Introduction

When the ground is excavated for a deep basement, the permanent removal of soil overburden leads to a reduction in long-term vertical effective stress, causing the remaining soil to swell. In over-consolidated clay strata such as London Clay, this process of swelling continues after the completion of the basement structure, generating heave displacement at formation level as the clay swells, or applying large swell pressures on the base slab where the clay is restrained from swelling by the structure [1]. This process is known as “long-term heave” and engineers must design the base slab to restrain or allow for these gradual movements and pressure changes, which often continue for over a decade beyond structural completion [2].

One aspect of basement construction that may affect long-term heave behaviour is the embedment condition of the base slab. Most basements in over-consolidated clay are built by first constructing diaphragm walls that extend into the clay below the formation level; secant pile walls and contiguous pile walls are also used in place of diaphragm walls. The soil is then excavated down to formation level. The base slab is cast, sometimes directly onto the clay, other times with a porous drainage layer placed between the clay and the slab. The length of diaphragm wall extensions below formation level is generally dictated by stability requirements in temporary conditions [3,4,5], whereas the use of a drainage layer is typically driven by concerns about groundwater buoyancy in steady-state conditions.

There is some guidance on how to account for heave loads generated by the swelling clay in the design of these elements of a basement structure [6, 7], considering the nonlinear stiffness of the clay soil, the stiffness of the structural slab, and any relaxation that may occur between excavation and base slab construction. However, there has been relatively little research on how these aspects of basement construction in turn influence heave behaviour and consequent soil–structure interaction.

Notable past research in this area includes studies on the effect of arrays of tension piles in restraining the basement slab heave [8, 9] and controlled flooding of the formation level [10]. The research presented in this paper aims to complement the existing body of research by investigating two aspects of slab embedment: extensions of diaphragm walls beyond formation level and under-slab drainage. This paper presents geotechnical centrifuge testing and numerical modelling of four basement construction scenarios for relatively flexible and stiff basement slabs in over-consolidated clay strata, which aim to discern the influence of these two aspects of embedment conditions on long-term heave displacements and swell pressures.

Representative Prototypes

This paper examines four scenarios of basement construction in over-consolidated clay, all of which were simulated in both centrifuge modelling and finite element (FE) modelling. Each scenario modelled a 12 ~ 15-m-thick, dry, dense sand layer underlain by a 16-m-thick layer of over-consolidated clay. The base of the clay layer was supported on a rigid but permeable base to simulate weathered bedrock with relatively high permeability (see Figs. 1 and 2).

Fig. 1
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Cross-sectional drawing of flexible basement prototypes (left: without embedment “fins”; right: with “fins”)

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Fig. 2
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Cross-sectional drawing of stiff basement prototypes (left: without keying; right: with 3 m keying into clay)

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Each basement was 15 m wide and buried 15 m into the ground. The length of the basement was 30 m in all cases. The length of the basement was chosen such that the mid-section can be reasonably approximated as a plane strain problem in the finite element analyses. Chan and Madabhushi [11] provide further discussion of the prototypes’ general configuration.

The four prototypes were divided into two pairs: two relatively flexible basement slabs and two stiff basement slabs. The stiff basements’ slabs and walls were specified to match the plate bending stiffness of typical basements in London Clay, whereas the flexible basements’ base slabs and walls were specified to be significantly more flexible than typical basements so that the models would attract large deformations to aid the identification of heave mechanisms. Table 1 shows the slab and wall thickness specifications, alongside the equivalent reinforced concrete slab stiffness according to a cracked stiffness analysis [12]. The water table was set at the clay–sand boundary to remove buoyancy loads from the heave problem.

Table 1 Basement structure specifications
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The stiffness of the two basement slab prototypes can be compared to the relative raft/soil stiffness ratio (K) defined by O’Brien et al. [7], taking the half-width of the slab (L/2 = 7.5 m) as homologous to the raft radius and the oedometric modulus (Eoed) as the representative stiffness of the clay (see Table 5). The flexible prototype gives K = 0.11 and the stiff prototype K = 3.5, falling on the two ends of the “intermediate stiffness” range. Chan et al. [13] compared the flexible base slab and the stiff base slab prototypes to discern the influence of base slab stiffness on heave behaviour; this paper will make comparisons within each pair of prototypes with the same slab stiffness but different embedment conditions, to discern the effects of embedment and drainage on heave behaviour.

