Materials and Methodology 74 . ( )
v d
acc g g r
(3.4)
1.0 0.00765 ; 9.15
rd z for z m (3.5)
1.174 0.0267 ; 9.15 23
rd z for z m (3.6)
. ( )
2 2
d v d
acc g g r
(3.7)
where, acc.(g) is the acceleration time history, σv is the total overburden vertical stress and rd is the stress reduction factor (Eqns. 3.5-3.6). Since, the strong motions, used in this study, were recorded at ground level, rd is considered to evaluate the stress at any particular depth ‘z’
(Youd et al., 2001). The different effective confining stress reflects that the soil specimens located at different confining depths below the ground level.
Table 3.7 Investigating parameters of the irregular seismic excitations Soil Irregular
excitation PGA (g) Relative density Dr (%)
Confining depth (m)
BS
Bhuj 0.103
30 5, 10, 15
Tezpur 0.360
Kobe 0.834
Bhuj 0.103
30, 60, 90 10, 15 Tezpur 0.360
Kobe 0.834
Bhuj
0.103 60 10
Tezpur Kobe Bhuj
0.360 60 10
Tezpur Kobe
Materials and Methodology 75 relative densities (Dr = 30% and 90%) and three σ′c (50 kPa, 100 kPa and 150 kPa). Before starting the test, fixity and calibration of the on-sample LVDTs are important tasks to achieve accurate response. The following sections deal with the assembly of the on-sample LVDTs to the specimen and calibration as well.
Assemblage of on-sample LVDTs on the specimen
Fig. 3.21 shows the photograph and schematic diagram of the assembly of submersible on- sample LVDTs to the soil specimen for the measurement of local strains. The attachment consists of two axially oriented LVDTs and one radially oriented LVDT; the entire attachment was placed at the mid-height of the specimen shown in Fig. 3.21a (Kumar et al., 2016).
Simultaneous measurement of both axial as well as radial deformations would provide the Poisson’s ratio of the soil specimen at different strain levels. Each axial transducer was initially fixed to the mounting block with the help of O-ring (Fig. 3.21a) and, then both axial transducers, along with the mounting blocks, were fixed to the specimen, with the aid of rubber bands. The axial LVDTs were placed diametrically opposite to each other, as shown in Fig. 3.21.
The rubber bands used to hold the mounting blocks in position has a width approximately 1 cm (shown in Fig. 3.21b), and are made up of the same material as the confining membrane used for the test specimen. The mounting blocks of each LVDT displace relative to one another as the specimen deforms, and allow free rotation to ensure accurate measurements of axial displacements during tests. As per the recommendation given in ASTM D3999, the thickness of membranes should not exceed 1% of the diameter of the specimen (i.e. 0.7 mm for the sol specimen of diameter 70 mm) such that no significant additional stresses are generated within the specimen. The thickness of the rubber band and the rubber membrane, as used for the present investigation, was in the range of 0.2–0.3 mm, which is well within the stated limit, thus eliminating the necessity of any membrane correction. The local axial strains in the specimens were estimated as the ratio of the average displacement measured by axial transducers to the
Materials and Methodology 76 gauge length (i.e. initial distance between mounting blocks).
