# Chapter 2 > Source: Tina Schwamb. *Performance Monitoring and Numerical Modelling of a Deep Circular Excavation*. PhD thesis, University of Cambridge, 2014. [University of Cambridge repository](https://www.repository.cam.ac.uk/items/04ec45a9-4b8b-4ece-b848-7806d4636412), CC0 1.0. The text is output of the `marker` models by Datalab, cleaned by raw2md, and the modified AI Pubs OpenRAIL-M license of the models applies to it: [MODEL_LICENSE](https://github.com/MikeDolg/raw2md/blob/v0.2.2/examples/MODEL_LICENSE). The whole result is [thesis.md](https://github.com/MikeDolg/raw2md/blob/v0.2.2/examples/thesis.md) on GitHub. ## Literature review on circular excavations ## 2.1 Preface Circular excavations are commonly used in the construction industry. In tunnelling projects they may serve a dual purpose when they are used to launch the tunnel boring machine (TBM) into the deep tunnel drive (Figure 1.1\); after construction they can be used to access the tunnel, e.g. staircases or lifts can be built into the shaft. Smaller diameter shafts serve ventilation purposes. In sewage treatment shafts are commonly built for pumping stations and drop shafts. While rectangular excavations usually require propping when exceeding a depth of 5 m, circular shafts are structurally stable and make use of the hoop forces in the retaining structure. Therefore they usually do not require propping. This maximisation of space for construction operations, the reduction of bulk excavation and the simplicity of the construction sequence make the circular excavation a 'dramatically simple solution' as stated by Powderham \(2000\). Due to vertical and horizontal arching effects, earth loading on the walls is smaller than under plane strain conditions \(Wong and Kaiser, 1988\). The wall length can furthermore be reduced in comparison to a rectangular excavation with the same floor area and therefore provides an economic solution \(Gaba et al., 2003\). The subsequent sections provide an overview of shaft construction methods, common design practice and field, model and theoretical studies on circular excavations. ## 2.2 Shaft construction methods Deep excavations require the construction of a retaining wall. Several types of walls can be used. The main criteria for or against a particular method is the water tightness, which is crucial if the excavation is below ground water table, the shaft dimensions (diameter and depth), ground conditions and the sensitivity of the surrounding infrastructure to ground movements. Some walls are installed during the excavation and others are built prior to excavation. CIRIA C580 \(Gaba et al., 2003\) and Puller \(2003\) review the most common methods: **King post wall:** Vertical posts are driven into the ground prior to excavation. Horizontal timber sheets or pre-cast concrete elements are then placed between the post with increasing excavation depth and the posts are anchored into the ground behind the wall (Figure 2.1a\). This method is economical, it is however not feasible in perfectly cohesionless soils; it is limited in depth and not water tight. It may also cause larger ground movements due to the low wall stiffness. **Sheet piling:** Sheet piles are driven into the ground and tied back with anchors as excavation progresses (Figure 2.1b\). This method is also not feasible in rock or soils with large boulders which hinders driving the sheet piles. It can however reach deeper and is water tight. **Caisson sinking:** Rings of pre-cast concrete segments are erected and driven into the ground with a steel cutting edge installed at the lowest ring (Figure 2.1c\). A lubricant (usually bentonite) is filled into the annulus behind the wall, a calculated jacking force is applied and simultaneously the shaft floor is excavated \(Allenby et al., 2009\). This method is applicable in dry and wet conditions (water will fill up inside the excavation and can be pumped). It is usually used for small diameters shafts (2 to 6 m). **Segmental linings:** As shown in Figure 2.1d the pre-cast concrete or cast-iron segments are put in place in an underpinning operation. To control ground movement the annulus behind the wall is filled with grout. This method is applicable in dry conditions and in soil that temporarily stands without support. (a) King post wall (timber) ([http://www.](http://www.learnz.org.nz/) [learnz.org.nz/](http://www.learnz.org.nz/)) (b) Sheet piling ([http://www.aeyates.co.](http://www.aeyates.co.uk/spi-appleton-ltd) [uk/spi-appleton-ltd](http://www.aeyates.co.uk/spi-appleton-ltd)) (c) Caisson sinking \(Newman and Wong, 2011\) (d) Segmental shaft lining ([http://www.](http://www.fpmccann.co.uk) [fpmccann.co.uk](http://www.fpmccann.co.uk)) (e) Shotcreting () (f) Secant piling ([http://kellergrundbau.](http://kellergrundbau.ae/) [ae/](http://kellergrundbau.ae/)) Figure 2.1: Overview of several shaft construction methods **Shotcreting:** Shotcrete is pneumatically conveyed onto the surface as excavation is progressing. The surface may have mesh reinforcement pinned to it to achieve tensile strength, or short reinforcing fibres will be added to the mix. It is only feasible in dry conditions and in stable ground \(Thomas, 2009\). **Contiguous piling:** The cast-in-place concrete piles are constructed with a spacing larger than the pile diameter, so there are gaps between the adjacent piles (typically ranging between 50 and 150 mm). Depth can be as deep as 55 m but in practice 25 m is usually not exceeded. This type of wall is only suitable for temporary support and does not provide water tightness. **Secant piling:** Secant pile walls (Figure 2.1f\) are also made from cast-in-place concrete piles where adjacent piles overlap (spacing smaller than a pile diameter). Verticality tolerances usually limit depths to approximately 20 m; up to 40 m depth can be achieved with special tools. The structure is feasible to be used in wet conditions. ### Diaphragm walls Diaphragm walls, also called slurry walls, are constructed prior to shaft excavation. Depths of around 50 m can be achieved with conventional grabs, but they cannot be used in bedrock. Hydrofraises on the other hand can penetrate very hard ground and reach up to depths of 100 m. Bachy Soletanche constructed one of the deepest ever diaphragm walls of 98 m depth and 1.8 m thick panels for the Thames Water Lee Tunnel project at Beckton \(Otta, 2012\). The construction method of a diaphragm wall is schematically displayed in Figure 2.2a. Firstly a guide wall is constructed; then a grab or hydrofraise is used to excavate the trench under a suspension liquid. After the panel excavation the reinforcement cages are lowered into the trench. Concrete is then filled into the trench from the bottom and displaces the bentonite liquid, which is pumped from the top to the storage tanks. To create a tight wall primary panels are built with a spacing and secondary panels are added in-between. The joints have to be constructed carefully to guarantee interlocking of adjacent panels and water tightness. Bilfinger Spezialtiefbau GmbH \(2013\) lists the most common joint construction methods: - **Steel stop-end pipes:** The principle is displayed in Figure 2.2b; stop-end steel pipes are installed on the short sides of the panel where the pipe has the same diameter as the panel width. The pipe is removed after the initial concrete setting to create a half-circular panel end; if overdigging occurred, concrete may flow around the pipe which has to be removed when the adjacent panel is excavated \(Fuchsberger, 1975\). - **Pre-cast reinforced concrete stop-end:** Pre-cast concrete panels (Figure 2.2c\) stay permanently in the ground. They are lowered into the trench along with the reinforcement. When the adjacent panel is being excavated it serves as guide for the grab. - **Steel joint element:** A picture of steel joint element is displayed in Figure 2.2d. The element contains one or two elastic joint tapes which will be cast into the concrete. After the adjacent panel has been excavated the element (without the tapes) can be removed. - **Panel versus panel joint:** At Abbey Mills shaft the hydrofraise cut into the concrete of the already constructed primary panels when excavating the trench of the secondary panels. Before installation the primary panels were prepared with styrofoam on the side of the reinforcement cage as shown in Figure 2.2e. This is important to ensure that the digging tool is cutting as straight as possible. Especially for deep shafts it is important to construct panels as vertical as possible, so that enough overlap is guaranteed at depth. This is important to transmit hoop forces in circular shafts and to ensure water tightness. On board equipment helps monitoring tolerances and verticality values of 1:400 can be achieved (i.e. a 100 m deep wall would be 0.25 m off vertical). Virollet et al. \(2006\) highlight that the thickness of the ring structure is further reduced by the rectangular nature of the diaphragm wall panels (Figure 2.2f\). At Abbey Mills this was less of a problem, as the long primary panels were excavated in three separate pieces as well as equipped with three trapezoidal reinforcement cages (Figure 2.2g\). Diaphragm walls are very stiff structures which reduce ground movements during excavation; the installation of the wall can however cause ground movement. (a) Installation procedure of diaphragm walls ([http:](http://www.bacsol.co.uk/techniques/retaining-walls/diaphragm-walls/) [//www.bacsol.co.uk/techniques/retaining-walls/](http://www.bacsol.co.uk/techniques/retaining-walls/diaphragm-walls/) [diaphragm-walls/](http://www.bacsol.co.uk/techniques/retaining-walls/diaphragm-walls/)) (b) Steel stop-end pipe - reproduced from Fuchsberger \(1975\) (c) Pre-cast concrete stop-end Figure 2.2: Diaphragm wall construction (d) Steel joint element (Bilfinger Spezialtiefbau GmbH, 2013) (e) Abbey Mills joint construction (Courtesy of Thames Water) (f) Diaphragm walls create imperfect circle Virollet et al. (2006) (g) Abbey Mills panel layout (Courtesy of Thames Water) Figure 2.2: (Cont.) Diaphragm wall construction ## 2.3 Design of circular shafts ### 2.3.1 Overview CIRIA reports are design aids which provide practical guidance in accordance with structural codes and exist for many different topics. The CIRIA C580 guideline \(Gaba et al., 2003\) deals with embedded retaining walls of any plan shape, but seems to mainly refer to excavations of non-circular shapes. However, due to the lack of specific guidelines for circular shapes CIRIA C580 \(Gaba et al., 2003\) is used by practitioners when designing circular shafts with embedded retaining walls. The design steps suggested are outlined below: 1. Estimate wall deflections and ground movements from case history data to check suitability of wall type and construction method. 