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Estimating The Settlement of The Millennium Tower in San Francisco

The contents of this article are for educational and illustrative purposes only. it is not meant to criticize, judge, or give any design advice and cannot be used for such purposes.

Introduction

The Millennium tower in San Francisco was constructed at the intersection of Mission and Fremont Streets. The tower became recognizable due to its tilt and the consequent damage to its architectural and functional components. The tower is 58-story and reaches a height of approximately 180 meters. It was built between 2005 and 2009. The tower began sinking during its construction and so far, it settled around 40 cm which is 2.5 to 4 times the predicted settlement of just 4 to 6 inches (10 to 15 cm) prior to construction. The tower also experienced tilting. The reason for this tilting is likely due to multiple factors which may include the dewatering and development projects near the tower site. Repairs were proposed to stop the tower from sinking even more and reverse some of the tilting. The proposed repairs require installing multiple piles around the tower raft. These piles will extend to the bedrock sand should prevent any additional settlement. In this article, the settlement of the tower due to primary consolidation is estimated. Basic soil mechanics theories were applied to estimate the settlement along with compiled data from multiple papers, soil reports, and theses. Focus of this article is on calculating the amount of the final settlement rather than its progress through time. The layout of the tower foundation is illustrated along with the soil stratigraphy. The equivalent raft approach is proposed to calculate the settlement and compare it with the current measured settlement.


The Foundation Layout

The foundation of the Millennium Tower consists of a mat foundation that is 3 meters thick and is supported on 945 piles that are around 15 to 17 meters long (Stewart et al. 2023). The raft is located below a 4.6-meter-deep basement. The Raft is 32 m by 47 m. The pile foundations’ cross-sectional area is 35.6 cm2. The piles center-to-center spacing ranges from 1.07 m to 1.42 m. The geometry of the piled raft is shown in Figures 1 and 2.


Stratigraphy

The piles penetrate layers of sandy bay mud, upper bay mud, marine sand, lower bay mud and finally reach a layer of marine Colma sand. Underlying the Colma sand is a layer of upper old bay clay followed by lower old bay clay. The bed rock is found at an approximate depth of 74 m below surface. The bed rock is a mix of very soft and weathered shale with blocks of serpentinite and sandstone. The ground water table is located 3.5 m below ground level. The soil stratigraphy and the foundation are shown in Figures 1 and 2.

The soil properties relevant to the settlement calculations are shown in Figure 3. The coefficient of the compressibility, the reconsolidation index, and the preconsolidation pressure were recompiled from Wagner et al. (2021). The trendline shown in figure 3 is the trendline of the moving average of the data. No data was given on the initial void ratio in the paper. However, the accompanied data file to the published paper has results on the consolidation tests conducted on the subsoil. Some of these tests were reported here and are shown in figure 4. These plots along with a review of Margaret Clair (2019) were used to estimate a reasonable value for the void ratio of the soil layers. It should be noted that the data shown in Margaret Clair (2019) is general for the San Francisco area and not specific to the tower site. A plot of the variation of the void ratio with depth adopted for the settlement calculations is shown in figure 5.

Groundwater table was located at 3 m below ground level before the construction started. The groundwater table at the tower site was lowered for excavation and construction purposes. The groundwater was also lowered for multiple construction projects in the vicinity.



Figure 1: Foundation geometry across longer dimension and subsoil stratigraphy reproduced from Stewart et al. (2023)



Figure 2: Foundation geometry across shorter dimension and subsoil stratigraphy reproduced from Stewart et al. (2023)


Figure 3: Data for subsoil settlement calculation. Left: preconsolidation pressure. Middle: coefficient of compressibility. Right: coefficient of swelling. Reproduced from Stewart et al. (2023).



Figure 4: Consolidation test data reproduced from Wagner et al. (2021).



Figure 5: Void ratio of data and trendline for subsoil. Compiled from Margaret Clair (2019).


Analysis Approach

The Equivalent raft approach was used to calculate the settlement of the piled raft. The equivalent raft assumes that the forces imposed on the pile group will be transferred to a deeper soil stratum. Below that depth the stress distribution will be similar as if a raft was placed at that depth. To use the equivalent raft approach, it is needed to determine the depth of that equivalent raft. In addition, it is also needed to determine how the loads will be transferred to this equivalent raft. These two parameters depend on the type of the soil along the pile length. Four cases for the layout of the equivalent raft were reported in NAVFAC 7.02 Foundations Manual. The same four cases were also reported in AASHTO LRFD Bridge Engineering Manual.

