Centrifuge Modeling of Seismically Induced Uplift for the BART Transbay Tube

The in situ cone penetration tests (CPT) and sampling of the fill materials around the tunnel are described by Fugro West, Inc. (2007a, b, 2008). Along with data from these investigations and analysis of the documented original construction procedures and specifications, the properties of the backfill materials and the idealized longitudinal cross sections along the TBT were determined and are summarized in Table 1.

Because the tunnel is approximately 5.8 km in length, and it passes near a port facility, Yerba Buena Island, and a shipping channel, there is a variety of geological conditions along the alignment of the tunnel. For the purpose of evaluating the TBT vulnerability to uplift, the alignment was divided according to the prevailing soil conditions into five primary zones. The zoning mainly reflected differences in the stiffness of the clay surrounding the trench and the thickness, depth, and type of overburden. The two centrifuge tests, JCC01 and JCC02, were designed to model two different subsurface conditions representative of the majority of the alignment. Fig. 2 shows the idealized cross section for the purpose of centrifuge testing. The primary difference between the two tests is the natural material (labeled “Trench Clay” in Fig. 2) into which the trench was excavated. For JCC01, the native prototype soil is a stiff, overconsolidated, low-plasticity silty clay in the Merritt-Posey San Antonio (MPSA) formation. For JCC02, the native “Trench Clay” is a normally consolidated to lightly overconsolidated, high-plasticity clay known as Young Bay Mud (YBM). The difference in strength of these two materials was very significant; the Young Bay Mud was soft enough that the bottom heave mechanism [Fig. 1(c)] was expected to be significant, whereas the MPSA material was not expected to undergo significant permanent deformations.

To decide the scale factor of the centrifuge tests, several goals were considered: (1) the model dimensions should be as large as possible so that important details could be included in the experiment; (2) the model must fit in the selected model container; and (3) boundary effects owing to the container boundaries should not dominate the model behavior. Considering these factors, a scale factor of $1:40$ was chosen for these two centrifuge tests. Table 2 lists the scale factors for different physical quantities. All results presented in this paper are presented in prototype scale units unless otherwise indicated.

Two model containers at the UC Davis Centrifuge facility—the rigid container and a flexible shear beam container—were considered in the experiment design phase. FLAC version 6.0 (Fast Lagrangian analysis of continua (FLAC)) simulations were performed to assess the extent of boundary effects for both types of containers. The FLAC mesh for the simulation in a “stiff” zone is shown in Fig. S2. Preliminary numerical analyses performed to facilitate experiment design indicated that the model in the rigid container would capture the key features of the system’s response, both qualitatively and quantitatively. The rigid container was selected because it has transparent side windows that would enable cameras to record the tunnel movement during the test.

The model tunnel segments were machined from solid polyvinyl chloride (PVC) to the shape of the prototype tunnel. Because there were concerns about the effect of side wall friction from the model container on uplift behavior, the tunnel was made of three independent segments (east, central, and west), separated from each other and the windows by grease and a sheet of Teflon. Grease was retained in the gap between the segments and windows by bands of latex visible in Fig. 3. Placement of the central segment is shown in Fig. 3. It is difficult to precisely quantify the undesirable wall friction. Since the displacements of each segment were not identical, however, and the observed relative movement at the tunnel-window interface was greater than the relative movement between the adjacent tunnel segments, it appears that the friction at the windows was not excessive. Before being placed in the model container, the unit weights of the tunnel segments were measured by submersion in water to be $10.62\mathrm{kN}/{\mathrm{m}}^3$ for the central segment, $10.41\mathrm{kN}/{\mathrm{m}}^3$ for the east segment, and $10.67\mathrm{kN}/{\mathrm{m}}^3$ for west segment.