2. Check ultimate limit state (ULS). This ensures that a structure does not collapse when subjected to the worst design load combination. To achieve a safety margin before actual collapse, the partial safety factor method is usually applied. 3. Check serviceability limit state (SLS). SLS refers to deflections or movements of a structure and the surrounding soil that shall not exceed a limiting value under working load. The characteristic unfactored design loading is applied. ### 2.3.2 Empirical approaches The first step in the design process is to estimate the wall deflections and ground movements from case history data to check the suitability of the wall type and the construction method. This is in line with Eurocode 7 which states that 'a cautious estimate of the distortion and displacement of retaining walls, and the effects on supported structures and services shall always be made on the basis of comparable experience' \(British Standards Institution, 2004a, p.110). Eurocode 7 also notes that the SLS may be fulfilled if this cautious estimate is within the tolerance. While Long \(2001\) for example compiled an extensive database for propped and cantilever non-circular excavations with data from more than 300 case histories, the number of field studies for circular excavations is very limited. This does not allow designers to pick a case that matches in dimensions, soil conditions and construction method. Therefore current British design practice, for the estimation of surface settlement around circular excavations, mainly relies on one study carried out by the Transport Research Laboratory on the Heathrow Express Trial Tunnel \(New and Bowers, 1994\). Although this case study has not been confirmed, the Geotechnical Consulting Group's \(2007\) report on 'Settlement Estimation Procedure: Box Excavations & Shafts' for the Crossrail project is primarily based on New and Bowers' \(1994\) case study and engineering judgement. With only little back-up, conservatism and cautiousness has to be adopted, which may lead to uneconomic wall design, over-predictions of movements and higher protective measures for adjacent structures. Further field data is certainly required to confirm the adequacy or inadequacy of New and Bowers \(1994\) and establish the influence of parameters such as shaft diameter, construction method and ground conditions. ### 2.3.3 Limit equilibrium The limit equilibrium approach can only be used for ULS. It assumes simple linear lateral stress distribution and full strength mobilisation of the soil at collapse conditions. It cannot be used to determine deformations for SLS, as the structure is close to collapse where deformations are large. Two commercially available and commonly used design programs are Re-WaRD \(Geocentrix, 2011\) and STAWAL \(Oasys Ltd., 2007\), which give the required embedment depth and structural forces. As both programs are only available for two-dimensional plane strain analysis, designers would either need to use hand calculation for axisymmetric conditions, which is tedious and prone to error, or incorporate the hoop stiffness by equivalent propping, which is difficult to determine accurately. The basis for limit equilibrium solutions is the assumption of an active earth pressure distribution. This is especially difficult to estimate for axisymmetric excavations due to vertical and horizontal arching. The approach does furthermore not take account of the beneficial earth pressure redistribution due to wall movement. Due to the above mentioned shortcomings the limit equilibrium approach has often been replaced by soil-structure interaction methods which can justify both ULS and SLS, and take the beneficial stress redistribution into account. ### 2.3.4 Soil-structure interaction CIRIA C580 \(Gaba et al., 2003\) considers soil-structure interaction approaches as more appropriate and economic, as wall movements and the redistribution of earth pressure can be considered. It can be divided into (1) the simpler approaches of subgrade reaction and pseudo finite element (FE) methods and (2) the more sophisticated approaches using FE or finite difference methods. #### 2.3.4.1 Subgrade reaction and pseudo FE methods The subgrade reaction method replaces the soil by linear horizontal springs (Figure 2.3a\). According to Simpson and Powrie \(2001\), speaking of plane strain conditions, this method generally gives similar bending moment predictions to FE programs, but coefficients of subgrade reaction are not easily determined. A software tool commonly used is WALLAP \(Gesolve, 2002\) which is designed for plane strain conditions. Designers using the subgrade reaction method for circular shafts need to account for the larger stiffness in comparison to plane strain conditions. Chandrasegaran et al. \(2006\) detail the procedure and advise to represent the cylindrical rigidity as continuous elastic vertical support on the excavation side of a plane strain wall. However, this seems to only crudely represent the hoop stiffness and does not take any potentially reduced circumferential stiffness nor its mobilisation into account. The pseudo FE approach replaces the soil by an elastic continuum and according to Simpson and Powrie \(2001\) it realistically redistributes earth pressure (Figure 2.3b\). A program frequently used in retaining wall design is FREW \(Oasys Ltd., 2010\) which has again been designed for plane strain conditions. It is argued that it can still be used for axisymmetric excavations when movements are small due to propping so that vertical arching dominates \(Oasys Ltd., 2010\). It does however not consider the beneficial hoop effect. For both subgrade reaction and pseudo FE methods the computation of initial active and passive earth pressures and their redistribution are conducted according to plane strain theory which overestimates values and is therefore on the safe but conservative side. CIRIA C580 \(Gaba et al., 2003\) furthermore highlights the crude characterisation of the soil stiffness and that ground movement cannot be obtained, i.e. the justification of SLS is not possible. It is crucial for both limit equilibrium and soil-structure interaction methods that the results are critically examined and calibrated against reliable measurements of well-monitored case histories. (a) Subgrade reaction model - reproduced from Simpson and Powrie \(2001\) (b) Pseudo FE model - reproduced from Oasys Ltd. \(2010\) Figure 2.3: Subgrade reaction and pseudo FE methods #### 2.3.4.2 Finite element and finite difference methods Using FE or finite difference packages is the most common design method, as they can account for various features, such as complex soil constitutive behaviour, construction sequences, structural and support details and consolidation and groundwater effects, as well as provide ground movements. As a trade-off the analysis is very time-consuming and the quality of the results highly depends on the availability of appropriate soil models and input parameters. Common packages used are SAFE, PLAXIS, CRISP, FLAC, ABAQUS and DYNA. #### Wall installation When designing diaphragm or bored pile walls it is important to take the effect of wall installation into consideration, as the installation process may cause lateral stress relief (in overconsolidated soil) or increase (where lateral earth pressure values are below 0.5). Powrie et al. \(1998\) argues that the installation changes the stress state in overconsolidated clays which may affect the soil stiffness during excavation. Simulations assuming a wished-in-place (WIP) wall cannot predict ground movements related to the construction of the wall, which may be significant. Several studies \(Conti et al., 2012; Gourvenec and Powrie, 1999; Lings et al., 1994\) give advise on how to incorporate the wall installation in FE analyses. CIRIA C580 \(Gaba et al., 2003\) acknowledges the importance of wall installation, but notes that the detailed modelling of the wall installation would be excessive and that further research is required. #### Soil models Using an appropriate soil model in FE analyses is often crucial for an accurate representation. This includes non-linear and anisotropic soil behaviour. Several studies have highlighted the importance of stiffness degradation for soil-structure interaction problems even at very small strain \(Burland, 1989; Jardine et al., 1986; Kung et al., 2007\). While strain at failure is large, it is small under working conditions and therefore small-strain stiffness plays a decisive role