Abstract
The two-lane bridge on State Highway 6 (SH6) at Kawarau Falls near Queenstown is scheduled to open in the second half of 2017. Designed to withstand a 1/ 2500 hazard level earthquake, the new bridge will provide better access into the Queenstown area and better account for closures and traffic congestion than the existing iconic bridge.
The Structural Designers adopted a two-group pile system for the bridge abutments and five monopile piers to support the deck spanning across the Kawarau River. Given the large loading demands and the anisotropic schist bedrock, the lateral pile performance governed the geotechnical design of the rock socket conditions.
The Elastic Continuum Method (ECM) was utilised for the pile-rock analysis. In this paper, the authors outline their design approach and compare their results with those derived from the Finite Element Method (FEM). The authors discuss the merits and limitations of each method and provide a framework for lateral pile analysis work.
Project Introduction
Queenstown is important to the New Zealand tourism industry and its local population also continues to grow. Over 8,000 vehicles per day cross the existing iconic single-lane Kawarau Falls Bridge which was originally built in 1926 as a dam structure to help with the recovering gold in river below the lake. To alleviate traffic congestion, the New Zealand Transport Agency (NZTA) proposed a new 250 m long and 14 m wide two-lane bridge to replace the existing bridge as the main carriageway.
A two-group pile system was adopted for the north and south abutments and five monopile piers were adopted to support the deck spanning across the Kawarau River. The piers were embedded directly into rock whereas the abutment piles were embedded in lake sediments and glacial till and socketed in rock. The minimum rock socket depths were 5 m for the abutment piles and 7 m for the piers. For Pier 2 (P2) a minimum 8 m rock socket was recommended as this pier had the longest free head length (approximately 17 m). For brevity, the analysis presented in this paper is for P2 only.
Geological and Seismic Setting
Queenstown and the surrounding Wakatipu Valley are underlain by schist of the Caples and Rakaia Terranes. The schist is actively being folded, faulted and eroded in response to regional compression and strain distributed across the mid to lower South Island. Geologists suggest that much of the fault activity and uplift in the area has occurred over the past five million years, and that the ongoing high-stress folding is reflected in the ruggedness of the local mountain ranges.
Repeated glaciations have carved deep troughs into the landscape, with Lake Wakatipu occupying the largest trough in the area. Lake Wakatipu covers an area of approximately 290 km2 and is over 370 m deep. Furthermore, during the last glacial (Otira) period, the glacial lake covered a much larger area and was significantly deeper.
There is a schist rock outcrop in the middle of the Kawarau River. However, the steeply dipping folded rock meant that that the top of rock elevation varied at each pile location.
The nearby mapped active faults – the Alpine Fault, Nevis Fault and Cardrona Fault – are all capable of producing earthquakes with moment magnitudes (Mw) greater than 7. According to a recent seismic hazard study undertaken by the Otago Regional Council for the Queenstown Lakes District, the primary seismic hazard facing the region is an Alpine Fault earthquake; which is predicted to have a 30% probability of rupturing in the next 50 years.
A 1/ 2500-year return period design peak ground acceleration (αmax) of 0.83 g was adopted for the site Class B (Rock) conditions.
Geotechnical properties of Schist Bedrock
The schist bedrock is technically referred to as a ‘quartzofeldspathic grey schist and green schist’. It is moderately weathered to unweathered along the pile socket depths. By observing the retrieved core specimen, the platy structure of the rock allows for it to break more readily in the lateral direction (parallel with the schistosity) than in the vertical direction.
The index properties of the schist are outlined below in Table 1 and a photo of the retrieved specimen is shown in Figure 1.
The rock mass shear strength was estimated using the Hoek and Brown failure criterion (edition 2002).
Figure 1: Photo of typical retrieved core specimen showing foliation patterns
Pile design Methodology & results
Choice of ECM over p-y curves method
The geotechnical analysis of the bridge foundations was carried out using the ECM (by means of in-house Coffey software), as presented in Poulos & Davis (1980). The pile is modelled as a thin elastic strip and the geotechnical layers are modelled as a continuous medium and are assumed to have an elastic stress-strain behaviour. Therefore, the load-deformation pile response output is for small-strain ground behaviour. This method adopts a simplified boundary element approach by limiting the axial and lateral ground pressures to ultimate values specified by the Designer.