In the first centrifuge test, JCC01, the trench material was modeled after the stiff MPSA silty clay. This stiff clay was modeled by compacted Yolo Loam, a locally available low-plasticity silty clay. The requirements for the compaction were to achieve (1) an undrained shear strength ($s_u$) greater than 100 kPa; (2) low swell potential to avoid strength loss while the trench materials were being saturated; and (3) a high degree of saturation so that the compacted clay would not swell under the vacuum applied during saturation of the fill materials. Compaction tests, pocket penetrometer tests, and a trial to monitor swelling resulting from the vacuum saturation procedure were performed on the Yolo Loam. These tests showed that compaction at a water content of 16% using a commercially available pneumatic compaction tool would provide 98.3% saturation, sufficient strength, and negligible swell potential under vacuum saturation. The Yolo Loam was compacted in 100 mm lifts. The trench slope was carved to the desired geometry after the compaction was completed.

In the second centrifuge test, JCC02, the trench material was made of Young Bay Mud obtained from the Hamilton Air Force Base site. The clay was consolidated from slurry inside the model container using a large hydraulic consolidation press to achieve the target strength profile. Vertical wick drains, made from 8-mm-diameter rope, at 100 mm center to center spacing to facilitate consolidation. There were two layers of YBM, with the final height of each lift being about 280 mm. After the consolidation was completed, the rope/wick drains were removed, and the trench was carved into the YBM to the desired geometry. The consolidation pressures for the bottom and top layer were 150 kPa and 85 kPa, respectively, to produce a lightly overconsolidated soil profile.

The gravel foundation course and gravel fill were modeled using Monterey $0/30$ sand, and the sand fill was modeled with Nevada sand. Key properties and element cyclic behavior of both sands have been characterized by others including Arulmoli et al. (1992) and Kammerer et al. (2000, 2004). Dry pluviation techniques were used to place the backfill materials. The sand was overpluviated into the trench, and then excess sand was removed using a vacuum to achieve the desired geometry. Table 3 lists the properties of Nevada and Monterey $0/30$ sand in JCC01 and JCC02. The as-built relative densities were slightly different from the targeted relative densities in both centrifuge tests, but the as-built relative densities were less than 50%.

After placement of backfill sands, the sands were saturated with a viscous pore fluid consisting of a dilute solution of hydroxylpropyl methylcellulose in water. The target viscosity was 10 times greater than that of the pure water. Achieved viscosities determined by testing the pore fluids with a viscometer are reported in Table 3. In preliminary numerical analyses, the tunnel uplift was found to be sensitive to the ratio of the permeabilities of the gravel fill and sand fill. The target ratio based on site investigations and preliminary numerical analyses was 20 ($1/0.05$ from Table 1), and the achieved ratio was 15 ($0.88/0.057$ from Table 3). The saturation process is described in the electronic Supplemental Data section of this paper; saturation tubes are shown in Fig. S3.

The surficial mud layer in Fig. 2 is a barrier that prevents water pressure dissipation from the top of the backfill materials. Yolo Loam mixed in a slurry/paste with tap water as the pore fluid at a water content of 1.2 times the liquid limit was used to model this layer. This layer was placed after the sand was saturated, and it was allowed to become normally consolidated during the spinning of the centrifuge prior to shaking the model.