The two basements within each pair differed in terms of embedment and drainage conditions beneath the slab. Different embedment conditions arise from the construction techniques used in the field. The flexible basements differed from each other in that the first prototype basement (“no fins”) was located entirely above the clay layer with a drainage layer separating the base slab from the clay; the diaphragm walls did not extend below the formation level. The second prototype basement (“with fins”) had diaphragm walls that extended 3 m into the clay stratum, forming “fins” that provided some restraint against tension due to embedment and offered groundwater cut-off between the clay below the basement and that in the free-field. These prototypes were used for direct comparison and to isolate the effect of tension embedment on long-term heave behaviour. Figure 1 presents the cross-sectional views of these two prototypes.

The next set of prototypes involved stiff basement slabs and were tested to investigate the effects of keying in the basement slab into the clay stratum, i.e. the formation level is in the clay. The stiff basements were structurally identical to each other, but the “unkeyed” basement was founded on top of the clay stratum with a thin layer of sand separating the base slab from the clay, whereas the “keyed” basement was sunk 3 m into the clay layer with direct contact between the base slab and the clay. Accordingly, the clay directly underneath the keyed basement slab was 13 m thick (as opposed to 16 m for the unkeyed basement) and the sand layer in this prototype was only 12 m thick (15 m for the unkeyed basement), to simulate similar initial and long-term vertical stress conditions at formation level. Figure 2 presents the cross-sectional views of these two prototypes.

Centrifuge Model

The centrifuge tests in this research were performed at 100 g (multiples of Earth’s gravitational acceleration), which means the prototype dimensions were scaled down by a factor of 100 to give the model dimensions. The centrifuge models were built inside a cylindrical strong box of 850 mm diameter, giving a simulation field of 85 m prototype width. The basement models were 150 mm × 300 mm in plan area, giving a prototype footprint of 15 m × 30 m. Two props 100 mm apart (10 m in prototype scale) from each other provided lateral support to the side walls following excavation and were located slightly above ground surface level (Fig. 3), to avoid submerging load cells in the electrically conductive heavy fluid solution during the experiment. This detail is slightly different from site practice, where the props are normally provided to support the diaphragm walls at some depth below the ground surface, and often at multiple levels.

Fig. 3
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Cut-out plan view of centrifuge model

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To prepare the over-consolidated clay layer, Speswhite kaolin powder was mixed with water in a vacuum mixer to give a slurry of water content w = 125%, or 1.6 times the liquid limit. The slurry was poured into the strong box and compressed in a hydraulic consolidometer to a maximum effective stress of 800 kPa. The load was then gradually reduced to from 800 to 80 kPa over a typical duration of one week, in decrements of 60–100 kPa. Care is taken to avoid cavitation by ensuring that the negative excess pore pressure never exceeded 100 kPa and by always supplying enough water to the clay surface [14]. The strong box and clay were then removed from the consolidometer.

The clay was trimmed to the target thickness of 160 mm to give a prototype stratum thickness of 16 m. The basement model was installed, and then, dry Hostun sand was poured around the basement using an automatic sand pourer [15] at a density of 1625 kg/m3. Tables 2 and 3 summarise the properties of the clay and the sand used in the centrifuge models, respectively.

Table 2 Properties of Speswhite kaolin clay in centrifuge model
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Table 3 Properties of Hostun sand in centrifuge model
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In each centrifuge test, the basement cavity would be filled with a heavy fluid (sodium polytungstate solution) of the same density as the dry sand outside the basement. Excavation was simulated by removing this heavy fluid from the basement cavity during centrifuge flight and draining it to the catch-tank at a lower elevation. This technique of using heavy fluid to support a cavity to establish initial equilibrium and its drainage to simulate the excavation process has been well established and used extensively by centrifuge modellers [16,17,18,19]. Subsequent to the drainage of the heavy fluid, an electrical actuator would apply a vertical load onto the top of the basement walls to model the construction of a light superstructure. Towards the end of the experiment, the actuator load would be increased to simulate the short-term effect of building a heavy superstructure (Table 1). The magnitudes of the superstructure loads were informed by the Horseferry Road case study [20], and the effect of heavy superstructure load on heave behaviour was discussed in Chan et al. [14]. The full experimental sequence is given in Table 4.