Fig. 3.21 (a) Soil specimen with on-sample LVDTs (b) Schematic diagram for the assemblage and fixities used in local strain measurement
On-sample LVDTs: Specification and calibration
Two LVDTs (LVDT1 and LVDT2) to measure axial deformation and one LVDT (LVDT3) for measuring radial deformation have been used as on-sample LVDTs for the determination of local strains. The on-sample LVDTs, used in the present study to measure the local strains, were supplied by Wykeham Farrance, and are fully functional in a water-submerged condition. The on-sample LVDTs requires a supply root-mean-square input voltage of 0.5 V–7 V r.m.s having 2-10 kHz sinusoidal frequency, while the calibrated supply voltage required is 5 V r.m.s having 5 kHz sinusoidal frequency at 30 mA power provision. Under the operating condition, the linearity or accuracy resides to 0.1% of the full range, allowing a tolerance phase shift of 10°
Radial LVDT3 Transducer holder
Mounting block Gauge length
Axial LVDT1
Axial LVDT2
Axial LVDTs
Radial LVDT
Rubber band o-ring
a
Soil
Mounting block Spring
Yoke
LVDT Screw
Actuator
External LVDT
Submersible load cell Top cap
Pedestal On-sample LVDT2 On-sample LVDT1
Gauge length Rubber membrane
Rubber band Soil
Load ram
Mounting block cap Radial LVDT
Plan and elevation of on-sample LVDTs
b
Materials and Methodology 77 during a 5 V–5 kHz excitation; the optimum output load is obtained as 100 kΩ. The operating temperature of the transducer lies between -20°C to +125°C, having both zero temperature and span temperature coefficients to be ±0.01% full scale/°C. The on-sample LVDT remains sealed by an outer cable sleeve and can remain fully functional under an operating pressure 3.4 MPa.
The on-sample LVDTs have been calibrated using the Geodatalog logger. The on-sample LVDTs have their own electrical zero and can be manually adjusted before starting the calibration. The calibration charts for the on-sample LVDTs are shown in Fig. 3.22, depicting the correlation between the measured values and predicted values.
Fig. 3.22 Calibration curve of on-sample LVDTs
It can be observed that the predicted and measured voltages have excellent agreement and correspond to a negligible scatter on a 45º line. The measuring capacity of the axial and radial on-sample LVDTs are 0–10 mm. After attaching to the specimen, to measure the local strains at the start of the testing, LVDT readings were manually adjusted to zero. The water- submersible on-sample LVDTs allow the measurements of axial and radial deformations of the soil specimens to accuracy of 1 micron with any of the 16 bit data logging systems. The total buoyant weight of water-submerged on-sample LVDTs is 68 g, thus imposing an average
-6 -4 -2 0 2 4 6 8 10
0 2 4 6 8 10 12
6 2
3: 5.067 1.016 1.989 10
LVDT y x x
5 2
2 : 1.725 1.259 8.161 10
LVDT y x x
5 2
1: 1.758 1.235 5.069 10
LVDT y x x
On-sample LVDT3 Measured data (V) Fitted data (V) On-sample LVDT1
Measured data (V) Fitted data (V) On-sample LVDT2
Measured data (V) Fitted data (V)
Measured and fitted data(V)
Ref. (mm)
Materials and Methodology 78 uniform stress of approximately 0.18 kPa on the central cross-section (70 mm diameter) of the undeformed specimen. Since, these excess stresses sue to the on-sample LVDTs are negligible in comparison to the range of applied effective stresses, the weight corrections were not accounted in the present study. Similar observations regarding the weight of the on-sample transducers have been mentioned by Cuccovillo and Coop (1997). The operating stress range of water-submersible on-sample LVDTs were is 0–3.4 MPa. Since, the applied confining stresses (range: 50 kPa–150 kPa), for the present study, were sufficiently less than the maximum operating stress limit, the on-sample LVDTs functioned efficiently during the experimental investigations. Scholey et al. (1995) and Cuccovillo and Coop (1997) have reported that the on- sample LVDTs respond accurately up to confining stress of 2 MPa under water-submerged conditions, while the response is accurate up to 70 MPa for oil-submerged conditions. The responses of the on-sample LVDTs during saturation and consolidation were found to be insignificant.
SUMMARY
This chapter presented the details of materials used in the study, i.e. cohesive soil, cohesionless soil, and their physical characterization as per the relevant standards. The cyclic triaxial test setup, its different hardware components and instrumentations, along with their function were described. Preparation of the soil specimens and the adopted techniques were also elaborated.
Details of test parameters adopted and planning of experimental program with different testing methodologies are explained. The test methodologies followed to conduct the monotonic or cyclic tests, strain- or stress-controlled, using regular and irregular excitations, were also presented in brief. The on-sample LVDTs used in the present study to delineate the generation of local strains in the specimen is also presented. Further chapters describe the results obtained from various tests conducted as per the experimental program and planning.