The strategy for placement of accelerometers, pore pressure transducers, displacement transducers, colored sand columns, colored sand layers, and cameras is described as follows: (1) the vertical and horizontal movements of all three segments of the model tunnel were recorded using vertical and horizontal displacement transducers. The bodies of displacement transducers (DTV1 to DTV4) were attached to an instrumentation rack which, in turn, was attached to the model container; the probes of the displacement sensors were attached to “flags” (as shown in Fig. 4), which consisted of fairly stiff sheet metal attached to the top surface of the tunnel segments; (2) the deformation pattern of backfill materials surrounding the model tunnel was documented by photographing the colored sand columns and layers during posttest excavations; (3) a vertical array of pore pressure transducers was used to measure the distribution and dissipation of pore pressures in the trench backfill materials; (4) a dense array of pore pressure sensors installed in the central tunnel segment was used to compute hydraulic gradients and flow of water under the tunnel; (5) dynamic response of the backfill materials was monitored using a vertical array of accelerometers from bottom to top of the backfill materials; (6) dynamic response of each tunnel segment was monitored by a sufficient number of accelerometers to define the six degrees of freedom; and (7) in JCC02, displacement transducers were used to monitor the bottom heave of the trench material (clay below the foundation course). A pad with an extension rod was placed on top of the clay and the extension rod passed through a 20-mm-diameter vertical hole drilled through the middle of the tunnel. The rod extended through the tunnel and above the ground surface. Linear potentiometers mounted on the instrumentation rack monitored the vertical movement of this rod to determine the bottom heave of the clay. The 20-mm-hole allowed for lateral movements of the tunnel relative to the rod and was backfilled with bentonite mud to seal it around the rod and prevent drainage of pore pressures through the hole.

Locations of all sensors in JCC01 are nearly identical to those in JCC02. Hence, the sensor locations for JCC02 shown in Fig. 4 adequately represent the sensor locations for both tests. Fig. 4 includes names of sensors for which data are presented in this paper. The detailed locations of all sensors in both tests are reported by Chou et al. (2008a, b).

During both centrifuge tests, the models were shaken by several different shaking events. The event number, name, and PGA for each shaking event are listed in Table 4. A small step wave event in both tests was used to verify that all systems and sensors were properly functioning. The models were also subject to a ground motion named “LP,” which simulated the shaking from the 1989 Loma Prieta event that the actual BART TBT experienced without suffering damage. The “TCU” event is the main target ground motion for this project and was obtained by spectral matching of the recordings from the TCU078 station during the 1999 Chi-Chi earthquake in Taiwan to the design spectrum for the project (Mark Salmon, personal communication, Jun. 30, 2006). The motion was further modified for use in the centrifuge experiment by filtering out the range of frequencies in which resonance of the centrifuge arm could occur. The Joshua Tree event, obtained by processing (filtering and scaling) motions at the Joshua Tree station during the 1992 Landers earthquake, was used in the second model test to check the behavior during a different long-duration design ground motion. Before the full amplitude LP, TCU and Joshua Tree events, smaller amplitude versions of these shaking events were applied to the models in order to calibrate the shaker controllers.

Fig. 5 shows data obtained from one pore pressure sensor and one displacement transducer in JCC01 (see Fig. 4 for sensor location) to illustrate the sequence of events in model time scale. Fig. S4 presents similar results for JCC02.

Figs. 6 and 7 and Figs. S5, S6, and S7 are pictures taken during the model dissection after JCC01 and JCC02. Fig. 6 shows the blue colored sand columns that were installed vertically during model construction in JCC01; it is apparent that soil near the bottom of the tunnel moved toward the bottom of the tunnel during shaking. Fig. S5 shows the blue colored sand columns in JCC02. This deformation pattern is consistent with the ratcheting mechanism [Fig. 1(a)] and the first mechanism described in Koseki et al. (1997). Because of uplift of the tunnel, the soil near the top of the tunnel moved away from the tunnel. Fig. 7 shows photographs of the gravel foundation course after removal of the central segment of the model tunnel. In Fig. 7(b) (JCC02) a 3-m-wide (8-cm-model scale) water gap (see shadow under ruler) apparently developed under the centerline of the tunnel, but no water gap was apparent in JCC01 [Fig. 7(a)]. This observation is consistent with the pore water migration mechanism described by Koseki et al. (1997) and illustrated in Fig. 1(b). In JCC01, the clayey soil below the trench was a stiff clay for which bottom heave was insignificant during the test. The bottom heave mechanism was significant in JCC02 because of the relatively soft Young Bay Mud trench material. Fig. S6 shows the excavated trench and a plot of the trench surface elevation before and after testing. Fig. S7 shows the model configuration and deformations caused by the earthquakes in before and after photographs for test JCC01. Fig. S7 clearly shows that the tube moved up, and soil beside the tube settled down.

