Introductory Geotechnical Engineering An Environmental Perspective by Hsai-Yang Fang

Bearing capacity of shallow foundations 355

thus considered as upper-bound solutions, provided that the velocity boundary
conditions are satisfied.
2 If the stress field within the plastic zone can be extended into the rigid region so
that the equilibrium and yield conditions are satisfied, then this solution consti-
tutes a lower-bound.
3 In view of limit analysis, each of the limit equilibrium methods utilizes the basic
concept of the upper-bound rule, that is, a failure surface is assumed and the least
answer is sought. However, it gives no consideration to soil kinematics, and the
equilibrium conditions are satisfied only in a limited sense. Therefore, limit
equilibrium solution is not necessarily an upper- or a lower-bound. However, any
upper-bound solution from limit analysis will obviously be a limit equilibrium
solution. Nevertheless, the method has been most widely used due to its
simplicity and reasonable accuracy.
4 By means of the finite element method, it is possible to calculate the complete
states of stress and strain within the soil beneath the structure (footing). The
method has been proved useful for studying the bearing capacity and other soil
related problems. It can locate areas of local failure and give a clear answer to the
overall stability. However, the results reported so far on the value of bearing
capacity of footings are not significantly better than those obtained from some
accurate limit equilibrium methods. Nevertheless, the finite element method is
undoubtedly of practical value since there are virtually no other methods capable
of predicting the movement, the states of stress and strain, and the localized
failure zones around the footing.
5 All above mentioned stability analysis methods are based on the mechanical energy
concept; however, some additional environmental factors relating to stability will
also be discussed in following chapters when the proper situation is encountered.

12.2.4 Planning for the foundation stability analysis

The type of ground stability analysis procedure needed to be performed depends on
the ground soil properties, upper structure conditions, and its surrounding environ-
mental situations. As illustrated in Figure 12.1, there are three general cases based on
geographical conditions. A brief discussion of each case is presented as follows; (a) If
the structure rests on flat firm ground (when ␤ ϭ 0), then, in general, the bearing
capacity and settlement analyses (Ch. 9) are sufficient; (b) If the structure is to be built
on a sloping hillside (when ␤ Ͼ ␾), and/or on weak soft ground soil deposits, then the
slope stability analysis (Ch. 14) must be carried out; and (c) For a vertical cut or
designing of a retaining wall (when ␤ → 90Њ), an additional lateral earth pressure
analysis (Ch. 13) is required.

Other conditions such as for offshore or waterfront structures, wave action needs
to be considered. In seismic or problematic soil–rock regions, such as earthquakes or
dynamic forces (Sec. 11.5), special attention to problematic soil behavior (Sec. 2.10)
is required. From the design point of view, the duty of the geotechnical engineer is not
only to analyze and design the foundation structure just beneath the main structure,
but must also consider all possible environmental conditions surrounding the area.
Some environmental conditions include topography, conditions of the right-of-the-way,
and surface and subsurface drainage patterns.

356 Bearing capacity of shallow foundations

y

Case II: when b > f (on sloping hillside)

Slope stability analysis is needed

Structure Case III: when b ⇒ 90° (vertical cut)

b = Backfill angle Additional earth analysis is required. If results
Ground surface
x do not meet the proper requirements, one or a
combination of the following ground improvements
must be applied.

Case I: when b = 0 (on flat ground) Ground improvement techniques: (Cases II and III)
Stability analysis: Retaining structures
Bearing capacity and settlement analysis are Bracing system
sufficient. If results do not meet the proper Anchors
requirements, one or a combination of the Reinforced earth
following ground improvements must be taken. Grouting and stabilization
Ground improvement techniques: Piles

Soil replacement

Pre-loading

Densification

Grouting and stabilization

Footings

Deep foundation (piles, caisson, etc.)

Figure 12.1 Ground stability analysis planning and its interaction.

12.3 Loads and allowable loads

12.3.1 Loads

Loads acting on a structure include static, dynamic, and environmental loads. Static
load (dead load) includes the weight of the structure and all material permanently
attached to it. Permanent and fixed service equipment is usually considered as part of
the dead load. Dynamic load includes live load and impact load. Live load includes
all loads that are not permanently a part of the structure but are expected to be super-
imposed on the structure during a part or all of its useful life. Vertical loads due to
wind or snow are not considered as live load. Human occupancy, partition walls,
furniture, warehouse goods, and mechanical equipment are major live loads. The
magnitude of live loads to be used in the design of various buildings is usually stipulated
in local building codes. Railroad and highway bridges subjected to traffic loading,
reaction from industrial cranes, and elevators sometimes constitute a large portion of
the live load. Total loads acting on the ground soil are calculated in three categories:
normal load, maximum and minimum loads, and horizontal load.

1 Normal load: Normal load is a vertical load, which includes static (dead load) as
illustrated in Equation (12.1).

PN ϭ PD ϩ PS ϩ PL ϩ PV Ϫ PB (12.1)

where PN ϭ normal load, PD ϭ dead load, PS ϭ snow load, PL ϭ live load, PV ϭ
vertical reaction due to lateral earth pressure, and PB ϭ buoyancy load.

2 Maximum and minimum loads: The maximum load includes the dead load, live
load, and vertical components of lateral earth pressure as shown in Equation (12.2).