for deformations. Kung and Ou \(2006\) used the field results from the excavation of the Taipei National Enterprise Center and compared the wall deflections and surface settlements with numerical results. The best results were achieved with the Modified Pseudo-Plasticity model \(Kung, 2003\) which is a hyperbolic model incorporating small strain non-linear stiffness behaviour. Natural soil is likely to behave in a transversely anisotropic manner due to its original sedimentation. Stiffness and strength depend on the direction and orientation of the applied stress \(Potts and Zdravkovic, 1999\). Wongsaroj \(2005\) compared numerical simulations and measured ground displacement fields (vertical and horizontal movements at surface and subsurface) caused by tunnel excavation through St. James's Park in London Clay. Even though the prediction of the anisotropic model did not entirely match the field data, it was closer than the isotropic. Laver \(2010\) improved Wongsaroj's \(2005\) model as further data on strength anisotropy and softening during triaxial extension had become available in the meantime. His constitutive model modified the yield surface size and rotation, used alternative parameters and added fissure softening to Wongsaroj's \(2005\) original model and therefore achieved a better fit of the field data. Although extensive research has highlighted the importance of above mentioned factors, academia and practice diverge how to conduct numerical analysis. In practice it is still common to use linear-elastic perfectly plastic soil models without consideration of anisotropy. This is partly due to the high amount of work associated with understanding, measuring and characteris ing input parameters for these complex soil models, which requires extensive ground investigation and laboratory testing. Therefore designers have to balance between model complexity and available data \(Soga and O'Sullivan, 2010\). However, accurate predictions of settlement cannot be achieved until simulations incorporate more realistic soil behaviour. ##### Wall stiffness In practice it is common to model the shaft wall as fully isotropic. However diaphragm walls are made from a series of panels with joints, which may cause lower stiffness in circumferential direction. The exact mechanism is not fully understood. Especially for circular excavations this plays an important role, as deformations significantly increase when reducing the full hoop stiffness. This is further discussed in Section 2.4.2.1. ### 2.3.5 Mobilized Strength Design method The Mobilized Strength Design (MSD) is a performance based design method extending the concept of limit equilibrium and used as an alternative to complex FE and finite difference simulations for deep excavations in soft soils. It is based on the conservation of energy, where the loss of potential energy by the formation of the trough must balance with the work done by deforming the retaining wall and the soil \(Bolton et al., 2010\). This principle was first applied to rigid and smooth cantilever walls by Powrie and Bolton \(1988\) and followed up by Osman and Bolton \(2006\) to include braced excavations. In comparison to numerical analyses which require a large number of soil parameters when using complex constitutive models, MSD can perform SLS and ULS in a single step and account for soil non-linearity based on few parameters. Therefore a direct simple shear test is required to yield the stress-strain curve of a representative sample. Lam \(2010\) and Bolton et al. \(2010\) investigated how MSD compares to numerical analysis and field data. MSD results fit numerical simulations carried out with the MIT-E3 model within ±30 %, which is satisfactory considering that no detailed account is taken for soil anisotropy. Comparisons to the measured wall deflections from 110 case histories of braced excavations demonstrate that the MSD predictions fit the field data with a factor of 1.4. They furthermore plotted the structural response ratio versus the soil-structure stiffness ratio from the 110 case studies and found that all field data fit an inverse relationship with a coefficient of determination of 0.964. From this they derived a simple formula to predict the maximum wall deflection ∆*u* normalised by the excavation depth *H* as follows, $$\frac{\Delta u}{H} = \frac{\gamma_{\rm u}}{400} \frac{\lambda}{H} \left(\frac{\rho g H}{c_{\rm u}}\right)^2 \tag{2.1}$$ where *γ*u is the reference shear strain, *λ* is the wavelength of the bulge the wall is forming (this is related to prop spacing) and *ρg* is the unit weight of the soil. Bolton et al. (2010) notes that this equation does not include the wall's bending stiffness EI. This shows that structural stiffness, across a range of walls from sheet piles to diaphragm walls, has a minor influence on the wall's deflection. For circular excavations, Equation 2.1 is perhaps not applicable as the factor 1/400 was derived from field data of braced excavations. It may be difficult to apply MSD to circular excavations, where hoop forces increase the system's stiffness, as the derivation is based on plane strain plasticity theory. ## 2.4 Experimental and theoretical approaches As outlined in Section 2.3 current design practice needs reliable and well-documented case studies to estimate ground movements and wall deflections and calibrate numerical models. An extensive literature search for case histories on circular shafts since 1980 has been carried out. The search comprised some of the most relevant journals and conference proceedings as listed below: - Géotechnique - Proceedings of the Institution of Civil Engineers (ICE) – Journal of Geotechnical Engineering - Canadian Geotechnical Journal - ASCE Journal of Geotechnical and Geoenvironmental Engineering - International Conferences on Soil Mechanics and Geotechnical Engineering (ICSMGE) - International Conferences on Underground Construction in Soft Ground (Technical Committee 204) - International Conferences on Physical Modelling in Geotechnics (Technical Committee 105) In comparison to the database for propped and cantilever non-circular excavations by Long \(2001\) which includes more than 300 case histories, the result of this search is rather disappointing. Only 17 case studies of circular shafts were found (Table 2.1\). This small number renders it unlikely to fulfil the requirements imposed by codes and standards. CIRIA C580 \(Gaba et al., 2003\) and Eurocode 7 \(British Standards Institution, 2004a\) strongly recommend the use of comparable case studies when estimating wall deflections and ground movements. Comparable refers to parameters such as shaft dimensions, construction method and soil conditions. This lack of case studies clearly imposes difficulties when considering the specific conditions of the available case studies. It is furthermore important to calibrate numerical simulations with well-documented case histories. The few existing full-scale case histories, as well as relevant model-scale case studies and theoretical approaches are reviewed in the following sections. ### 2.4.1 Surface settlement #### 2.4.1.1 New and Bowers' (1994) case study and settlement prediction There is one well-documented case study of a circular shaft frequently referred to in practice. It was conducted by the Transport Research Laboratory \(New and Bowers, 1994\) which measured surface settlement during a 26 m deep shaft sinking in London Clay for the Heathrow Express Trial Tunnel. Two arrays (S and T line) of five and six movement stations radiated from the shaft wall and were monitored. The settlement *S*v(*d*) measured at a distance *d* behind the shaft wall is normalised with the shaft excavation depth *H* and plotted versus *d*, which is also normalised with *H* (Figure 2.4a\). The S line data was subject to heavy plant movement and hence this data was discarded. The T line gave a maximum settlement *S*v,max of approximately 15 mm next to the shaft wall (*d* = 0) and a zone of influence that is approximately equal to the depth of the shaft *H* when the shaft was approaching full depth. A parabolic curve was fitted through the data to obtain an empirical formula for the surface settlement *S*v(*d*) behind the shaft wall, $$S_{\rm v}(d) = \frac{\alpha (H-d)^2}{H} \tag{2.2}$$ Table 2.1: Overview of case studies on circular excavations | Reference | Location | Ground conditions
thickness of layers [m]
Dredge level | Wall
depth [m] | Wall thick-
ness [m] | Exc depth
H [m] | Diameter
D [m] | Ratio
D/H[-] | Construc- | Monitored and
documented parameters
(Monitored parameters
without documentation) | |---|---|---|---|---|---|---|---|---|---| | Anagnostopoulos
and Georgiadis
(2001) | Greece | 8 m loose silty sand
2.5 m loose sandy silt
medium dense silty
sand | 16 | 0.6 | 9 | 20.8 | 2.3 | diaphragm | wall hoop forces
wall bending moments | | Ariizumi et al. (2000) | Tokyo,
Japan | 25 m sand & silt layers
24 m sand
11 m gravel
8 m sand & silt
clay | 70 | 1.2-
1.4 | 29 | 144 | 5 | diaphragm | earth pressure on wall
wall deflection
wall hoop stresses
vertical wall stresses | | Cabarkapa et al.
(2003) | Dublin,
Rep. of
Ireland | 2 m made ground
1 m weather boulder clay
12 m up. black oulder clay
12 m brown boulder clay
3 m lo. black boulder clay
limestone | 32.5 | 1.5 | 27-
29 | 56.6 | 2 | diaphragm | wall deflections
(rebar strains)
(surface settlement)
(water table) | | Enami et al.
(1996) | ? | 26 m alluvial fine sand
11 m diluvial clay/sand
mud stone | 36.5 | 1.4-
1.7 | 36.5 | 30.4 | 0.8 | open caisson
method,
reinforced
concrete
rings | earth pressure on wall
reaction force at
cutting edge
friction force on
peripheral surface | | Gerolymos et al.