Fig. 7 also shows black colored sand lines that originated at the bottom corner of the tunnel, indicating approximately 3 m in JCC01 and 1 m in JCC02 of maximum lateral soil deformation toward the tunnel centerline. In Fig. 7(a), the maximum movement of the black colored sand along the surface of the gravel foundation course was about 3 m. The black colored sand may have been carried along the interface between the tunnel and the gravel foundation course by erosion and smearing. The average movement of the black sand along the surface was significantly less than 3 m. The large movement of the sand at the interface between the tunnel and the gravel foundation course for both JCC01 and JCC02 is evidence that flow was a result of ratcheting and not the viscous flow of liquefied sand mechanism. If the flow was viscous, the displacement profiles would be approximately parabolic with zero relative displacement at the interface.

Fig. 8 shows isochrones and time histories from selected sensors during the TCU event in JCC01. Fig. S8 shows a similar set of plots for JCC02; although results are similar, there are some notable differences in behavior of JCC01 and JCC02, but both plots could not be included in the printed paper because of space limitations. Figs. 8(a-d) show isochrones of the excess pore pressure at selected times indicated in the legend, and time series plots are shown in Figs. 8(e-h). Fig. 8(a) presents data from the vertical array (P4, P9, P10, P12, and P18) in the soil near the tunnel; the pore pressure is observed to oscillate, and the peak values are very close to the initial effective overburden stress beside the tunnel indicated by the black straight line. Figs. 8(b) (PT1, 8, 10, 11, and 12) and 8(d) (PT7, 9, and 13) show that pore pressure recorded at the sides of the tunnel oscillate and approach the free field initial overburden and that the bottom sensor records a smaller pressure because it is under the corner of the tunnel where the overburden is lower owing to the low density of the tunnel; this would result in water flow toward the bottom of the tunnel. Fig. 8(c) shows pore pressure distributions on the base of the tunnel (PT1, 2, 3, 4, 5, 6, and 7) which generally had a U shape during the shaking, indicative of a hydraulic gradient toward the middle of the base of the model tunnel; water (and soil) are drawn under the tunnel to fill the space vacated by the uplifting tunnel. The selected isochrones times from $\mathrm{\text{Time}}=15.1$ to 15.3 s were chosen to illustrate that pore pressures oscillated significantly and quite rapidly during shaking, and the one for 117.8 s shows that the less permeable backfill maintains high pore pressures long (about 70 s, in this case) after shaking, but excess water pressures [see Figs. 8(a-c)] are very uniform in the more permeable fill (gravel in prototype). After shaking, at times of 100 to 120 s, the distribution became a flat line very close to the average initial vertical effective stress under the tunnel, indicated by the dashed black line in Fig. 8(c). The pore pressure at the centerline (PT5) in Fig. 8(c) actually increases after shaking because the hydraulic gradient drawing water under the tunnel nearly vanishes when the upward velocity of the tunnel reduces [see DTV1 in Fig. 8(f)]. Figs. 8(e, f) show horizontal accelerations which extend over about 35 s of strong shaking. The horizontal acceleration of the tunnel (Sensor AH13) is much smaller than the base acceleration for JCC01. Similar behavior in JCC02 is shown in Figs. S8(e) and (f). Especially for JCC02, however, the tunnel acceleration (curve labeled “Tube Hor Acc”) is quite similar to the acceleration of the liquefied soil (Sensor AH19 for JCC01 and AH9 for JCC02). This indicates that the relative movement between the tunnel and the backfill was relatively small in JCC02. The U-shaped pore pressure profiles along the base of the tunnel with a stiff clay trench [Fig. 8(c)] are more exaggerated than those for the soft clay trench [Fig. S8(c)]; this difference is attributed to the smaller strain demands in the foundation course of JCC02 owing to isolation by the soft clay. Figs. 8(g, h) show vertical displacement of the tunnel (DTV1) and excess pore pressures at two points along the base of the tunnel at two different time scales. DCV1 in Figs. S8(g) and (h) shows the heave of the soft clay at the base of the trench; a noticeable part of the uplift of the tunnel was caused by the clay heave. Fig. 8(h) shows the generation and dissipation of excess pore pressure underneath the model tunnel before and after the shaking event. The uplift of the tunnel during shaking and the settlement of the tunnel caused by the dissipation of excess pore pressure after shaking are also indicated in Fig. 8(h).

