Attaching tactile pressure sensors to box culvert model. 

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... ␴ a is atmospheric pressure (= 100 kPa), ␴ 1 is vertical effective stress, E eod is oedometer modulus, E eod a is normalized stiffness, and v e is a coefficient. The model thin and thick culvert cases are also plotted in Fig. 2 to show the range of relative stiffnesses that can be achieved using these two sections. The graphs show that the two chosen sections have up to one order of magnitude difference in relative stiffness in terms of EI values. Strain gauges (Vishay 350 Ohms) were placed on the top slab and side wall to measure strains on the outside and inside faces of the box culvert. The strain measurements were then converted to bending moments using calibration factors. Two tactile pressure sensors (Tekscan model number 5101) were used to measure the normal soil pressure on the culvert. One of the pressure sensors was placed on the culvert top surface to measure vertical pressure of the soil and one adjacent to the side to measure horizontal pressure. The tactile pressure sensor used can measure up to 1034 kPa (150 psi) and can record up to 225 frames per second. The square sensing area is 111.8 mm × 111.8 mm. To protect the sensor from damage due to friction with the sand particles, it was laminated with a plastic sheet and then covered with a Teflon sheet using vacuum grease. The dimensions of the centrifuge rigid box container were 876.3 mm (length L ) × 368.3 mm (width W ) × 355.6 mm (height H ). The target relative densities for the test sand were 50% and 90%. The sand was placed in the centrifuge box in 25.4 mm thick layers. The volume of each sand layer was calculated for both 50% and 90% relative densities, knowing minimum and maximum density values. After several trials, it was concluded that placing the sand using the raining technique (air pluviation) could achieve the 50% relative density. To achieve 90% relative density, each sand layer was additionally tamped after air pluviation. Figure 3 shows the configurations of the test models. Four main test configurations were performed. Tests 1 and 2 involved the thick culvert with sand densities of 90% and 50%, respectively, while tests 3 and 4 were for the thin culvert and the sand densities were 50% and 90%, respectively. The total height of the sand model was 330.2 mm, simulating 19.812 m at a prototype scale of 60 g . The models were built after placing the empty centrifuge box on the centrifuge platform to avoid any disturbance in the sand prior to testing. The tactile pressure sensors were attached to the box culvert model using double-sided tape as shown in Fig. 4 and the culvert model was then placed at the pre-determined height within the box and levelled in its position. All sensors used in the model were checked and connected to the data-acquisition sys- tem. The centrifuge was then accelerated incrementally and held at the following acceleration levels, to check stability of the sensor readings: 10 g , 20 g , 30 g , 40 g , 50 g , and 60 g . Data from all sensors were recorded continuously during the test. The SCI parameters are in terms of the bending moments and soil pressures, because they are important for engineering design. The interaction between the box culvert and the sand was evaluated considering the results obtained from the strain gauges and tactile pressure sensors. The static bending moment was derived using the strain gauge data recorded at 60 g . The strain data was measured on the top slab and side wall. At each strain gauge location, the strain was recorded on the inside and outside faces of the culvert. Using the measured strains and calibration factor, the bending moment profiles were obtained. Due to the symmetry of the bending moment on the top slab and because there was a limited number of strain gauges used, mirror points of each strain gauge location were applied to produce double the number of bending moment points. That was not possible on the side wall due to lack of symmetry along the wall. The results are presented in the form of comparisons to infer the effect of the sand density and culvert thickness on the SCI as illustrated in the following sections. The effect of soil density on the culvert bending moments is demonstrated by comparing the prototype scale results (at 60 g ) of test 1 (thick, Dr = 90%, where Dr is the relative density) with test 2 (thick, Dr = 50%) (and test 3 (thin, Dr = 50%) with test 4 (thin, Dr = 90%)), as they have the same culvert thickness but different soil density. Figure 5 shows that for the thin culvert (tests 3 (thin, Dr = 50%) and 4 (thin, Dr = 90%)), the bending moment decreased as the soil density (and hence its elastic modulus) increased. On the other hand, the bending moments for tests 1 (thick, Dr = 90%) and 2 (thick, Dr = 50%) are almost the same for the top slab, but differed slightly at the centre of side wall. This indicates that the thick culverts were relatively rigid, and hence the soil pressure and bending moment values were not affected by the soil density. Figure 6 illustrates the effect of culvert thickness on the bending moments at the culvert top slab and side wall. Tests 1 (thick, Dr = 90%) and 4 (thin, Dr = 90%) (and tests 2 (thick, Dr = 50%) and 3 (thin, Dr = 50%)) are compared as they have the same soil relative density values but different culvert thicknesses. Generally, the bending moments at the top slab decreased as the culvert thickness decreased. This is attributed to the soil arching effect, i.e., as the culvert thickness decreases, its displacement increases and hence reduces the imposed loads. The soil prisms on either side of the culvert will take some of the soil pressure and therefore, reduce the pressure on the culvert. The bending moment of side walls for the thick culvert was positive throughout the height. As the culvert thickness decreased, the bending moment decreased, resulting in some negative moment near the centre, which is also attributed to soil arching. Soil contact pressures on the culvert were used to determine the SCI factors. These pressures were evaluated using strain gauge data and tactile pressure sensors. The measured strain values were converted to bending moments by applying calibration factors, which in turn were curve- fitted with appropriate polynomial functions. The equations of the fitted curves were then subjected to double derivation to obtain the soil pressure. The Tekscan tactile pressure sensors were calibrated using the methods developed by El Ganainy et al. (2014) to achieve accurate, repeatable results. The equilibration was performed by applying uniform pressure on the active sensors. This accounted for the compliance of the sensors at the interface. The pressure sensors were calibrated with two steel plates: the sensor was inserted between the plates and the load was applied using air pressure. During centrifuge testing, however, the sensors experienced two conditions that werere different than the loading state in the calibration machine: the test was run at 60 g not 1 g and the test pressures occured between two different materials (i.e., sand and aluminum) not two steel plates. Therefore, the calibration was conducted inside the centrifuge box by placing the sensors at the base of the centrifuge aluminum container and by placing the test sand over them as would occur in the actual centrifuge tests. The tactile pressure sensors measured the soil pressure on the top slab and side wall of the culvert. By applying the equilibration and calibration files to the recorded data by using the I-Scan (2006) software, the ...