012. Understanding Effects of

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1 Seismic Slope Safety Dr Sarada K Sarma Emeritus Reader of Engineering Seismology Senior Research Fellow Imperial College London SW7 2AZ UK Seismic Slope Safety Understanding Effects of Earthquakes Toe Cutting Toe Wetting Rainfall 24 January Seismic ground motion The Seismic Ground Motion is represented by the Peak Acceleration in a strong motion record. It is derived using an Attenuation Relationship Either in a Deterministic manner i.e. The position of the source of the earthquake and therefore the distance to the site is assumed known; Also the magnitude of the earthquake is assumed known. That earthquake is assumed to be definite to occur at some time. Or in a Probabilistic manner i.e. The position of the source and the magnitude of the earthquake is considered to be probabilistic. Also the chance of its occurring is probabilistic based on past history. Often, the peak acceleration is reduced by a factor for pseudo-static design analysis. Ground Motion Source Characteristics Attenuation Relationship Size of the Source (Magnitude) Distance of the site from the Source Geology of the path from the source to the site Local soil conditions There are many attenuation relationships available in literature. We should use these with caution

2 Acceleration (g) Joyner & Boore (1981) Attenuation Relationship fault distance (km) Attenuation Relationship Joyner & Boore (1981) log(a g )= M-log r r +0.26p M= Moment magnitude r 2 = d d = Closest distance to the surface projection of the fault rupture p = 0 for mean value and =1 for 1 standard deviation away from the mean. 5 6 The Source-Causative fault Macro scale Plate teconics Micro scale Individual faults exposed and buried Normal faulting Thrust faulting Strike- slip faulting Causative fault Hypocentre and Epicentre Expressed as points but in reality it approximates the starting point of the faulting process Determined from first arrivals of waves around the world 7 8 2

3 Size of earthquakes Released Energy and Magnitude log E = a + bm one Magnitude higher approximates to about 30 Times bigger energy release Magnitude is measured from the maximum amplitude of ground motions as measured in instruments at a distance scaled for the distance Site effect Geometrical relationship of the site with respect to the fault Near Source Hanging wall/foot wall effect Directivity effect Fault propagations towards or away from the site Distant Source - Geology of the path- Wave velocity model 9 10 Local site effect Depth of rock from the surface Soil layer Geometry of the layering system Wave velocities of the soil system Strength of the soils Water table conditions General topography of the site Hill, plain, deep valley etc Local site effect Extreme soil conditions Liquefaction of sites Slope failures

4 Example of slope failure in Assam earthquake of 15 August 1950 in India. [After Mathur (1953)]. About km 2 area was affected. 13 Example of slope failure in Assam earthquake of 15 August 1950 in India. The figure shows the damaged valley of the river Simen north of Dibrugarh [After Gee (1953)] 14 Characteristics of ground motion Near source effect High frequency content High amplitude Effects high frequency structures Fewer number of important pulses effects structures of brittle natures Enhanced ground motion due to shallow strong soil layers 15 Characteristics of ground motion Distant source effect Low frequency content Low amplitude Effects low frequency structures Many important pulses effects structures of flexible natures Enhanced ground motion due to deep week soil layers 16 4

5 Ground Motion Slope It is a complex phenomenon and cannot be determined in an absolute manner. More often than not, it is determined in a probabilistic manner taking into account various sources around the site. Being probabilistic, there is always a probability that the design ground motion will be exceeded at some time, however remote the time. Reservoir Water Slip Surface Slope Safety of a slope is determined by a factor of safety F for a given ground motion. F>1 represents safe condition, F<1 represents unsafe condition and F=1 is the critical condition. This is determined for the most critical slip surface. Alternatively, the safety can be determined by a critical acceleration k c g. The critical acceleration is defined by the ground acceleration that is required to bring the factor of safety to 1. Therefore k c > k d represents safe condition, k c <k d represents unsafe and k c =k d represents critical. Acceleration (g) k c g Time (sec)

6 Slope failure The simple effect of the ground motion being greater than the critical can be assessed by calculating the possible displacement of the mass above the slip surface. (Newmark sliding block technique) The slope is considered safe if the amount of displacement is small(?). Slope=1/5;Φ =20 o ;c =5kn/m k c =0.25; E=120kN; X=61kN Effect of Toe cutting In the last slide, if we remove the marked section from the toe, then for the given slip surface, the critical acceleration will drop, from k c =0.25 to about k c =0.2 But, the removal of the section will change the critical slip surface itself and the k c for the new slip surface may change drastically to very nearly zero. (may be even negative implying unsafe situation). Effect of Toe Wetting For example, due to reservoir build up, the toe of the slope will become saturated. As a result, the critical acceleration will drop. Depending on the level of the reservoir, the critical acceleration may become smaller by as much as a factor 2. In the example slope, if we fill a reservoir to the crest level, k c will drop to

7 Effect of Rainfall Rainfall induces flow of water in the slope which creates pore water pressure in the soil. The pore water pressure depends on the depth of the phreatic line and the slope angle. This in turn reduces the shear strength of the soil. Therefore, the critical acceleration drops. Rainfall Effect Flow parallel to the slope Phreatic line at surface r u =Pore Pressure Ratio= 0.5 cos 2 β For the example slope r u = Rainfall Effect For the example slope, with r u =0.4 Using Sarma(1999), k c =0.094 With r u =0.5, the k c will be even less. The critical acceleration drops from 0.25g to less than.094g Conclusions Understanding ground motion is very important It is a very complex problem depends on many factors both known and unknown Statistical analysis gives probabilistic answers not absolute Ground motion can always exceed the design parameters- Therefore, failure must be in a safe way so that hazard to life is reduced Analysis of consequences of failure is therefore very important

8 Conclusions The stability of a slope depends on the seismic ground motion and other factors such as Toe cutting, Toe wetting Rainfall Toe cutting and wetting may be natural or man made Rainfall is natural. The effect may be reduced by different means e.g by forestation (Outside the scope of this presentation). Seismic Slope Safety Thank you Seismic Slope Safety Assessment Kobe Earthquake, Nikawa Landslide 31 8