The piles of the Millennium Tower penetrate through young bay mud and marine sand to finally reach the mid depth of the Colma sand layer. It can be reasonably assumed that the layout of an equivalent raft as provided by Duncan and A. L. Buchignani (1976) and shown in figure 6 is applicable to the Millennium Tower case. The young bay mud material represents the upper soft layer, while the marine sand and the Colma sand represent the lower firm layer. The location of the base of the equivalent raft will be two-thirds of the pile penetration depths in the marine and Colma sand layers as shown in Figure 7. This is approximately at the beginning of the Colma sand layer. The stresses beneath the raft will be calculated as a rectangular area over an elastic half-space rather than using the 2:1 method.


Figure 6: Equivalent raft concept as provided by Duncan and A. L. Buchignani (1976) and applicable to the Millennium Tower piled raft.


Figure 7: Location of the equivalent raft.


Table 1 shows the layers of the soil below the equivalent raft. The layers where consolidation is expected were divided into sublayers of thickness 0.5m. The coefficient of the compressibility, the swelling index, and the pre-consolidation pressure were calculated at mid sublayer using the trend line on the moving average. The effective stress was calculated at mid sublayer. One-dimensional consolidation theory is used to calculate the settlement of the piled raft using the properties of each sublayer. The total settlement is the sum of the settlement of the individual layers. The settlement was calculated at the center of the piled raft. The GeoMechanica desktop application was used to perform consolidation settlement calculations. The input in the application is shown in figure 8.



Figure 8: Screenshot of using the consolidation module of Geomechanica Desktop to calculate the total consolidation settlement of the Millennium tower.


Results

The in-situ stresses and the increase in stress due to the tower load at the center of the equivalent raft are shown in figure 9. It can be seen from Figure 9, that the values of the increase in stress combined with the effective stress are greater than the preconsolidation pressure. The total settlement calculated was 0.482 m which is far greater than the initial estimated settlement. The calculated settlement is greater than the current value of settlement of the tower at the center which is around 0.425m as of the beginning of 2021. This might suggest that the consolidation hasn’t stopped yet. However, luckily for the occupiers of the tower, additional piles were installed around the building to arrest the ongoing settlement and reverse some of it.

Figure 9: Stresses under the piled raft of the millennium tower.


Conclusion

The Millennium Tower saga has been ongoing since 2009 until now. The tower has settled and tilted which raised concerns about its structural integrity, especially in the face of a major earthquake. In this article it is shown how soil mechanics principles can be used to estimate the settlement of a piled raft. The equivalent raft principle and the theory of 1-D consolidation were used. Average soil properties along with some reasonable assumptions on the void ratio and the unit weight were made. The settlement was found to be around 0.482m. This is greater than the current settlement at the center of the tower. This suggests that the tower might yet experience further sinking and tilting were it not for the new piles that were installed around the raft. The settlement calculated here did not consider the variation of the soil properties away from the average values. It also didn’t consider any dewatering activities that happened during the tower construction and the construction works around the tower area. The calculated settlement could be different from the final settlement of the tower due to these facts. In another article, the time-rate of consolidation principle will be used to try and predict what the final settlement of the tower could have been in comparison to the predicted value in this article.




References:


Duncan, J. M., and A. L. Buchignani. 1976. An Engineering Manual for Settlement Studies. University of California, Berkley.


Margaret Clair, California. 2019. “Engineering Properties and Geologic Setting of Old Bay Clay Deposits, Downtown San.” University of California, Berkeley.


Stewart, Jonathan P., Debra Murphy, Micaela Largent, Hannah Curran, and John A. Egan. 2023. “Foundation Settlement and Tilt of Millennium Tower in San Francisco, California.” Journal of Geotechnical and Geoenvironmental Engineering 149(6). doi: 10.1061/jggefk.gteng-10244.


Wagner, Nathaniel, Micaela Largent, Jonathan P. Stewart, Christine Beyzaei, Debra Murphy, Jeremy Butkovich, and John A. Egan. 2021. “Stress History–Dependent Secondary Compression of San Francisco Bay Region Old Bay Clays.” Journal of Geotechnical and Geoenvironmental Engineering 147(7). doi: 10.1061/(asce)gt.1943-5606.0002525.


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