Theory to Practice of Unsaturated Soil Mechanics - Unsaturated Soil Mechanics in Engineering Practice - page 10

1.4.3 Formulation Stage
The formulation stage involves combining the constitutive
behavior of a material with the conservation laws of physics
applied to a representative elemental volume (i.e., a REV).
The result is generally a partial differential equation that
describes a designated physical process for an element of
the continuum.

State Variable Stage
- Stress state
- Deformation state

Constitutive Stage
- Soil-water characteristic curve
- Flow laws
- Shear strength equation
- Stress-versus deformation, etc

1.4.4 Solution Stage
The solution stage involves solving specific examples repre-
sentative of a class of problems. The solving of formulated
equations constitutes an independent stage since it is possi-
ble that fundamental equations can be derived; however, the
solution to the equations may not be possible. The solution
stage for unsaturated soils generally involves solving partial
differential equation(s) that are placed into a numerical solu-
tion form (e.g., finite difference of finite element form) that
can be solved using computer software. Other solvers may
also be used as is the case for limit equilibrium solutions of
slope stability problems.

Formulation Stage
- Derivation pertaining to an element
- Partial differential equation

Solution Stage
- Numerical modeling mode
- Boundary values applied

Design Stage
- Application of the computer
- Use of "what if ---" scenarios

1.4.5 Design Stage
There is a gradual increase in engineering confidence as
research progresses from the formulation stage to the solu-
tion stage and on to the design stage. The design stage
focuses on the primary unknowns that must be quantified
from a practical engineering standpoint. The design stage
generally involves the quantification of geometric and soil
property variables that become part of an engineering design.
The computer will generally be an important tool in the
design of most earth structures. The computer has truly
changed the manner in which geotechnical design is con-
ducted. Nowadays, geotechnical engineering design gener-
ally takes the form of a series of parametric-type studies.

Verification and Monitoring Stage
- Observational approach

Implementation Stage
- Accepted as part of prudent
engineering practice

Figure 1.7 Stages leading toward implementation of unsaturated
soil mechanics in engineering practice.

soil are the stress state variables: the net normal stress ( σ − u a ,

where σ = total stress and u a = pore-air pressure) and the

matric suction ( u a − pore-water pressure).

These stress state variables are later shown to take on the
form of two stress tensors (i.e., 3

u w , where u w =

1.4.6 Verification and Monitoring Stage
There is need to “observe” the behavior of an engineered
structure during construction and during operation of the
structure in order to provide feedback to the designer. Only
through field monitoring and feedback can confidence be
firmly established in the design procedures. The “observa-
tional method” as defined by Peck (1969) extends beyond
the verification of design and is considered to be part of the
design process.

×

3 matrices). The stress
state variables have become widely accepted and illustrate
the need to separate the effects of total stress and pore-water
pressure when pore-water pressures are negative. The stress
state variables also satisfy the need for a smooth transition
between the saturated and unsaturated states.

1.4.2 Constitutive Stage
The constitutive stage becomes the point at which empir-
ical, semi empirical, and possibly theoretical relationships
between state variables are proposed and verified. The veri-
fication of proposed constitutive relations must be conducted
for a wide range of soils in order to ensure uniqueness and
subsequent confidence on the part of practicing geotechnical
engineers. Extensive research studies on constitutive relation-
ships for unsaturated soils were made in the 1970s, but earlier
and later developments have also contributed to our under-
standing of the constitutive behavior of unsaturated soils.

1.4.7 Implementation Stage
It is possible that the implementation stage may not be
realized in engineering practice even when theoretical for-
mulations and design procedures have been fully studied
and verified. Implementation is the final stage in bring-
ing an engineering science into routine engineering practice.
There are other factors that also need to be addressed at the
implementation stage, such as (i) the cost of undertaking