(2007) | Athens,
Greece | 8 m sandy clay
weathered conglo-
merate | 33.7 | 1.2 | 24.5 | 26.5 | 1.1 | Contiguous
pile wall | wall deflections
(soil displacements)
(water table) | | Goto and Iguro
(1989) | Tokyo,
Japan | 16 m reclaimed sand/silt
10 m diluvial sand
18 m diluvial sand/silt
42 m diluvial sand
diluvial sand/silt | 100 | 1.2 | 46 | 68 | 1.5 | diaphragm | wall head movements
earth pressure on wall
(wall deflections) | | Kim et al. (2013) | South
Korea | 6 m top soil
7 m weathered soil
weathered rock | 16.6 | 0.8 | 15 | 8 | 0.5 | H-piles &
ring wale | earth pressure on wall
(soil pressure)
(lateral soil movement)
(water level) | | Marten and
Bourgeois (2005) | Nantes,
France | 2.8 m sandy & silty fillings
10 m clayey silts
10 m clay
1 m fine to coarse sand
weathered mice-slates
Sound Mica-slates | s 24 | 0.8 | 14.7 | 46.3 | 3.2 | diaphragm | wall deflections
wall head movement | | McNamara et al. (2008); Morrison et al. (2004) | London,
UK | 26 m London Clay
14 m Lambeth Group
14 m Thanet Sand
Chalk | 40 | 0.35 | 40 | 8.2 | 0.2 | segmental
lining &
secondary
lining | wall deflections
(soil displacements)
(water table) | | Muramatsu and
Abe (1996) | Musashino,
Japan | 8 m loam layers
15 m Musashino gravel
Tokyo layer group
Joso layer group | 98 | 1.2 | 60.3 | 28.2 | 0.47 | diaphragm | earth pressure on wall
water pressure on wall
wall stresses
wall deflections
surface settlement | | New and Bowers
(1994) | London,
UK | 0.5 m made ground
3 m Taplow Terrace gravel
London Clay | 26 | ? | 26 | 11 | 0.42 | shaft
sinking | surface settlement | | Parashar et al.
(2007) | Singapore | 10 m sand
5 m soft marine clay
deposits
old aluvium | 68.5
72.5 | 1.2
1.2 | 65
69 | 30
37 | 0.46
0.54 | diaphragm
diaphragm | wall deflection wall bending moment hoop strain (surface settlement) | | Placzek and
Londong (1994) | Bottrop,
Germany | 14.5 m made ground
7.5 m silty sand
0.5 m coarse silt
marl | 31 | 1.3 | 27 | 44 | 1.6 | diaphragm | wall head movements
earth pressure on wall
water pressure on wall
basal heave
(surface settlement) | | Powderham (2000, 2002) | London,
UK | 6 m Terrace gravels
London Clay | 40 | 0.9-
1.2 | 30 | 60 | 2 | contiguous
& secant
pile wall | wall deflections | | Tan and Wang
(2013) | Shanghai,
China | 5 m firm silty clay
11 m soft muddy clay
4 m stiff silty clay
dense silty fine sand | 36 | 1 | 18 | 100 | 5.6 | diaphragm | wall deflections
bending stresses
hoop stresses | | Walter and
Tarallo (1985) | Zeebrugge,
Belgium | 8 m hydraulic embank.
7 m sandy clay
7 m fine sand
9 m medium compact sand
Tertiary clay | 40
d | 1.2 | 20 | 88 | 4.4 | diaphragm | wall deflections
(wall head movement)
(soil displacements) | | Wong and Kaiser (1988) | London,
UK | 7 m sand/clay layers
14 m till
clay shale | 20 | ? | 20 | 3.2-
2.4 | 0.16-
0.12 | shaft
sinking | (sub)surface settlement
hori. ground movement
earth pressure | where $\alpha$ is an empirical constant that depends on ground conditions and construction method; for this study $\alpha = 6 \times 10^{-4}$ provided the best match. Although this formula is frequently used, it has drawbacks, such as neglecting the diameter of the excavation and the uncertainty of $\alpha$ . New and Bowers (1994) also measured the horizontal soil movement with moderate success. One array of boreholes was disturbed; the other showed consistent movements of approximately 5 mm. #### 2.4.1.2 Settlement predictions for shafts in the Crossrail project The Crossrail project, the construction of a major railway link underneath London, includes several box and circular excavations. The settlement estimation guidelines (Geotechnical Consulting Group, 2007) mainly rely on the above mentioned study by New and Bowers (1994). Geotechnical Consulting Group (2007) however add a dependency on the diameter D; the maximum vertical settlement $S_{v,max}$ (which is equal to $S_v$ at d = 0) is defined as $$S_{\text{v,max}} = \alpha H \cdot \frac{D}{10 \,\text{m}} \tag{2.3}$$ which is slightly more conservative as New and Bowers (1994) due to high uncertainty. To avoid high values of settlement for large diameter shafts, an upper bound is set for D > 25 m $$S_{\text{v,max}} = 15 \times 10^{-4} \cdot H \tag{2.4}$$ The extent of the settlement trough $E_t$ is assumed to be 1H (for $D < 10 \,\text{m}$ ) and 2H (for $D > 25 \,\text{m}$ ); for diameters between $10 \,\text{m}$ and $25 \,\text{m}$ it is linearly interpolated. The formula for the settlement distribution is given in Equation 2.5. $$S_{\rm v}(d) = S_{\rm v,max} \cdot \exp(0.5) \cdot \exp\left(-\frac{(d + 2E_{\rm t}/3)^2}{8E_{\rm t}^2/9}\right) \tag{2.5}$$ Case histories of circular shafts that can be used to reliably derive formulations for horizontal soil movement are almost non-existent. Therefore Geotechnical Consulting Group (2007) assume the same Gaussian distribution as for the settlement, which is the same method as for rectangular excavations. The maximum horizontal movement $S_{h,max}$ is assumed to be equal to the maximum vertical settlement $S_{v,max}$ , i.e. $S_{h,max}/S_{v,max} = 1$ . #### 2.4.1.3 Settlement predictions from 1 g model tests by Pairaudeau (2011) Pairaudeau \(2011\) used 1 g small model tests in dry sand to investigate the surface settlement around circular shafts in relation to the diameter *D*. A set of four tests was carried out. The model shafts were all 500 mm deep and the diameters ranged from 100 mm to 400 mm. The settlement profiles were used to obtain empirical relationships for the maximum settlement *S*v,max (Equation 2.6\) and the extent of the trough *E*t (Equation 2.7\); both depend linearly on the diameter *D*, $$\frac{S_{\text{v,max}}}{H} = 0.0008 \cdot \frac{D}{H} + 0.0008 \tag{2.6}$$ $$\frac{E_{\rm t}}{H} = 0.3 \cdot \frac{D}{H} + 0.12 \tag{2.7}$$ Pairaudeau \(2011\) modified the Gaussian settlement profile derived above by Geotechnical Consulting Group \(2007\) by normalising the parameters *d* and *E*t by *H*, as given below in Equation 2.8 $$S_{\rm v}(d) = S_{\rm v,max} \cdot \exp(0.5) \cdot \exp\left(-\frac{(d/H + 2E_{\rm t}/H)^2}{(8E_{\rm t}/9)^2}\right) \tag{2.8}$$ #### 2.4.1.4 Comparison to field data Three approaches were introduced above: (1) New and Bowers \(1994\), (2) Geotechnical Consulting Group \(2007\) and (3) Pairaudeau \(2011\); these are plotted in Figure 2.4b using the dimensions of New and Bowers' \(1994\) shaft. The figure also contains New and Bowers' \(1994\) measurement points. As mentioned above, the formula by New and Bowers \(1994\) was based on the T line measurements. Geotechnical Consulting Group \(2007\) adopted a slightly more conservative approach due to limited evidence; it is however still fitting the data well. It can be seen that the formula based on very small 1 g model tests \(Pairaudeau, 2011\) predicts maximum settlement almost twice as large as New and Bowers \(1994\) and Geotechnical Consulting Group \(2007\). The extent of the settlement trough is however less than half the size in comparison to the other two formulas. Several reasons for the mismatch of Pairaudeau's \(2011\) formula are possible. The ground conditions were different; whereas Pairaudeau \(2011\) used dry sand, the Heathrow trial tunnel was constructed in London Clay. Pairaudeau's \(2011\) formula is based on small 1 g model tests and therefore has limitations of being transferred to real scale. On the other hand, the measurements by New and Bowers \(1994\) have not yet been confirmed by another study with similar conditions. Another well-documented case study was conducted by Muramatsu and Abe \(1996\) in layered soil in Tokyo (Table 2.1\). The extensive monitoring scheme for the 60 m deep diaphragm wall shaft of 28 m diameter also included the measurement of vertical and horizontal surface movement during diaphragm wall installation and excavation. Despite the large dimensions the maximum settlements in the immediate proximity of the shaft were only between 4 and 7 mm (diaphragm wall installation and excavation), while New and Bowers \(1994\) measured 15 mm. In Figure 2.4c the measurements along with the three formulas are plotted. All approaches overestimate the settlements significantly. This indicates that diaphragm wall shafts are likely to result in smaller ground movements than shaft sinkings. The horizontal ground movements measured by Muramatsu and Abe \(1996\) are slightly above the values for the vertical settlement, e.g. monitoring line No. 1 predicts 4 mm settlement next to the shaft wall and 6 mm horizontal movement; for lines No. 2 and 3 the ratio *S*h,max/*S*v,max is also approximately 1.5, slightly above the Geotechnical Consulting Group's \(2007\) recommendation of 1. Wong and Kaiser \(1988\) implemented a large monitoring scheme for a shaft sinking of 20 m depth and 3.2 m diameter in layered soil comprising sand, clay and till (Table 2.1\). The surface settlement measurements from their case study are included in Figure 2.4a; they are approximately between the measurements from New and Bowers \(1994\) and Muramatsu and Abe \(1996\). It is reasonable that the soil surface measurements by Wong and Kaiser \(1988\) are smaller than those by New and Bowers \(1994\), as the diameter of the shaft is smaller while the depth is similar. When applying the formula by Geotechnical Consulting Group \(2007\) which takes the shaft diameter into account, the predictions are slightly smaller than the actual measurements, but seem to match the data relatively well (Figure 2.4d\). Pairaudeau \(2011\) and New and Bowers \(1994\) overestimate the settlement. (a) Overview of measurements of three case histories \(Muramatsu and Abe, 1996; New and Bowers, 1994; Wong and Kaiser, 1988\) Figure 2.4: Normalised surface settlement of three case studies and predictions (c) Data from Muramatsu and Abe \(1996\) in comparison to predictions (d) Data from Wong and Kaiser \(1988\) in comparison to predictions Figure 2.4: *(Cont.)