In order to clarify the sustainability assessment approach, a case study was evaluated using the methodology as described in the previous sections. This section explains the work of the evaluation system in practical application and supports designers in distinguishing the strengths and weaknesses in the design, improvement, and development of the sustainability of geotechnical projects. Based on the effect of the scale and dimensional analysis, the small scale model can be converted to a prototype model. In this section, the sustainability assessment will be studied with prototype dimensions, which include the case is to study the sustainability assessment of raft footing constructed on oil decontaminated soil and deep foundations (driven and bored piles). In order to study the sustainability methodology in evaluating the environmental, economic, and social aspects of the physical model and the potential of improving and developing the sustainability of the design, this project evaluated by using this scenario a traditional geotechnical approach was used. This case consists of a building has a foundation of dimensions 15×15 m and 0.45 m thickness constructed on silty clay soil and contaminated by residues oil contaminant. Three types of foundations are suggested to carry the building load as illustrated in Fig. 3. These types, scenarios are suggested to enhance the role of sustainability in geotechnical engineering and select the best design contribution to sustainable development. The design includes three scenarios given in Table 1.
Table 1
Scenario
|
Dimensions
|
No. of piles
|
Area of foundation
|
Raft footing with lime piles
|
0.45 m thickness
|
0
|
225 m2
|
Driven piles
|
0.3 dia.×14.3 m length
with pile cap of 0.45 m thickness
|
16
|
Bored piles
|
0.4 dia.×14.3 m length
with pile cap of 0.45 m thickness
|
16
|
Dimensional analysis in its simplest form proposes to reduce an engineering parameter to its fundamental Mass-Length-Time “measures of nature” while developing scale factors for each of the three quantities. Rocha (1957) was the first to describe scale modeling for problems in soil mechanics systematically. Also, Rocha (1957) differentiated between total stress and effective stress conditions, deriving separate similitude relations for each case. To account for the different stress levels presented in a 1-g scale model from the prototype. Rocha proposed that the soil constitutive behavior be scaled, and therefore assumed that both the stress and strain held a linear relationship between the model and prototype.
Kana et al. (1986) described the application of the Buckingham Pi theorem to the problem of scale modeling the dynamic interaction of a pile in clay and suggested the following non-dimensional equation:
$$\frac{\mathbf{y}}{{\mathbf{D}}_{\mathbf{P}}}=\left(\frac{{\mathbf{E}}_{\mathbf{P}} {\mathbf{I}}_{\mathbf{P}}}{{\mathbf{E}}_{\mathbf{s}} {\mathbf{D}}_{\mathbf{P}}^{4}} , \frac{{\mathbf{M}}_{\mathbf{c}}}{{\mathbf{D}}_{\mathbf{P}} {\mathbf{M}}_{\mathbf{P}}} , \frac{\mathbf{F} {\mathbf{D}}_{\mathbf{P}}^{2}}{{\mathbf{E}}_{\mathbf{P}} {\mathbf{I}}_{\mathbf{P}}} , \frac{{\mathbf{M}}_{\mathbf{P}}}{{{\rho }}_{\mathbf{s}} {\mathbf{D}}_{\mathbf{P}}^{2}} , \frac{{\mathbf{M}}_{\mathbf{P}} {\mathbf{D}}_{\mathbf{P}}^{4} {{\omega }}^{2}}{{\mathbf{E}}_{\mathbf{P}} {\mathbf{I}}_{\mathbf{P}}} , \frac{{{\omega }}^{2} {\mathbf{D}}_{\mathbf{P}}}{\mathbf{g}}\right)$$
1
Where
y is a displacement of pile;
DP is the diameter of pile;
Ep is the modulus of elasticity of piles;
Es is the modulus of elasticity of soil;
Ip is the moment of inertia of pile;
Es is the modulus of elasticity of soil;
MP is pile mass per unit length;
ρs is soil density;
Mc is pile cap mass;
M is pile mass per unit length;
F is applied load;
ω is the frequency of oscillation; and
g is the acceleration due to gravity.
The scale effect of the model and prototype of the pile and pile cap characteristics are given in Eq. 2 to Eq. 12.
$$\frac{\mathbf{y}}{{\mathbf{D}}_{\mathbf{P}}}=\frac{{\mathbf{E}}_{\mathbf{P}} {\mathbf{I}}_{\mathbf{P}}}{{\mathbf{E}}_{\mathbf{s}} {\mathbf{D}}_{\mathbf{P}}^{4}}$$
2
$$\frac{\mathbf{y}}{{\mathbf{D}}_{\mathbf{P}}}= \frac{{\mathbf{M}}_{\mathbf{P}}}{{{\rho }}_{\mathbf{s}} {\mathbf{D}}_{\mathbf{P}}^{2}}$$
3
$${\lambda }=\frac{{\mathbf{L}}_{\mathbf{M}}}{{\mathbf{L}}_{\mathbf{P}}}= \frac{{\mathbf{D}}_{\mathbf{M}}}{{\mathbf{D}}_{\mathbf{P}}}$$
4
Where
λ is length scale factor;
LM is the model length;
LP is the prototype length;
DM is the model diameter;
DP is the prototype diameter.
