ORGANIZACIÓN DEL ERS

The dynamic centrifuge experiments of this research require direct contact between the physical model and water. Therefore, stainless steel and aluminum were selected to be used for the construction of the physical model to prevent corrosion of the model. Figure 3-24 (a) and (c) shows a photograph of SFSM along with dimensions and materials used in the construction of the model. Several properties of the prototype structure were selected to be considered in the design of the physical model. These properties are:

1. The first fixed-base natural frequency 2. Foundation bearing pressure

3. The ratio of the mass of the foundation to the mass of the superstructure 4. Width and thickness of the foundation

Figure 3-24. (a) a photograph of SFSM; (b) ABAQUS numerical model of SFSM; (c) dimensions and materials used for SFMS.

The scale factors of the centrifuge modeling were used to convert the properties from the prototype scale to the model scale. Table 3-3 summarizes the scale factors used in the design.

Table 3-3. Scaling factors to design of the Steel Foundation Structure Model (SFSM).

Quantity Scaling factor (Prototype/model)

Linear dimension 50 Density 1 Strain 1 Acceleration 0.02 Time (dynamic) 50 Frequency 0.02 Displacement 50 Velocity 1 Stress 1 Stiffness 1 Axial force 2500

The columns of the physical model should be designed in a way that they would stay elastic when a suite of target seismic motions is applied to the physical model. Thus, this condition was considered as one of the criteria for the design. Furthermore, the factor of safety of the physical model against the overturning should be sufficient enough that the model would not overturn when the model is excited with the seismic motions. The two other criteria, which should be considered in the design, are related to the settlement and the bearing capacity of the physical model during the centrifugation. The bearing pressure of the model should be selected in the way that when the model is spun, bearing capacity failure and excessive settlement will not occur.

Dimensions of the components of the physical model were altered until all the mentioned criteria were satisfied with error from target values less than five percent. A significant amount of hand calculation was performed for the design; furthermore, the natural frequency of trials was estimated by performing numerical modeling using the ABAQUS program (Simulia, 2012). The

design consists of checking several trials. Figure 3-24 (b) shows a photograph of a numerical model of the final trial performed for designing of SFSM. When the design was completed, all components of the model were drawn in AutoCAD program.

After the construction of the model, dimensions of the constructed model were compared with target dimensions, and strong similarities were observed between actual dimensions and target dimensions of the model. The modal hammer test was performed to measure the actual natural frequency and damping of the model. It is critical to constrain the lateral and rotational degree of freedoms of the foundation of the model in all directions to measure the fixed-base natural frequency of the physical model. The following method was implemented to create the mentioned condition.

1. The bottom part of the foundation was detached from the physical model. 2. The rest of the physical model was connected to a steel plate.

3. The steel plate was used to secure the physical model to the large metal plate of the 1-g shake table of the University of New Hampshire. The 1-g shake table was only used to constrain movements of the base of the physical model.

Figure 3-25 shows the test setup that was used to measure the fixed-base natural frequency of the physical model. It can be seen that the physical model was connected to the steel plate, and the steel plate was secured to the shake table. The physical model was instrumented with a set of accelerometers, as shown in the figure. The physical model was hit with a modal hammer, and the accelerometers recorded the model vibration at various locations and direction. Figure 3-26 (a) shows the horizontal vibration of the superstructure part of the physical model when the model

Figure 3-25. Photograph of modal hammer test to measure natural frequency and the damping ratio of the physical model.

The acceleration time history was converted from the time domain to the frequency domain to find the natural frequency of the physical model, as shown in Figure 3-26(b). According to the figure, the fixed-base natural frequency of the model was about 168 Hz (in the model scale). The damping ratio of the model was also estimated at 0.3%, using the logarithmic decremented method (Chopra, 1995).

The properties of the physical model, SFSM, are presented in Table 3-4 in the prototype scale. Furthermore, Veletsos and Nair (1975) suggested a set of dimensionless parameters, that significantly control the SFSI effects. Some of these parameters were calculated for SFSM and are presented in the table.

Figure 3-26. Horizontal vibration of the superstructure of SFSM, when it is excited by a shock of a modal hammer: (a) acceleration time history; (b) Fourier amplitude spectra.

Table 3-4. Properties and SFSI-controlled parameters of SFSM on the prototype scale.

Properties Value

Foundation width (m) 3.50

foundation thickness (m) 0.96

Base pressure (kPa) 143.39

𝑓̅ (Hz) 3.37

𝑚𝑓⁄𝑚 0.50

ℎ 𝑟⁄ 1.51

𝜎 19.35

𝛾 1.98

𝜎 = 𝑉𝑠, 𝑎𝑣𝑔⁄(𝑓ℎ), ratio of structure-to-soil stiffness 𝛾 = 𝑚 (𝜌𝜋𝑟⁄ 2ℎ), the ratio of sstructure-to-soil mass

𝑉𝑠, 𝑎𝑣𝑔= average shear wave velocity of soil 𝑓̅ = fixed-base first natural frequency of the structure

ℎ = height of structure 𝜌 = soil density

𝑚 = mass of superstructure 𝑚𝑓= mass of foundation

𝑟 = √𝐴𝑓⁄𝜋, equivalent radius of foundation 𝐴𝑓 = Area of foundation

It is worth mentioning that the friction between the physical model and the soil should be sufficient to prevent excessive slippage between the foundation and soil when a specimen is excited by a seismic motion. Therefore, medium-coarse sand particles, shown in Figure 3-27, were glued to the bottom of the foundation of the physical model.

Figure 3-27. Sample of medium-coarse sand glued to the base of the physical model to increase friction between the model and the soil.