**1. Introduction**

According to the generalized soil stress–strain diagram shown in **Figure 1**, after the strain in firm or dense soil exceeds the point of maximum stress, the stress decreases with increasing strain (known as strain softening) and finally approaches the residual stress.

The deformation of various structures under the action of external loads has previously been determined under Drucker stability postulates [1, 2], *i.e.*, *dσ* : d**ε**<sup>p</sup> ≥0, where *dσ* is the stress increment tensor and d**ε**<sup>p</sup> is the incremental plastic strain tensor. For this reason, limit analysis methods have been proposed for analysis

**Figure 1.**

*Results of a typical triaxial compression test for strain softening soil and perfectly plastic soil. (a) Stress-strain relationships for a confining pressure. (b) Shear strength-confining pressure relationships for three different confining pressures.*

of foundation ultimate bearing capacity, the active earth pressure of retaining walls, and slope stability. Based on the requirements of limit analysis, the strain softening behavior of soil has been ignored and been replaced with a perfectly plastic model. **Figure 1a** is the stress–strain relationships of soil obtained from a typical triaxial compression test. **Figure 1a** shows that when the strain is greater than the strain corresponding to the peak strength, the soil strength should decrease with the increase of the strain, so the phenomenon of strain softening occurs. However, since the traditional analyses of soil mechanics and foundation engineering are carried out under the conditions of Drucker stability postulates, the experimental result of strain softening is modified to be perfectly plastic.

When foundations, retaining walls, and slopes are designed using limit analysis and safety factors are used in accordance with seismic design codes, geotechnical failures such as those shown in **Figures 2**–**4** should not be prevalent during tectonic *Plasticity Model Required to Prevent Geotechnical Failures in Tectonic Earthquakes DOI: http://dx.doi.org/10.5772/intechopen.107223*

#### **Figure 2.**

*Tilting failure of a new building [3] after the Meinong earthquake in 2016 (Tainan,Taiwan).*

#### **Figure 3.**

*Failure of retaining walls under different conditions [4]: (a) during no rain and no earthquake (Formosa expressway 3.1 K, Keelung,Taiwan); (b) during the rainy season (Lincoln County in New Taipei City,Taiwan); (c) during an earthquake (Quanjiafu Community in Taichung,Taiwan).*

#### **Figure 4.**

*Shear failure of slopes under different conditions: (a) normal conditions [5] (Formosa expressway 3.1 K, Keelung, Taiwan); (b) during the rainy season (Tai-8 route 109 K,Taichung,Taiwan); (c) during an earthquake (Jiufen-Ershan, Nantou,Taiwan).*

earthquakes. Therefore, it is necessary to further explore the suitability of the perfectly plastic model as used in limit analysis.