* Normalised surface settlement of three case studies and predictions #### 2.4.1.5 Comparison to centrifuge measurements Lade et al. (1981) carried out centrifuge tests on circular shafts in dry sand. The model shaft was 450 mm deep and 115 mm in diameter. At a g-level of 111.8 this corresponds to a prototype shaft of 12.9 m diameter and 50.3 m depth. The surface settlement $S_{\rm v}(d)$ at three points behind the wall at three different excavation depths ( $H=18\,\rm m$ , 33 m and 50 m) were recorded and are plotted in Figure 2.5. The measurements show that the majority of settlement occurred during Stage 2 ( $S_{\rm v}(2.5\,\rm m)=13\,\rm mm$ ); Stages 3 and 4 only cause a small increase ( $S_{\rm v}(2.5\,\rm m)=17$ and 21 mm respectively). This indicates that the ratio D/H might be a relevant factor for the settlement magnitude, i.e. that shafts with large diameters in comparison to their depth might undergo more relative settlement. Figure 2.5: Surface settlement of centrifuge tests by Lade et al. (1981) in comparison to predictions (prototype dimensions) The figure also contains the predictions from the three formulas discussed above. The maximum settlement predictions by New and Bowers (1994) and Geotechnical Consulting Group (2007) at Stage 2 fit the measurements well; however with increasing excavation depth both the formulas overestimate settlements. The extent of the settlement trough at Stage 2 is however underestimated by both formulas. The predictions by Pairaudeau (2011) again overestimate the maximum settlement behind the wall and underestimate the extent of the trough. Equation 2.8 however normalises d and $E_t$ by H and hence predicts larger settlements for shallower shafts with larger *D*/*H*-ratios, as confirmed by Lade et al.'s \(1981\) measurements. The above comparisons show that adopting empirical formulas to shaft excavations in other ground conditions and with different construction methods is highly inconsistent. The empirical formulas have several deficiencies, as they neglect factors which are likely to influence movements significantly. The effects of ground conditions, dewatering scheme, geometry, construction method and workmanship have not been considered in the calculations. To make more confident prediction on ground movements for circular excavations under different conditions further field data is needed, which underpins the necessity of this study. #### 2.4.1.6 Additional model tests Model data on the other hand is obtained more easily, but has limitations. Transferring the results from centrifuge or 1 g studies to derive empirical relations to be applied to real field studies might not be appropriate, as model shaft exhibit differences to prototype shafts. However, this data can be used to calibrate theoretical models or computer simulations that can then be utilised to predict field behaviour \(Lade et al., 1981\). Hagiwara et al.'s \(1998\) and Tobar and Meguid's \(2011\) research concentrated on earth pressure measurements acting on shaft walls in dry sand, but both also presented measurements of the surface settlement in relation to the displacement of the shaft wall. Hagiwara et al.'s \(1998\) centrifuge model shaft had a diameter *D* of 120 mm and a depth *H* of 500 mm. Figure 2.6 presents the normalised surface settlement *S*v(*d*)/*H* with respect to the lateral wall movement *u*. The recorded settlement increased approximately linearly up to wall movements between 5 and 7 mm. Then the surface settlement increases more rapidly with wall movement (Figure 2.6\). Tobar and Meguid's \(2011\) 1 g model shaft was 150 mm in diameter, 1000 mm deep and placed in dry sand. They incrementally increased the wall movement to *u* = 4 mm and recorded the surface settlement at two points behind the wall. Figure 2.6 shows the reproduced results of both studies in comparison. It can be seen that the surface settlement *S*v(*d*) normalised by the excavation depth *H* of both studies agrees well when considering the different distances behind the shaft wall *d*. Figure 2.6: Laboratory tests from Hagiwara et al. \(1998\) and Tobar and Meguid \(2011\) on surface settlement depending on lateral wall movement Kusakabe \(1982\) focused on the failure mechanism of unsupported axisymmetric excavation in soft clay by comparing analytical, numerical and centrifuge results. During centrifuge tests various parameters were monitored; among them the surface settlement at collapse. Two undrained and one drained test with a 188 mm deep model shaft were conducted varying the diameter between 60 and 77 mm. Figure 2.7 shows the results of the centrifuge tests compared with his upper bound predictions. For all three tests the settlement extended to approximately 0.7 *H*; the upper bound solution predicted a shorter extent of the trough. The magnitude of the settlement for the drained test agreed with the predictions while the two undrained tests did not match well. Another finding was that the horizontal ground movements were small in comparison to the vertical movements, e.g. in the two undrained tests vertical movements of around 12 mm and horizontal movements of 1 to 2 mm were recorded. This yields ratios of horizontal to vertical maximum movement *S*h,max/*S*v,max of 0.08 to 0.16 which does not agree with Muramatsu and Abe's \(1996\) measurements and Geotechnical Consulting Group's \(2007\) suggestion of *S*h,max/*S*v,max = 1.5 and 1, respectively. It should be noted that Kusakabe's \(1982\) tests are based on unsupported axisymmetric excavations at failure, which are not suitable to use as a base for SLS settlement predictions. Figure 2.7: Results from Kusakabe's \(1982\) unsupported axisymmetric centrifuge studies: Comparison of measurements with upper bound predictions. ### 2.4.2 Structural wall behaviour #### 2.4.2.1 Wall anisotropy Cabarkapa et al. \(2003\) presented results from a 28 m deep and 56.6 m diameter shaft in Dublin Boulder Clay (Table 2.1\). The predicted and measured wall deflections for different excavation stages for three representative panels are shown in Figure 2.8. Firstly, it can be observed that panel 6 exhibits significantly larger deflections than panel 15 indicating an asymmetrical deformation pattern. Secondly, the disagreement of wall movements, those measured and those computed by the Imperial College Finite Element Program (ICFEP), can be observed. This could be explained by the uncertainty of the input parameters for the soil and hoop stiffness of the shaft walls. The latter refers to a key point of the paper: Diaphragm walls and piled walls have joints and are therefore not continuous in the circumferential direction. In FE simulations the stiffness in the circumferential direction is therefore usually reduced. However, the factor of reduction is an area of high uncertainty. Cabarkapa et al. \(2003\) used a factor of 2 based on previous experience, but initially experimented with factors between 1 and 10 to obtain bounds for likely results. When comparing the measured wall deflections with the numerical predictions (Figure 2.8\), the reduction factor of 2 appears too large and the shape does not match well. On the other hand, it is also questionable how trustworthy the inclinometer data is. Zdravkovic et al. \(2005\) who numerically investigated rectangular excavations using ICFEP also concluded that the horizontal stiffness of discontinuous walls has to be reduced (independent on the plan shape of the excavation). An indication on the magnitude of reduction is however not given. Several axisymmetric 'reference' analyses were carried out where the ratio of circumferential to vertical Young's modulus *E*θ/*E* was varied between 1 and 0. The maximum deflection of a wall with reduced stiffness of *E*θ/*E* = 1 × 10−5 is only approximately 60 % of the value obtained from a plane strain analysis, as shown in Figure 2.9. The 'stiff wall' where *E*θ/*E* = 1 gave negligible wall movements. Zdravkovic et al. \(2005\) consider such a simulation clearly unrealistic; however without any comparison to field data. Cabarkapa et al.'s \(2003\) further observations even complicate matters. The deflections trends shown in Figure 2.8 indicated two phases: In phase 1 at shallow excavation levels (Figures 2.8a and 2.8b\) the diaphragm wall panels were discontinuous and behaved like independent cantilevers with larger move- Figure 