Planar failure

The seismic effects are generally considered as pseudo-static forces to be added to the other static forces. A detailed review ofthe literature regarding the computation of passive earth pressure using planar failure, composite failure mechanism and experimental investigations are presented in the following sections. In addition, the review of the literature for the computation of earthquake-induced displacements is also presented. 

Choudhury and Nimbalkar (2007) extended the work of Zeng and Steedman (2000) for the retaining wall under passive condition considering vertical seismic excitation and presented the results of rotational displacements of rigid retaining walls using planar failure mechanism. Basha... 

Planar Failure Mechanism versus Composite Failure Mechanism... 

It can be noted from Table 2 that the values of K,. predicted by employing the composite failure mechanism are lower than the planar failure mechanism reported in Kramer (2003) for the case of <5 > 0.4 and the difference increases for higher values o 8 / 4>. Similar observations can... 

Planar failure Composite failure Planar failure Com- posite failure Planar failure Compos ite failure Planar failure Composite failure Planar failure Composite failure Planar failure Composite failure... 

For example, it can be found in Figure 8 that the assumption of planar failure surface overestimates the critical acceleration values (k g ) to the extent of 11.52% for = 30°. In addition, for a constant value of k = 0.46 and

mechanism predicts the magnitude of sliding displacement (-9) value as 10 cm, whereas composite failure mechanism predicts S value as 70 cm, the difference reaches as high as 85.71%. It may be noted in Figure 9 that the assumption of planar failure surface overestimates the value of k and difference reaches as high as 34.48% for 4> = 30°, and further for a constant value of = 0.40, planar failure mechanism predicts a rotational displacement (6) of 2.0°, whereas compos-... 

It is shown that planar failure mechanism overestimates the passive earth pressure for rough soil wall interfaces (i.e. <5 > 0A). 

For = 30° and 6 = 15°, the assumption of planar failure mechanism overestimates the critical seismic acceleration values for sUd-ing and rotation by 11.52 and 34.48% respectively, and further it underestimates the sliding and rotational displacements to the extent of 85.71 and 76.47% respectively. Accordingly the error in the estimation can be magnified as magnitude of 6 approaches 4> hence the planar failure mechanism is notthe appropriate one to predict the passive... 

Figure 1. View of studied slope showing the distribution of sedimentary rock (darker) and quartz porphyry (paler color). The mold from a planar failure can be seen at the right-upper part. Discontinuity orientation data are presented stereographically as follows (a) all, (b) shale, (c) quartz porphyry and (d) contact boundaries.

In the method of slices basically circular failure surfaces are considered. However some slice methods have also been developed to analyse non-circular failure surfaces and arbitrarily defined multi-planar failure surfaces. In Table 8.12 an overview is given of different slice methods, the type of failure surface considered and the equilibrium equations that taken into account. 

One of the simplest and most useful tests performed on reflow-attached flip chips to determine the adequacy of the solder joints (i.e., C4) is a tensile pull test (Fig. 31). This is done by adhesively attaching a metal stud to the back of a joined chip and pulling the joints in tension at a slow strain rate (approximately 1.0x10 sec ). The pull force is measured during the test using an appropriate load cell. The pull strength is a useful parameter, but the failure mode is a very important indicator of joint quahty. Planar failure at the solder joint interfaces is indicative of a weak and unacceptable interface condition. 

Fig. 21 is a plot that depicts the relative strengths of several features of a solder joint. In a properly fabricated joint, the intermetallic compounds are very strong and deform elastically, but should never fracture. In a tensile test, a properly formed high Pb/Sn solder joint always fails within the bulk solder which implies that the strengths of the interfaces depicted in Fig. 25 are greater than the strength of the solder. Note that the stress-strain behavior of only one interface is shown in Fig. 26. Although each interface shown in Fig. 25 exhibits a different stress-strain behavior, each must possess a tensile strength greater than the solder. If an interface in the structure is weaker than the solder, it will result in a brittle, planar failure in a tensile pull test. A change in fracture mode from plastic solder fracture to brittle elastic interface fracture is usually an indication that a terminal is defective. Lead-rich solders are usually weaker and more ductile than tin-based solders (Fig. 26).

---