INTRODUCTION

One planning standard that controls development in Malibu is the landslide safety factor. A safety factor is a number that expresses the probability a particular undesirable event will not occur. It can be applied to just about any kind of event for which measurement is possible. The safety factor against the failure of an earth slope is the most fundamental geotechnical criterion used by public agencies in California, and almost certainly elsewhere, in determining whether slopes in earth materials, either natural or graded, are sufficiently safe for some particular situation, e.g, that of developing residential property. The safety factor against landsliding refers to landslides that occur due to shearing rather than flowage. It is a pure number calculated as the ratio of assumed forces that can be mobilized along a specific or potential surface of shear capable of resisting shearing, call them the "resisting forces," to the forces similarly mobilized along that surface tending to cause shearing, call them the "driving forces." Any such surface has some degree of shear strength. In the development of property in Malibu, as in many other California jurisdictions, the costs to determine shear strength is a substantial part of the costs of the geotechnical investigation required for issuance of the building permit. Furthermore, the determination of safety factors are required for both static and dynamic conditions, the latter associated with earthquakes. There is no accepted safety factor for landslide that occur by flowage.

STATIC SAFETY FACTOR

In a stable slope, according to the second law of motion, the actual resisting and driving forces along any potential surface of shear are at all times equal to the point where failure actually occurs. In almost all cases involving the static safety factor, it is because ground-water conditions reduce the resisting forces that failure occurs. In other words, the resisting forces are reduced thereby reducing the shear strength along any surface while the driving forces remain essentially constant. For this reason, it is necessary not only to show an adequate safety factor for the building permit, but also some sort of design to control ground water so that is cannot reduce the shear strength.

It has been established, apparently by consensus in the engineering community, that for residential construction, a slope with a static safety factor of 1.5 is sufficiently safe against landsliding in shear, absent the development of some unusual condition such as the introduction of ground water or, less commonly, the static overloading of the slope increasing the driving forces. It is to be noted that slope with a calculated safety factor of 1.5 is no more stable than one with a calculated safety factor of, say, 1.3. This is because, according to the third law of motion, at all times before failure, the mobilized resisting forces and driving forces are equal and act opposite to each other. The design static safety factor standard for Malibu is 1.5.

SEISMIC SAFETY FACTOR

A so-called seismic safety factor against landsliding also is established for the dynamic conditions from forces generated during an earthquake. The fundamental problem in this case is that the forces due to shaking during an earthquake are transient leading to the question of how much, if any, landslide movement is to be expected as a result of the passing of seismic waves and then a return to static conditions. The most common method of estimating a seismic safety factor is through what is known as pseudostatic analysis initially applied 70 years or more ago. However, within about the past 50 years, another method referred to as Newmark analysis has been developed. Both require certain assumptions concerning the manner in which earthquake shaking affects a slope.

Pseudostatic analysis amounts to increasing the driving forces by assuming a vector of force acting horizontally calculated by multiplying it by a "seismic coefficient" ranging from zero to 0.5 depending, arbitrarily, on estimated values of earthquake intensity or design estimated accelerations ranging from about 0.1 to 0.6 for earthquake magnitudes in the range of 5.5 to 8.0 (Hunt, 1986, pp. 505 - 507). In either case, the selection of a seismic coefficient to be used is strongly dependent on "site specific conditions." An especially informative discussion of the determination of relevant site specific conditions is provided in California Geological Survey (formerly Division of Mines and Geology) Special Report 117 entitled, "Guidelines for Evaluating and Mitigating Seismic Hazards in California." The seismic coefficient to be used in pseudostatic analysis in Malibu is 0.2g and the calculated safety factor no less than 1.1.

Newmark analysis can be used for any set of the known required variables, but it is most commonly applied for regionally. Newmark analysis, involves estimating the cumulative permanent displacement to be expected of a slope considered to be a block when there is applied to it seismically induced critical acceleration. An excellent explanation of the Newmark analytical method is given by Jibson et al., (1998). Whereas pseudostatic analysis produces a safety factor, Newmark analysis produces a displacement. Such displacements commonly are found to range from zero to more than 100 centimeters (cm). In the range of 0 to 10 cm, serious landside damage is considered unlikely, from 10 to 100 cm, ground cracks and reductions in shear strength sufficient to reduce the static safety factor are to be expected, and greater than 100 cm imply earthquake-induced landsliding. The design Newmark analysis standard in Malibu is 50 cm.

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