Fig. 9 shows calculated displacement trajectories for the major shaking events in JCC01 and JCC02. In Fig. 9, the vertical axis represents the vertical movement recorded from the vertical displacement transducers, and the horizontal axis represents the horizontal movement of the tunnel obtained by integration of relative horizontal acceleration of the tunnel with respect to the top of the clay just below the trench. Because the accelerometers can only provide accurate data at frequencies greater than 0.2 Hz (prototype scale), a high-pass, zero phase shift filter was applied in the frequency domain to eliminate the inaccurate low frequency data. The resulting data present an accurate view of cyclic behavior of the tunnel but do not indicate the permanent horizontal displacements; permanent horizontal displacements were 4 mm and 160 mm for JCC01 and JCC02, respectively. Fig. 9 shows that the resultant uplifts in the large TCU events were similar in JCC01 and JCC02, even though the dynamic horizontal relative displacements are quite different. It should be noted that the horizontal displacement of the tunnel relative to the trench is proportional to the average shear strain in the gravel foundation course layer. From Fig. 9, cyclic horizontal relative displacements are seen to be about 0.12 m for JCC01 and about 0.05 m for JCC02. As the gravel foundation course is about 1 m thick, the shear strains may be estimated by the ratio of lateral displacement to layer thickness, which comes to $\pm 12\%$ in JCC01 and about $\pm 5\%$ in JCC02. Strains are thought to be smaller in JCC02 because yielding of the soft clay in JCC02 attenuated ground accelerations below the trench. The stronger stiff clay made the trench material move intensely along with the container in JCC01. As mentioned in a previous section, a water gap was found in JCC02 but not in JCC01. Figs. 8 and S8(c) indicate hydraulic gradients toward the centerline of the tunnel, so water gaps might have been expected in both JCC01 and JCC02. A possible explanation for the lack of a water gap in JCC01 is that large shear strains of the gravel foundation course in JCC01 smeared out the water gap [as indicated in Fig. 1(a)] and/or caused shear-induced dilation that absorbed the pore water as it flowed into the foundation course beneath the tunnel. Another possible explanation for the lack of a water gap in JCC01 could be that the water gap was developed in the Joshua Tree event of JCC02. The Joshua Tree event was longer but less intense than the TCU event, and the Joshua Tree motion was not imposed on JCC01. The difference in duration and intensity might have allowed more uplift owing to pore water migration and less smearing to smooth out the gap [see Fig. 1(a)]. The trajectories during the smaller shaking events (Loma Prieta, small TCU, and small Joshua Tree) are also plotted in Fig. 9 (see oval labeled “Other Events”), but the relative movements are so small that they are not apparent.

Figs. 10 and S11 show the spectral accelerations at different elevations for selected events in JCC01 and JCC02. From these figures, it is clear just how small the Loma Prieta event was compared with the design motions (TCU and Joshua Tree) for the tunnel. From Fig. 10, there appears to be amplification of the base motion between the base and the top of the clay (trench) below the tunnel. At the period range around 1.2 s, there is a large difference between the tunnel motion and the trench motion for JCC01, but the motions are quite similar for JCC02. This observation agrees with behavior discussed previously: the shear strains in the soft clay in JCC02 isolated the trench from the intense shaking, resulting in smaller shear strains in the gravel foundation course in JCC02 than in JCC01.