The ground reaction-pile displacement (p-y curves) analysis method is the most widely used method for laterally loaded pile design. The ground reaction–pile displacement response is represented by a series of independent bi-linear springs so that at each depth the ground reaction is a non-linear function of lateral pile displacement. This non-linear relationship is represented by the differential equation proposed by Hetenyi (1946):
EI. d4y/dx4 + Px.d2y/dx2 – p – W = 0
Equation 1
Where: EI = pile flexural stiffness, P = axial load on pile, p = lateral ground reaction (per unit length), w = distributed load along length of pile. The integration of this original formula then produces profiles for shear (V), bending moment (M), bending slope (S) and lateral displacement (y).
Over the years, full-scale lateral load tests on various types of soils have led to established p-y curves being adopted for soil but only a limited number of load tests have been carried out for rock strata. The most commonly used p-y curve rock is the one proposed by Reese (1997) for bored piles in ‘weak rock’ (σci = 0.5 – 5 MPa). Although this approach is commonly used within the industry, it was not adopted as the primary lateral pile design methodology for the Kawarau Falls Bridge due to its limitations and sources of uncertainty.
These sources of uncertainty are:
- It is based on intact rock strength (σci) and does not account for rock mass strength, which is important given the schist anisotropy.
- It is based on a limited number of full-scale load tests – one carried out on a brittle coral limestone in Florida and another carried out on sandstone in California. And further, these load tests were for 1.2 m and 2.25 m diameter piles. In reality, the lateral ground reaction depends on the size (diameter) of the foundation.
- It represents an elastoplastic deformation behaviour. The schist rock at Queenstown, being a harder material, is expected to have a more brittle and bi-linear deformation behaviour.
The theoretical advantage of the ECM over the p-y curves method for rock is that the p-y curves method is cruder due to the spacing between the lateral springs acting on the pile.
Geotechnical strength reduction factor
The geotechnical strength reduction factor (Φg) for pile foundations was derived using the risk-based methodology set out in the Australian piling standard (AS2159-2009) and was calculated to have a value of 0.52.
Modelling of the pile free length
The free length of the monopiles was modelled as a “virtual layer” (i.e. minimal stiffness values input [E = 0.001 MPa]) because the ECM software program requires input parameters for every layer along the pile length.
Modelling of pile head and pile toe conditions
As there is no true free head or fixed head condition, both head conditions were modelled to provide a displacement range for the structural modelling to account for. To adopt a reasonable rock socket depth, the toe condition was not fixed against rotation but was fixed against translation (i.e. pinned). Poulos (1972) suggests the pinned toe condition be adopted to model a pile bearing on (but not socketed into) rock. Poulos (1972) initially proposed modelling a rock socketed pile by completely fixing the toe against rotation and displacement. However, for this particular design case, the pinned toe model was adopted to ensure that the stiffness of the surrounding rock was suppressing the pile rotations and bringing the system to equilibrium.
Analysis of P2
The input parameters for P2 are outlined in Table 2.
To account for the anisotropic behavior in relation to lateral pile performance;
- A lower bound Em value was adopted for design.
- A reduced lateral yield pressure value within the top 1.5 m of rock was adopted due to the increased likelihood of failure along pre-existing fractures at low overburden pressures.
The results of the maximum pile actions for both the fixed head and free head conditions is presented in Table 3.
Table 3: P2 Maximum Pile Actions
| Pile Action | Fixed Head | Free Head |
| Bending moment (MN.m) | 6 | 20 |
| Lateral displacement (mm) | 12 | 120 |
| Shear force (MN) | 1 | 5 |
Evaluation – Comparing ECM with FEM
To further evaluate the use of the ECM, the authors comparatively assessed the P2 pile response using a Mohr-Coulomb constitutive model with 3D FEM software. In addition to the elastic properties of the pile and rock, using the FEM software required the rock shear strength properties and unit weights of the rock and the pile be input into the model. A concrete unit weight of 25 kN/m3 was assumed for the pile.
The meshed 3D model showing a free head pile embedded into the ground is shown in Figure 3 and the comparative assessment of the results is shown in Figure 4.