2.8: Deflection of individual diaphragm wall panels compared with FE predictions for different excavation stages - reproduced from Cabarkapa et al. (2003) Figure 2.9: Axisymmetric analyses with different circumferential stiffness - reproduced from Zdravkovic et al. \(2005\) ments at the top. In phase 2 (Figures 2.8c and 2.8d\) when the initial movement closes any gaps between the panels and activated the hoop stiffness, panels 15 and 20 started bulging at mid and lower depths with a rotation around the ring beam. This indicates that the hoop stiffness of the wall was not realistically modelled by generally reducing the circumferential stiffness by a factor, but that its mobilisation should have been taken into account. The amount of mobilisation can involve parameters such as time, magnitude of deflection, excavation depth and quality of joints. Another study investigated hoop compression forces, Anagnostopoulos and Georgiadis \(2001\) present results from an instrumented shaft of 20.8 m diameter and 9 m depth constructed in sandy soil in Greece (Table 2.1\). The measured hoop forces in the circumferential direction of the 0.6 m thick diaphragm walls are compared to axisymmetric FE simulations (PLAXIS) and simple hand calculations using *K*0 earth pressures (Figure 2.10\). For both cases, the circumferential stiffness was not reduced despite the horizontal discon tinuity of the diaphragm walls. Good agreement was obtained as shown in Figure 2.10 and the authors considered the hand calculations assuming the shaft as a circular hollow cylinder loaded with at-rest earth and pore-water pressures appropriate. They furthermore observed small bending moments at the final excavation stage and hardly any wall deflections. Therefore it might be argued that, in this case of short walls with good quality joints, the full hoop stress was mobilised from an early stage and contributed significantly to the structure's stiffness. Small movements would also not mobilise active earth pressure and therefore justify the good agreement with the simple *K*_0-analysis. Figure 2.10: Comparison of measured hoop force with predictions from a numerical analysis and a *K*_0-analysis - reproduced from Anagnostopoulos and Georgiadis \(2001\) A recent study by Tan and Wang \(2013\) on a 100 m diameter excavation of 18 m depth in Shanghai (Table 2.1\) measured hoop stresses in ring beams and the diaphragm wall in great detail. It was found that the stresses in the ring beams increased directly after their construction when excavation progressed. While the ring beams were only monitored once excavation level reached the particular depth, the stresses in the diaphragm walls could be monitored throughout the shaft excavation. Maximum compressional hoop stresses in the circumferential rebars were approximately 40 MPa which is well within the allowable steel yield strength of 320 MPa. The measured stresses could however not be compared to design predictions, as this was carried out with a two-dimensional plane strain subgrade reaction program. Parashar et al. \(2007\) made similar observations measuring hoop strain on three adjacent large diameter and deep excavations (Table 2.1\). Hoop stresses increased when excavation reached the level of hoop measurements and decreased when the base slab was cast. Both studies Tan and Wang \(2013\) and Parashar et al. \(2007\) did not compare their measured hoop forces with design and hence it was not possible to advise on potential anisotropy in the wall. Anisotropy is usually accounted for with a global reduction factor, which is not yet fully understood and requires further research. As assumed by Cabarkapa et al. \(2003\), the detailed mechanism behind the reduced circumferential stiffness might be more complex than just applying a reduction factor. Stiffness may be mobilised with movement of the walls when gaps between the panels close. This area is particularly important for circular excavations as the realistic modelling of the circumferential stiffness significantly influences the whole system's stiffness and therefore wall deflections, soil movements and surface settlement. Nevertheless, only little research has been carried out. #### 2.4.2.2 Other case studies Marten and Bourgeois \(2005\) presented results of a nearly 15 m deep excavation of 46.3 m diameter retained by 0.8 m thick diaphragm walls in France (Table 2.1\). Monitoring wall head movements and deflections, they found an asymmetric deformation pattern despite the symmetric structural and ground conditions (Figure 2.11\). With the help of three-dimensional FE simulations (CESAR-LCPC) it was shown that the influence of the asymmetric construction sequence was a crucial factor for the deformed shape. Another study by Placzek and Londong \(1994\) of a circular diaphragm wall excavation of 27 m depth and 44 m diameter also showed an asymmetric deformation pattern from the wall head monitoring. Movements towards the retaining soil of 32 mm and 24 mm were observed at two locations due to leakages in the wall. The study by Goto and Iguro \(1989\) of a 46 m deep excavation of 68 m diameter also showed an oval deformation pattern from the wall head monitoring. Figure 2.11: Displacements of diaphragm wall head - reproduced from Marten and Bourgeois \(2005\) Ariizumi et al.'s \(2000\) study on a 144 m diameter excavation presented wall deflections, circumferential and vertical stresses in the diaphragm walls. It was shown that bending stresses were dominant throughout the excavation and that temperature had a significant effect on the measured stresses. Figure 2.12 shows the lateral wall deflections in comparison with numerical predictions; analysis-2 which takes temperature variations into account represents the measurements better. Some other case studies used monitoring schemes in the spirit of the observational method to ensure safe accomplishment and maximum economy given that design can be modified during construction \(Peck, 1969\). One of the main reasons for the implementation of a monitoring system is usually difficult circumstances, such as disturbed and unstable ground conditions or close proximity to other infrastructure. The former was the case for the construction of a 60 m diameter and 30 m deep shaft for London's Heathrow airport \(Powderham, 2000, 2002\). A maximum wall deflection of 15 mm was observed 25 m below ground level (mbgl) - approximately half of the predicted value, which allowed the implementation of design changes, such as a deeper excavation depth. Figure 2.12: Deflections of two diaphragm wall panels in comparison with numerical analyses \(Ariizumi et al., 2000\) The reports by Morrison et al. \(2004\) and McNamara et al. \(2008\) presented the design and construction of a 8.2 m diameter and 37.4 m deep shaft for Crossrail. Very tight constraints were placed on the ground movement due to proximity to piled foundations. Trigger values had been set in case excessive movements were recorded. As in the previous study, the measurements were approximately half of the predictions. This shows the conservatism that has to be adopted due to highly uncertain design assumptions. Gerolymos et al. \(2007\) reported a case study for the shaft constructed for the opening ceremony for the Athens' Olympic Games. Design was carried out with the most probable and favourable conditions but also for the worst-case scenario which included unfavourable soil properties, water conditions and disregarded the hoop effect. For the final excavation step the favourable design predicted a maximum deflection of 13 mm at 12 mbgl, whereas the unfavourable conditions predicted 40 mm. Contingency measures were planned in case this scenario occurred which was not the case; the measured deformations agreed reasonable well with the predictions for the most probable conditions. However, the ratio between the upper and lower bound, 40 mm/12 mm, gives a factor of 3.3 which highlights the uncertainty of the construction. #### 2.4.2.3 Model scale Not much work at model scale has been done to observe wall deflections of circular excavations. As mentioned above, Kusakabe \(1982\) conducted extensive centrifuge tests and also measured lateral soil displacements of an unsupported excavation; however at collapse and not under working conditions. Figure 2.13 shows the observations and the measurements predicted by his upper bound theory which agree reasonably well. The upper part of the 185 mm deep excavation of 30 mm diameter (model scale) moves 8 mm vertically downwards while the lower part bulges 13 mm towards the excavation. The field observations related to the mobilisation of hoop stiffness by Cabarkapa et al. \(2003\) have to date not been investigated in model studies and require further research - in the field as in the laboratory. Figure 2.13: Kusakabe's \(1982\) measured and predicted failure surface ### 2.4.3 Subsurface settlement and earth pressure #### 2.4.3.1 Theoretical approaches For most design approaches it is essential to understand the failure mechanism and to have a good understanding of the earth pressure distribution on the