Table 4 Experimental sequence
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The centrifuge model provided five types of instruments:

  • Linear variable differential transducers (LVDT) measured the vertical displacements of several points of the base slab and of the far-field clay surface;

  • Strain gauges along the centre line of the basement models measured the bending curvature of the slab and walls;

  • Load cells measured the axial load in each prop;

  • Pore pressure transducers in the clay were used to monitor the progress of each experiment and measure the pore pressure response to excavation and superstructure loading;

  • Tekscan tactile sensing mats measured the distribution of slab–soil contact pressures for some experiments and wall–soil contact pressures in others.

Numerical Model

The software package used in the FE models in this research was PLAXIS 2D 2017-01 [21]. The over-consolidated clay was represented by a small-strain hardening (HSS) model [22] to capture the nonlinear stiffness of the clay. This constitutive model combines several stiffness and yield characteristics that are appropriate for over-consolidated clay behaviour:

  • Cap surface (Fig. 4, cf. Modified Cam Clay) to model the wet-side volumetric yield behaviour of the clay, though this is seldom triggered in a simulation of construction in over-consolidated clay beyond model initialisation;

  • Mohr–Coulomb yield surface and tension cut-off to approximate the dry-side shear yield behaviour of the clay, addressing the common observation that Cam Clay-type models over-estimate dry-side yield strength (Fig. 4, cf. Hvorslev surface);

  • Shear hardening mechanism to capture the gradual change in stiffness as the soil approaches ultimate strength;

  • Small strain stiffness degradation mechanism to capture the very high initial shear stiffness and subsequent rapid drop of stiffness with increasing strain (Fig. 5).

Fig. 4
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Illustration of yield surfaces in HSS model, after Chan et al. [13]

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Fig. 5
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Stiffness degradation curve of the HSS model used in this research, after Chan et al. [13]

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The “Undrained (A)” pore pressure generation algorithm and the “Consolidation” construction stage simulation method were used, leading to fully coupled simulations of effective stresses and pore pressures.

The constitutive parameters of the clay were calibrated using triaxial test data on Speswhite kaolin from Vardanega et al. [23] and one-dimensional compression data from the preparation process of the clay samples used in the experiments reported in this paper. The sand was represented by a Mohr–Coulomb model with constitutive parameters for Hostun sand obtained from the experiments reported in Heron [24] and Deng and Haigh [25]. Table 5 summarises the constitutive parameters used in the finite element simulations. The software package and soil constitutive models were chosen to match current practices in industry where finite element models of basement heave in over-consolidated clays are needed.

Table 5 Properties of soils used in finite elements model
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The models were simulated in plane strain conditions. The basement slab and the side walls were modelled as linear–elastic plate elements whose bending stiffness values matched the equivalent basement models in the centrifuge tests, and the soil–structure interfaces were specified to be fully waterproof and to mobilise full friction. The props were included in the FE model, but the stiffness of the end walls of the basements was not included (Fig. 6), owing to the plane strain assumptions. The plane strain assumption is considered satisfactory for the mid-section of the basement, far away from the end walls. The stiffness of the two props in the centrifuge model was converted to an equivalent plane-strain prop stiffness of 1.98 × 109 N/m for the finite element model. The permeability of the clay was calibrated using experimental data, and the permeability of the drainage layer was assumed to be 10 times that of the clay.

Fig. 6
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Annotated FE results of vertical stress contours of flexible basement without embedment

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Each simulation was initialised with geo-static conditions. The soil in the space to be occupied by the basement was then replaced by the basement structure and line loads representing the pressure exerted by the heavy fluid. The model was then allowed to reach equilibrium; this equilibrium would be taken as the datum of subsequent displacement measurements. The excavation, construction, and consolidation stages were then performed according to the sequence listed in Table 4, matching the prototypes represented by the centrifuge test sequence. The durations of these phases are listed in Table 4. For the stages where the model was left to consolidate to equilibrium, an excess pore pressure limit of 1 kPa was used.