Figure 3: P2 meshed model and for free head pile socketed in rock
Figure 4: Comparison of ECM with FEM for P2
The results in Figure 4 show that the pile-rock interaction along the rock socket length are almost identical and that the differences between the 1D and 3D analyses along the free head length lie within reasonable limits.
The ECM and FEM are similar in that both methods consider the geotechnical and structural failure of the piles. While they do not account for all the structural details (e.g. the presence and configuration of pile reinforcement), they do provide a reasonable assessment of how the structural element interacts with the surrounding ground. The limitation of FEM, in this particular case, is that it could only model a free head condition because no other superstructure element was constructed in the model to restrain the head movement. However, this limitation also demonstrates an advantage of FEM in that if the ground-structure interaction was modelled for the entire superstructure rather (as opposed to being limited to a single pile element), this would better indicate the actual pile actions at each location. However, the use of the ECM to model a single pile element with both head conditions is a quicker process.
Design process recommendations
Given the complex pile-rock interaction, an iterative collaborative process between Geotechnical and Structural Engineers is needed throughout the design process for laterally loaded piles. It is recommend that preliminary geotechnical modelling be carried out on trial design lengths, pile diameters, rock socket lengths, etc. Based on the subgrade reaction profile, the Geotechnical Engineers then provide lateral spring values for the Structural Engineers to model the superstructure (and revise loads where necessary). The iterative process is repeated until both the geotechnical and structural models provide comparable pile displacement behaviour (e.g. values within a 10% range) where the pile structural capacity and the geotechnical capacity of the ground have not been exceeded.
Conclusions
Given the complex pile-rock interaction, an iterative collaborative process between Geotechnical and Structural Engineers is needed throughout the design process for laterally loaded piles. Based on this case study, the authors consider that utilising the ECM for piles socketed in rock provides reasonable results when the applied lateral ground pressures are not exceeding the given lateral yield pressure. Further, the results of the ECM are comparable with those of the FEM. Alternatively, more full-scale field load tests on various rock types are recommended and the subsequent p -y curve parameters should be related to the rock mass properties, not only intact rock properties.
Acknowlegements
The authors wish to acknowledge the NZTA and McConnell Dowell Contractors.
REFERENCES
Awad, A., and Searle, J. (2016) Liquefaction potential of the micaceous lake sediments in the Queenstown area, Proceedings from the ANZ 11th Young Geotechnical Professional Conference, Queenstown, New Zealand.
Hetenyi, M. (1946) Beams on elastic foundation. Ann Arbor: The University of Michigan Press.
Hoek, E., C. Carranza-Torres, and B. Corkum (2002) Hoek–Brown Failure Criterion—2002 Edition, Proceedings, North American Rock Mechanics Society Meeting, July 8–10, 2002, Toronto, ON, Canada.
Otago Regional Council. (2015) Seismic Hazard in Queenstown Lakes District: Study Report.
National Corporate Highway Research Program, NCHRP Synthesis 360. (2006) Rock-Socketed Shafts for Highway Structure Foundations, Transportation Research Board of National Academics, Washington D.C.
Poulos, H.G. and Davis, E.H. (1980) Pile foundation analysis and design, John Wiley, New York.
Poulos, H.G. (1972) Behaviour of Laterally Loaded Piles: III Socketed Piles, Journal of the Soil Mechanics and Foundations Division, Vol. 98, No. SM4, pp. 341–360.
Reese & Van Impe (2011) Single Piles and Pile Groups under Lateral Loading (2nd Edition), CRC Press – Taylor and Francis Group, Netherlands.
Reese, L.C. (1997) Analysis of Laterally Loaded Piles in Weak Rock, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 123, No. 11, pp. 1010–1017.
Standards Australia (2009) Piling – Design and Installation, AS 2159-2009 (Incorporating Amendment No. 1), Standards Australia, Sydney, Australia.
Turnbull, I.M.(compiler). (2000) Geology of the Wakatipu Area, Institute of Geological & Nuclear Sciences 1:250000 geological map 18. 1 sheet + 72 p. Institute of Geological & Nuclear Sciences Limited, Lower Hutt, New Zealand.