wall. Both are linked very closely, as earth pressure theories are based upon the assumption of a failure surface. The classical earth pressure theory by Coulomb \(1776\) is based on the limit equilibrium of a sliding wedge and is well established for two-dimensional conditions. Starting with Terzaghi \(1920\) extensive research has been conducted to establish relationships between wall movement and active earth pressure. However, most of these approaches are only valid for plane strain conditions. Designers using these formulas for axisymmetric cases neglect the beneficial arching effects and obtain more conservative results. Much effort has also been made to extend these two-dimensional theories to axisymmetric conditions which was reviewed by Tobar and Meguid \(2010\). Analytical methods based on classical Rankine theory were proposed by Westergaard \(1941\) for small unlined drilled holes and extended by Terzaghi \(1943\) for large lined holes. Although Terzaghi's \(1943\) solutions agreed well with other proposed methods (Figure 2.14a\), the assumption of the plastic zone renders the theory inadequate according to Prater \(1977\). Coulomb's failure surface leading to a sliding mass cone with downward pointing tip (Figure 2.14b\) is a more realistic shape and was adopted for Prater's \(1977\) limit equilibrium approach (Figure 2.14a\). Berezantzev \(1958\) firstly extended the slip line method to axisymmetric conditions (Figure 2.14a\). Both, Prater \(1977\) and Berezantzev \(1958\), are however limited to *c* ′ or *φ* ′ soil only, to vertical, smooth walls and level ground \(Cheng et al., 2007\). Berezantzev's \(1958\) method was extended by Cheng et al. \(2007\) and Liu and Wang \(2008\) to included further parameters, such as wall friction, backfill slope, surcharge load and soil cohesion. Prater \(1977\) also highlighted the sensitivity to the earth pressure coefficient *λ*r , which is defined as the ratio of circumferential stress to vertical stress and determines the tangential force *T* due to the axisymmetric arching effect (Figure 2.14b\). He argued that the assumption of *λ*r = 1, as adopted by Berezantzev \(1958\) and Terzaghi \(1943\), underestimated the earth pressure. Therefore, Cheng and Hu \(2005\) modified Berezantzev's \(1958\) theory to include *λ*r as a parameter, with *λ*r = *K*0 as a lower and *λ*r = 1 as an upper bound (Figure 2.14a\). (a) Overview of several approaches to estimate lateral earth pressure for axisymmetric conditions (b) Prater's \(1977\) wedge theory for axisymmetric conditions using tangential and radial force *T* and *F* Figure 2.14: Lateral earth pressure and failure mechanism for axisymmetric conditions Most of the above mentioned approaches are displayed in Figure 2.14a. It also includes the conventional plane strain distributions with the lateral earth pressure at rest *K*0 and under active conditions *K*a, which are significantly higher than the pressures under axisymmetric conditions. The theories based on *λ*r = 1 produce the lowest lateral earth pressures, while *λ*r = *K*0 is suggested for engineering applications to give a safe lower bound approximation \(Cheng and Hu, 2005; Prater, 1977\). It can be seen that the existing approaches vary significantly especially with increasing depth. Tobar and Meguid \(2011\) highlight that there is high uncertainty of the required wall movement *u* to reach active conditions. Previous studies by Fujii et al. \(1994\), Herten and Pulsfort \(1999\) and Chun and Shin \(2006\) propose a wide range of values for the required wall movement *u* normalised by the excavation depth *H*, 0.05% ≤ *u*/*H* ≤ 1.8%, or normalised by the shaft diameter *D*, 0.07% ≤ *u*/*D* ≤ 3.3%. This is not surprising, as *u*/*H* and *u*/*D* are expected to vary according to the strain mobilisation. Vardanega and Bolton \(2011\) show that strain required to mobilise half the strength varies from about 0.1 % for low-plasticity silty clays to 3 % for high-plasticity clays. #### 2.4.3.2 Experimental data To remedy the uncertainty inherent to the above mentioned approaches it is essential to conduct field and model studies that can be compared to the theoretical data. As earth pressure is closely linked to the assumed failure mechanism, the measurement of both, the earth pressure itself and the subsurface movements, are equally important. A few case histories investigated the earth pressure acting on the shaft wall. Enami et al. \(1996\) concentrated on earth pressure measurement during a caisson sinking of 36.5 m depth and 30.4 m diameter (*D*/*H* = 0.83, Table 2.1\). They found that the earth pressures above 10 m were approximately 2 times larger than predicted by a *K*0 value of 0.5. Below 10 m depth the measured earth pressures were significantly lower than *K*0 predictions. Kim et al. \(2013\) reported similar pressure distributions from the measurements at their field test shaft of 15 m depth and 8 m diameter (*D*/*H* = 0.53, Table 2.1\); the results are presented in Figure 2.15. At shallow depth the earth pressure is similar to the Rankine predictions, but at deeper depth the pressure decreases significantly. This shows that the arching effect of axisymmetric excavations and the nontriangular distribution is predominant for deep excavations with small *D*/*H*ratios. This is supported by field studies with large *D*/*H*-ratios \(Ariizumi et al., 2000; Goto and Iguro, 1989\) which show a triangular earth pressure distribution and no decrease with depth. Muramatsu and Abe's \(1996\) earth pressure measurements of a deep shaft (*D*/*H* = 0.47) showed, against above theory, a triangular pressure distribution. They reported initial *K*0-values of 0.6 only dropped insignificantly to 0.5 after excavation. This small reduction is in line with the small surface settlement (Figures 2.4a and 2.4c\). Unfortunately, the subsurface ground movements next to real axisymmetric excavations have not been reported much. During the works for the Heathrow express trial tunnel extensometers and inclinometers were used to record subsurface movements due to tunnelling, but not for the shaft excavation \(New and Bowers, 1994\). Wong and Kaiser \(1988\) used multi-point extensometers to measure vertical movement and inclinometers for horizontal movement. The purpose of the obtained measurement were the comparison to FE predictions, but no further conclusions were drawn. In general it is difficult to get an overview of ground movements from field studies, as data is limited to the instrumentation locations, which is again Figure 2.15: Kim et al.'s \(2013\) measurements of lateral earth pressure for a circular excavation in comparison to their predictions and Rankine theory limited by the available budget. Therefore model tests, especially centrifuge tests, can provide a better picture of the failure mechanism. In his centrifuges studies in undrained soft clay Kusakabe \(1982\) investigated the failure mechanism of unsupported excavation, as this is crucial for a good upper bound solution. Figure 2.13 presents the discontinuity lines obtained by his theoretical prediction (dashed lines) compared with the centrifuge results (continuous lines). Good agreement for the wall movement as well as for the inclined rupture zone is achieved, but not for the vertical slip surface. Therefore it cannot be clearly concluded whether the assumed failure mechanism is correct. In their centrifuge tests in sand Lade et al. \(1981\) varied the radial stresses inside a circular excavation (*D*/*H* < 0.34) and measured earth pressure at different depths. They observed earth pressures slightly larger than Berezantzev's \(1958\) but much lower than at rest and active predictions. While Lade et al. \(1981\) decreased stabilisation fluid pressure to simulate the excavation process, Ueno and Yokoyama \(1996\) used an in-flight excavator and conducted an extensive study on the flexibility of the shaft wall. Firstly, they again confirmed the underestimation of Berezantzev \(1958\) and the conservatism of Rankine's active earth pressure at depths deeper than two times the shaft radius. They secondly found that the stiffness of the lining dominates the magnitude of the earth pressure and established a fudge factor *α*f that relates the 'real' lateral earth pressure *σ*r (based on their measurements) to Berezantzev's \(1958\) active earth pressure *σ*rB $$\alpha_{\rm f} = \frac{\sigma_{\rm r}}{\sigma_{\rm rB}} = 1 + 1.15 \cdot 10^{-4} \cdot \frac{Et/r}{\sigma_{\rm a}} \tag{2.9}$$ where *Et*/*r* is the apparent Young's modulus where *E* is the Young's modulus of the wall material, *t* is the wall thickness and *r* is the radius of the excavation. *σ*a is the atmospheric pressure datum equal to 98 kPa and used to make the formula's units consistent, but has no logical meaning. It is also difficult to apply the results of this idealised centrifuge test to apply to real-scale shafts. Hagiwara et al. \(1998\) measured horizontal active and at rest earth pressure on centrifuge model shaft (*D*/*H* = 0.24) which were equipped with moving parts. At rest pressures were in agreement with the *K*0 