Figure 6 shows the general arrangement, the mesh, and the long-term equilibrium vertical effective stresses from the finite element model of the flexible basement without embedment. Chan and Madabhushi [11] and Chan et al. [13] discussed the goodness of fit between the centrifuge data and the FE results for similar basement problems.

Influence of Tension Embedment on Heave Response

The flexible basement prototypes, which aimed at generating large heave displacements, were investigated to aid the identification of the deformation mechanisms. By comparing the profiles of vertical displacement of the base slabs with and without the fins, the influence of the tension embedment fins could be determined.

The experimentally determined profiles of vertical displacement are shown in Fig. 7. The data points are locations at which LVDT measurements were taken and the trend lines are quadratic best-fit lines assuming axis of symmetry. In both centrifuge tests, the centre of the slab showed a large heave displacement of about 100 mm upon first excavation. This was followed by a further rise of about 25 mm during the hiatus phase (see Table 2). There was some redistribution of load during the construction of the light superstructure, which led to a small settlement of the centre of the slab in both experiments.

Fig. 7
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Centrifuge measurements of vertical displacement of flexible basement prototypes

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When the clay layer was allowed to consolidate to equilibrium after the construction stage, the centre of the base slab continued to rise, giving an overall heave magnitude of about 200 mm in the long-term (i.e. 5 years after the excavation stage). The basement with fins appeared to have a larger mid-span vertical displacement than the basement without fins.

The edges of the slabs were restrained by the slab-wall connections. The deflections recorded near the ends of the base slabs were less than 50 mm. The ends of the basement slab without fins tended to rise slightly between first excavation and long-term equilibrium, while the ends of the slab with fins tended to settle slightly after construction.

The FE models reproduced the same trends as the centrifuge tests. The lines in Fig. 8 are FE-calculated profiles of displacements, and the corresponding centrifuge results are also given for displacements immediately after excavation and in long-term equilibrium with light superstructure load. The FE model and the experiments were in agreement that the centres of the slabs heaved significantly upon first excavation, and the heave displacement rose gradually to about 200 mm in the long term (i.e. 5 years after excavation) when equilibrium was reached. The addition of fins would lead to a small increase in mid-span vertical displacement in the long-term equilibrium state.

Fig. 8
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FE predictions of heave displacement of flexible basement prototypes

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The main discrepancies appear in the modelling of undrained stiffness. The FE model underestimated the amount of heave upon first excavation, and does not capture accurately the effect of load redistribution caused by light superstructure construction. Both the centrifuge test and the FE model predicted that the addition of tension embedment has reduced the amount of upward displacement near the slab-wall connection, but the difference is greater in the centrifuge results.

Some discrepancy in the amount of undrained displacement is to be expected, because the soil stiffness in the HSS constitutive model was defined in terms of effective stress parameters. Undrained stiffness values were obtained by superposing the stiffness of water onto the soil stiffness (known as the “Undrained (A)” algorithm). Previous research has shown that HSS generally over-estimates the undrained stiffness of stiff clays [26].

The impact of base slab heave on the serviceability of the basement is determined by the amount of vertical displacement that occurs after the end of construction due to excess pore pressure dissipation. Figure 9 plots the change in heave displacement between the end of construction (“light superstructure construction” phase in Fig. 8) and long-term equilibrium for both prototypes, showing both centrifuge and FE results. The additional heave at mid-span due to excess pore pressure dissipation was about 80 mm in all cases, though there is some discrepancy between centrifuge and FE data as to whether adding the fins would raise or lower this amount, again most likely because the HSS constitutive model had over-estimated the undrained stiffness of the clay.

Fig. 9
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Change in heave displacement after construction

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The addition of tension embedment fins also affected the speed of heave movements. Figure 10 plots the vertical displacement at the middle of the slab against time since the start of excavation. The centre of the basement slab with fins appeared to undergo more heave and took significantly more time to approach equilibrium than the basement without fins.

Fig. 10
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Variation in mid-span vertical displacement with time for flexible basement centrifuge tests

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A square root of time fit per BS 1377-5:1990 [27] suggested that the basement with fins took 30 months from the end of light-superstructure construction (dip at 5 months in Fig. 10) to achieve 90% consolidation (t90), whereas the basement without fins only took 21 months.