$${\left(\frac{{\mathbf{E}}_{\mathbf{P}} {\mathbf{I}}_{\mathbf{P}}}{{\mathbf{E}}_{\mathbf{s}} {\mathbf{D}}_{\mathbf{P}}^{4}}\right)}_{\mathbf{M}}= {\left(\frac{{\mathbf{E}}_{\mathbf{P}} {\mathbf{I}}_{\mathbf{P}}}{{\mathbf{E}}_{\mathbf{s}} {\mathbf{D}}_{\mathbf{P}}^{4}}\right)}_{\mathbf{P}}$$
5
$${\left(\frac{{\mathbf{E}}_{\mathbf{P}} {\mathbf{I}}_{\mathbf{P}}}{{\mathbf{E}}_{\mathbf{s}} }\right)}_{\mathbf{M}} {\mathbf{D}}_{\mathbf{P}}^{4}= {\left(\frac{{\mathbf{E}}_{\mathbf{P}} {\mathbf{I}}_{\mathbf{P}}}{{\mathbf{E}}_{\mathbf{s}} }\right)}_{\mathbf{P}} {\mathbf{D}}_{\mathbf{M}}^{4}$$
6
$${{\lambda }}^{4}=\frac{{\mathbf{D}}_{\mathbf{M}}^{4}}{{\mathbf{D}}_{\mathbf{P}}^{4}}={\left(\frac{{\mathbf{E}}_{\mathbf{P}} {\mathbf{I}}_{\mathbf{P}}}{{\mathbf{E}}_{\mathbf{s}} }\right)}_{\mathbf{M}}/{\left(\frac{{\mathbf{E}}_{\mathbf{P}} {\mathbf{I}}_{\mathbf{P}}}{{\mathbf{E}}_{\mathbf{s}} }\right)}_{\mathbf{P}}$$
7
A laboratory model was designed to simulate the behavior of three types of suggested foundations and get information about the behavior of soil under applied load of building. Depending on Young’s modulus and moment of inertia, the prototype is converted from steel and aluminum materials to equivalent concrete material, so the full scale changed from steel material for plate and aluminum material for pile shafts into concrete material for the both. Esoil = 12 MPa, Esteel = 200 GPa, Ealumimum = 69 GPa, and Econcrete = 24 GPa.
$${{\lambda }}^{4}= {\left(\frac{{\mathbf{D}}_{\mathbf{M}}}{{\mathbf{D}}_{\mathbf{P}}}\right)}^{4}=\frac{3.678\times {10}^{-5}}{{\left(\mathbf{E}\mathbf{I}\right)}_{\mathbf{P}}}$$
8
$${\lambda }=\frac{{\mathbf{D}}_{\mathbf{M}}}{{\mathbf{D}}_{\mathbf{P}}}=\frac{0.019}{0.66}=0.028$$
9
Prototype scale = \(\frac{1}{{\lambda }}=\frac{1}{0.0285}=35\) (10)
Prototype scale = Model scale/Scale factor.
$${{\lambda }}_{2}= \frac{{\mathbf{B}}_{\mathbf{s}\mathbf{t}\mathbf{e}\mathbf{e}\mathbf{l}}}{{\mathbf{B}}_{\mathbf{c}\mathbf{o}\mathbf{n}\mathbf{c}\mathbf{r}\mathbf{e}\mathbf{t}\mathbf{e}}}$$
11
$${{\lambda }}_{3}= \frac{{\mathbf{B}}_{\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{m}\mathbf{i}\mathbf{n}\mathbf{u}\mathbf{m}}}{{\mathbf{B}}_{\mathbf{c}\mathbf{o}\mathbf{n}\mathbf{c}\mathbf{r}\mathbf{e}\mathbf{t}\mathbf{e}}}$$
12
Where
Bsteel is the steel plate width;
Bconcrete is the concrete raft width;
Baluminum is the diameter of aluminum shaft.
a) Raft footing (Pile cap)
The value of \({\lambda }_{2}\)is 0.316, thus the width of square raft footing is equal to 15 m and thickness of raft is 0.45 m.
b) Pile shafts
The value of \({\lambda }_{3}\) is 0.58, thus the diameter of the pile shaft is equal to 1.2 m and the length of the pile shaft is 19 m and 16 piles are used below the pile cap with 0.3 m diameter. Figure 3 explains (a) raft footing of building rested on improved soil by lime piles; (b) building foundation plan and superstructure, and (c) piled foundation system. The soil layer properties obtained from experimental works are unit weight is 19.3 kN/m3, and the allowable bearing capacity of soil and used in the design of foundations is 47 kPa.