## Earthquake Damage to Structures

18.1 Introduction 18-1

Earthquakes • Structural Damage

18.2 Damage as a Result of Problem Soils 18-4

Liquefaction • Landslides • Weak Clay

18.3 Damage as a Result of Structural Problems 18-16

Foundation Failure • Foundation Connections • Soft Story • Torsional Moments • Shear • Flexural Failure • Connection Problems • Problem Structures

18.4 Secondary Causes of Structural Damage 18-41

Surface Faulting • Damage Caused by Nearby Structures and Lifelines

18.5 Recent Improvements in Earthquake Performance.. 18-44 Soil Remediation Procedures • Improving Slope Stability and Preventing Landslides • Soil-Structure Interaction to Improve Earthquake Response • Structural Elements that Prevent Damage and Improve Dynamic Response

References 18-58

### 18.1 Introduction 18.1.1 Earthquakes

Most earthquakes occur due to the movement of faults. Faults slowly build up stresses that are suddenly released during an earthquake. We measure the size of earthquakes using moment magnitude as defined in Equation 18.1:

where M0 is the seismic moment as defined in Equation 18.2:

where G is the shear modulus of the rock (dyne/cm2), A is the area of the fault (cm2), and D is the amount of slip or movement of the fault (cm).

The largest-magnitude earthquake that can occur on a particular fault is the product of the fault length times its depth (A), the average slip rate times the recurrence interval of the earthquake (D), and the hardness of the rock (G).

For instance the northern half of the Hayward Fault (in the San Francisco Bay Area) has an annual slip rate of 9 mm/year (Figure 18.1). It has an earthquake recurrence interval of 200 years. It is 50 km long and 14 km deep. G is taken as 3 x 1011 dyne/cm2.

M0 = (0.9 x 200)(5 x 106)(1.4 x 106)(3 x 1011) = 3.78 x 1026

Therefore, about a magnitude 7.0 earthquake is the maximum event that can occur on the northern section of the Hayward Fault. Since G is a constant, the average slip is usually a few meters, and

Attenuation curves: Mualchin and Jones [2]

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