predictions. Only at a large wall movement of approximately *u*/*H* = 4 × 10−3 (where *u* is the wall movement and *H* the excavation depth) the measurements agreed well with Berezantzev's \(1958\) values. Tobar and Meguid (2010) concluded that the theoretical approaches are reasonable for shallow shafts with *H* < *D*, but there is high uncertainty for deep shafts with *H* > *D* due to the high influence of the ratio between vertical and horizontal arching at these depths. The upper bound solution, Berezantzev \(1958\) with *λ*r = 1, and the lower bound solutions, Prater \(1977\) and Cheng and Hu \(2005\) with *λ*r = *K*0, yield largely different earth pressures. Apart from this, there is a complete lack of understanding of the required wall movement for active conditions. Further studies of the failure mechanism and subsurface movement of real scale excavations as well as model studies are needed to establish more reliable approaches. ### 2.4.4 Wall installation effects The earth pressure on a retaining wall does not only depend on wall movement, but can also change due to construction of the wall itself. Installation effects can be caused by the excavation of soil with a slurry wall grab or a hydrofraise and the use of stabilising fluid or fluid concrete \(Gunn and Clayton, 1992\). These effects may render the common numerical assumption of WIP walls as not appropriate. Neglecting installation effects, especially for heavily overconsolidated soils, such as London Clay, where the earth pressure coefficient *K*0 can range between 1 and 2 at greater depth and up to 4 near the surface \(Hight et al., 2007\), can yield conservative results of earth pressure loading on the wall \(De Moor, 1994\). On the other hand, when considering installation effects but under plane strain conditions, the reduction of the lateral earth pressure can be overestimated. De Moor \(1994\) and Gourvenec and Powrie \(1999\) highlighted the importance of three-dimensional influences, such as horizontal soil arching and the installation sequence of diaphragm wall panels. De Moor \(1994\) numerically investigated the stress relief due to wall installation and compared her results to Symons and Carder \(1993\). Using the two-dimensional FE program CRISP and focusing on stiff overconsolidated finegrained soils such as London Clay, De Moor \(1994\) analyses a plan (horizontal) section through a series of diaphragm wall panels rather than a cross-section. The results agree well with field data from Symons and Carder \(1993\) and suggest that initial *K*0 in London Clay of 1.5 reduced to 1.1 after wall installation. De Moor \(1994\) furthermore produced non-dimensional graphs to estimate the change in lateral earth pressure for different panel geometries and stress changes. Ng and Yan \(1999\) and Gourvenec and Powrie \(1999\) conducted full three-dimensional analyses of diaphragm wall installation and concluded that the amount of lateral stress relief decreases with panel length. Furthermore, they confirmed that the stress relief on a single panel could be partly reversed during the construction of neighbouring panels. Sideri \(2012\) focused on the installation effect for circular excavations of different construction methods and varying diameter-to-depth-ratios in London Clay. Figure 2.16a shows the development of the lateral earth pressure coefficient (averaged over wall depth) throughout the construction of a diaphragm wall, determined from two-dimensional numerical simulations with ICFEP. The initial value of 1.44 reduces rapidly when the panels are excavated under bentonite, but increases again during wall concreting. Concrete hardening decreases the earth pressure again and shaft excavation has almost no effect. Sideri \(2012\) also studies the influence of wall anisotropy (due to joints between the panels) on the earth pressure during shaft excavation. The excavation reduces the lateral earth pressure more significantly for walls with very low circumferential stiffness. For *E*θ/*E* = 1 × 10−5 for example the lateral earth pressure coefficient reduces from 0.95 to 0.6 due to larger wall movements. For jacketed shafts the lateral earth pressure reduces progressively with increasing shaft depths (Figure 2.16a\). CIRIA C580 \(Gaba et al., 2003, p. 255-259) lists a number of case studies conducted to investigate wall installation effects. Richards et al. \(2006\) for example thoroughly investigated the changes in horizontal water and earth pressure during installation of a bored pile wall and found a reduction of *K*0 from 1 to 0.8 and no further change over 10 months after the installation. The changes in lateral loading due to borehole excavation, fluid and concrete pressure also resulted in surface settlement. This shows that 'even the most rigid diaphragm or secant pile wall cannot be totally effective in preventing loss of ground' \(Gunn and Clayton, 1992\). Similar observations were made by Burland and Hancock \(1977\). They recorded the surface settlement behind a shaft wall of a rectangular excavation in London and found that approximately 50 % of the deformation had occurred during installation of the diaphragm wall. Muramatsu and Abe \(1996\) measured the horizontal and vertical movements around a circular shaft during wall construction, as shown in Figure 2.16b. From this it can be observed that again approximately half of the total horizontal and vertical ground movement had occurred during the construction process of the diaphragm wall. This is a significant amount that cannot be reduced by increasing wall stiffness, since it is inherent to the construction process. Even for rectangular excavations where more field and case studies exist, CIRIA C580 \(Gaba et al., 2003\) states that 'it is difficult to give general advice on the magnitude and extent of lateral stress reduction during wall installation', as this depends on the in situ *K*0, soil and ground water conditions, pile or panel geometry, construction sequence and the detailed method. They generally suggest to reduce the lateral earth pressure coefficient to 1.0 (for overconsolidated soils) but use the in situ *K*0 = 1 − sin*φ* ′ (for normally consolidated soils) where *φ*′ is the effective stress friction angle. (a) Development of lateral earth pressure coefficient (averaged over wall depth) throughout construction and excavation of a diaphragm wall shaft and a shaft sinking - reproduced from Sideri (2012) (b) Vertical and horizontal surface displacement during wall installation and excavation reproduced from Muramatsu and Abe (1996) Figure 2.16: Effect of wall installation ## 2.5 Summary and key points This chapter reviewed the existing literature on circular excavations. Common shaft construction methods were discussed in Section 2.2. Section 2.3 highlighted that most existing design approaches were produced for plane strain conditions, whereas shafts are axisymmetric. A detailed review of on-going research, covering field and model studies, as well as theoretical approaches, was carried out in Section 2.4; the key points are summarised below. The literature contains a very small number of well-documented case histories on circular excavations, while box excavations are significantly better documented. Thus, the British tunnelling industry relies on the study carried out by the Transport Research Laboratory on the Heathrow Express Trial Tunnel shaft sinking \(New and Bowers, 1994\). The formula has several limitations, such as not considering the shaft diameter, the construction method and the ground conditions. The settlement estimation guidelines for the Crossrail project Geotechnical Consulting Group \(2007\) are based on New and Bowers' \(1994\) formula, but include the shaft diameter, which results in very large settlements for large-diameter shafts. The predictions from these empirical approaches were compared to the field measurements of two case studies, which showed highly inconsistent results. Especially for Muramatsu and Abe's \(1996\) diaphragm wall shaft the predictions were significantly larger than the measured data. Conservative design approaches resulting in larger settlements than probably occur in reality lead to more expensive structures and protective measures. For diaphragm wall shafts further uncertainty arises from the discontinuous nature of the wall, as it is made of individual panels. Previous research \(Cabarkapa et al., 2003; Zdravkovic et al., 2005\) suggests that the wall's circumferential stiffness has to be reduced to account for the joints between the panels. A potentially lower hoop stiffness could have high influence on wall and ground movements. Only a few studies have investigated the wall anisotropy and hence there is a lack of understanding on how to incorporate this in design. With the forthcoming Thames Tideway Tunnel for which several deep excavations are required, there is high need for a better understanding of ground movements and structural performance. This underpins the necessity for the field study at Abbey Mills to measure structural forces and ground movements around a shaft with a typical London geology.