The effects of the fins on the heave behaviour of the basement may be explained by the fact that the fins had confined the mechanism of deformation. This can be illustrated by plots of excess pore pressure upon first excavation (Fig. 11). For the basement without fins, the clay could absorb water from the drainage layer between the slab and the clay, limiting the under-slab excess pore water pressure. In contrast, the fins acted as groundwater cut-off layers. The lack of a drainage layer allowed the generation of large excess negative pore pressures at formation level. The drainage distances in the clay under the slab were increased significantly, leading to a much slower consolidation process (Fig. 10).

Fig. 11
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Plots of excess pore pressures immediately after excavation (Stage 3 of Table 2) from FE models of flexible basement prototypes. (a, top:) no fins; (b, bottom:) 3 m fins

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The fins also influenced how the stiffness of the clay stratum was mobilised. For the basement without fins, the clay immediately beneath the basement was contiguous with the clay outside the basement footprint. The resulting mechanism can mobilise the stiffness of the clay outside the footprint. In contrast, when fins were added, they cut off the clay outside the basement from the deformation mechanism, as illustrated by the large difference in excess pore pressures on the two sides of the fins (Fig. 11). This meant that a greater proportion of the stress changes due to excavation was absorbed by the clay immediately beneath the slab. Figure 12 shows FE-predicted displacement fields in the clay underneath the two flexible basement prototypes, between the pre-excavation stage (Stage 2 in Table 2) and equilibrium with light superstructure (Stage 6). Compared to the basement without fins, the tension embedment fins caused a zone of stationary clay to form around it, narrowing down the zone of the heave displacements underneath the basement footprint, thereby leading to a slight increase in heave displacement at the centre of the base slab.

Fig. 12
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Plots of displacement vectors in the clay layer predicted by FE models of flexible basement prototypes. (a, top:) no fins; (b, bottom:) 3 m fins

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Influence of Keying on Heave Response

Due to construction requirements and/or the soil stratigraphy at the site, it is sometimes required that the formation level of the basement slab is keyed into the clay stratum. This aspect is investigated for the case of stiff basement slabs shown in Fig. 2. The two stiff basement prototypes differed from each other in terms of the keying conditions. The basement without keying was founded entirely above the 16-m-thick clay layer with a thin drainage layer of sand separating the base slab from the clay. The basement with keying was sunk 3 m into the clay layer, with direct contact between the base slab and the clay, and consequently a thinner stratum of clay between the base slab and the bedrock (approximately 13 m), and a slightly longer drainage path for the clay immediately beneath the slab.

In both centrifuge tests, the vertical displacement of the centre of the slab was much less than their flexible counterparts. As shown in Fig. 13, the centres of the stiff slabs heaved by about 25 mm immediately upon excavation, followed by another about 25 mm during the hiatus owing to drainage, then settled by about 25 mm upon the imposition of a light superstructure load. These displacements were an order of magnitude smaller than those reported for the flexible prototypes (Fig. 10) due to the differences in structural stiffness. Further discussion on the influence of slab stiffness on heave displacements and swell pressures can be found in Chan et al. [13].

Fig. 13
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Variation in mid-span vertical displacement with time for stiff basement centrifuge tests

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Afterwards, the centre of the keyed-in base slab heaved more and took longer to reach equilibrium, than the slab without keying. However, the time of consolidation could not be determined reliably because of the small magnitude of displacement.

The profiles of experimentally determined vertical displacement at different construction stages are shown in Fig. 14. The data points are locations at which LVDT measurements were made, and the trend lines are quadratic best-fit lines assuming axis of symmetry.

Fig. 14
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Centrifuge measurements of profiles of heave displacement of stiff basement prototypes

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The most prominent difference between the two plots in Fig. 14 is that, in the excavation and hiatus stages, the basement without keying showed significant differential heave, meaning that the sides exhibited less heave at formation level than the middle of the slab. In contrast, the keyed-in basement showed an almost uniform profile of upward displacement, suggesting that the whole soil body moved upwards, mobilising a different undrained heave mechanism, which will be discussed in further detail below.

The centrifuge tests of these two prototypes also included tactile pressure sensor measurements of slab-soil contact pressure, which can shed further light on the heave mechanism. Figure 15 plots the profiles of slab pressure obtained by tactile pressure sensor measurements and by FE modelling, showing distributions of pressure at the end of excavation and in long-term equilibrium.

Fig. 15
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Profiles of slab-soil contact pressure of stiff basement prototypes

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For both prototypes, the pressure at the centre of the slab was 100–150 kPa at the end of excavation, rising to 150–200 kPa in long-term equilibrium. The pressure near the edges of the slab was about 200 kPa at the end of excavation, rising to about 250 kPa in long-term equilibrium. The experimental measurements of the basement without keying, where the mat was in contact with sand, showed greater variability than the keyed-in basement, where the mat was in contact with clay. This is expected because previous investigations suggested that the inherent error of tactile pressure sensors tended to increase with grain size [28,29,30].

The FE results suggest that the keyed basement was subject to higher contact pressures at equilibrium than the basement without keying. This agrees with Evelyn-Rahr [31], who performed a parametric study of FE models of basement heave and observed that a reduction in clay thickness tends to confine the heave mechanism and cause an increase in equilibrium heave pressure.

The plots of slab-soil contact pressure raised a question: why did the profiles of short-term heave differ significantly between the two embedment conditions if the profiles of slab–soil contact pressure on first excavation were similar? The plots of excess pore pressure at the end of the excavation stage could explain this difference.

Figure 16 shows FE contour plots of excess pore pressure at the end of the excavation stage. The drainage layer under the un-keyed basement had pushed the zone of high excess pore suction into a bulb underneath the basement. The excess pore pressure was approximately constant along the slab-soil interface of the un-keyed slab.

Fig. 16
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Plots of excess pore pressures immediately after excavation from FE models of stiff basement prototypes. (a top:) no keying; (b bottom:) 3 m keying into clay

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In contrast, for the keyed basement where there was no drainage layer, the zone of high excess pore suction was centred on the middle of the slab. Excess pore pressures varied significantly across the slab (from 70 kPa of suction near the edges to 120 kPa near the centre). The effective stresses were therefore approximately uniform in the clay immediately under the keyed slab, which agrees with the experimental observation that the vertical displacement was approximately uniform upon first excavation.

The plots of excess pore pressures also illustrated the increase in drainage distance when the drainage layer was removed. This agreed with the qualitative observation that the clay under the keyed basement seemed to re-consolidate less quickly after excavation. However, the magnitude of displacement and pore pressure changes during this stage of the experiment was too small to compare the time of consolidation quantitatively.

Conclusions

This paper presented centrifuge and numerical modelling of four prototype basements subject to long-term heave in over-consolidated clay, focusing on the influence of changing embedment conditions on overall heave behaviour.

When the diaphragm walls were lengthened to act as tension embedment in the stiff clay layer, the vertical displacement of the edges of the slab was reduced. However, this came at the expense of increasing the displacement of the middle of the slab. This may have been due to the tension embedment cutting off the clay outside the basement footprint from the clay under the basement, thereby reducing the overall stiffness of the clay engaged in the heave mechanism. This increased displacement in the centre of the basement with fins was more apparent in the centrifuge results than the Plaxis results. The tension embedment also acted as a groundwater cut-off, slowing down the dissipation of excess pore pressures after construction.

When the drainage layer between the base slab and the clay was removed and the basement was keyed into the clay, the base slab tended to undergo more total heave and less differential heave upon first excavation. The keyed-in basement also appeared to consolidate to equilibrium more slowly. These may be because of the direct contact between the slab and the clay that allowed greater variation in excess pore pressure at formation level and increased drainage distances slightly.

Nevertheless, the changes to heave behaviour caused by these changes to embedment conditions were small either compared to the overall magnitudes of heave displacement and swell pressure, or compared to the influence of slab stiffness on the heave behaviour: the observed vertical displacements of the stiff slab were an order of magnitude smaller than those of the flexible slab. While many construction projects use drainage layers to eliminate buoyancy loads from the finished structure, drainage condition may not be a significant factor in determining a basement’s long-term heave behaviour. The magnitudes of heave displacement and swell pressure are mainly governed by the stiffness of the slab and walls, and the provision of any tension embedment.