Key words – light-weight fill, gravel raft, settlements, numerical modelling
Abstract
The use of Mainmark’s Terefil as an alternative to reinforced gravel raft for liquefaction mitigation and to minimise total static settlements and foundation differential performance under the building loads over soft cohesive and loose cohesionless soils was investigated and presented. Numerical modelling has been undertaken to investigate the system performance by comparing between a typical foundation slab on grade and 1.0m thick reinforced gravel raft subject to static and post-cyclic induced deformations. Results indicate the feasibility of using a Terefil raft over variable thickness and density, with due consideration of the site-specific conditions and especially the depth of the ground water, as an alternative to the reinforced gravel raft, demonstrating better model results in terms of estimated displacements and improved foundation behaviour.
1. Introduction
Terefil® from Mainmark Ground Engineering (NZ) Limited (Mainmark) is an engineered cementitious fill material providing an alternative solution to granular fills. Terefil is highly flowable material which can be easily placed without requiring compaction, and contains a uniformly distributed cell structure encapsulated by cementitious materials creating an engineered, low density solution used across a wide range of civil, infrastructure, construction and mining projects. It can be designed to meet the project specific density and strength requirements, with a pervious or impervious mix to suit a range of applications.
The use of Mainmark’s Terefil as an alternative to reinforced gravel raft for liquefaction mitigation and to minimise static settlement under the building loads over soft compressible soils, is not new in New Zealand. A case study in Christchurch with unfavourable ground conditions, where four standalone dwellings founded on Terefil rafts constructed in 2017, presented in the 2019 Pacific Conference on Earthquake Engineering (Sai Louie, et al, 2019), highlighted the key properties of the system, the analysis undertaken, as well as critical construction aspects.
As part of Mainmark’s continual internal research and development, Tetra Tech Coffey undertook a comparative geotechnical numerical modelling to assess the anticipated performance between the untreated ground, the Terefil raft and a ‘typical’ reinforced gravel raft, under ‘static’ and ‘seismic / post-cyclic loading’ conditions.
A simple framework was adopted with representative stages in a way to simplify the post-liquefaction anticipated performance, without modelling the development of liquefaction or cyclic softening with advanced constitutive models and dynamic analyses.
The purpose of this paper is to present the numerical methodology used, outline the key input parameters for the 2D models used, and the estimated deformations, for the comparison between the Terefil and the gravel raft to reduce the static and post-cyclic (liquefaction and cyclic softening) differential settlements.
2. Model Description
Two different ground profiles were used, as presented in Figure 1. The model used a 30x10m wide grid, and a 10x10m waffle slab with 400mm and 200mm wide edge and internal beams respectively, and Polystyrene EPS pods. These were modelled under plane strain condition using PLAXIS 2D v22. 25kN/m/m and 1.5kN/m/m uniform line loads assumed acting on the edge beam and across the slab as those resulting from a single storey timber-framed dwelling.
Figure 1: Modelling details (ground profile, soil layers, waffle slab with gravel and Terefil raft)
The ground profiles and geotechnical properties used for the typical ground conditions represented soft to firm cohesive, and loose to medium dense sandy soils respectively. The modelling parameters are set out in Table 1.
Table 1: Modelling material properties
The layer-specific geotechnical input parameters for the numerical modelling are outlined below:
- Void ratio, unit weight and strength parameters – eo, ϒsat, ϒdry, Su, c’, ψ’, φ’
- Compressibility – Cc, Cα, k
- Stiffness/deformation – E’, Eu
- Hardening soil model reference values – Eref50, Erefoed, Erefur
A waffle slab founded directly on the subgrade at 200mm depth, or on a 1.0m thick reinforced gravel raft with two layers of geogrids, and on a Terefil raft with 400, 600, 800 and 1000mm variable thickness assumed for our comparative study.
The low-density Terefil mix is an impervious, closed-cell structure produced due to the encapsulated air added to be the base mix (2000kg/m3), and was modelled as non-porous material, i.e. pore water pressures cannot develop. The material properties used for our analysis are derived and evaluated from the laboratory testing completed by WSP on different Terefil density mixes. The testing included ‘concrete’ compression, unconfined compression with Young’s modulus measurement, cylinder tensile splitting, and constant head permeability tests.
The constitutive models utilised in our analysis were:
- Linear Elastic [LE] for concrete and EPS pods
- Elastic-plastic Mohr Coulomb [MC] for Terefil and gravel raft
- Hardening Soil [HS] for granular and cohesive soils assuming ‘drained’ and ‘undrained A’ behaviour respectively.
- Soft Soil [SS] as a second constitutive model for the cohesive soft and firm soils with undrained behaviour (Undrained A), in which stiffness and strength are defined in terms of effective values (c’ and φ’) and excess pore pressures are calculated, followed by a consolidation phase (dissipation of excess pore pressures). Equivalent c’ and φ’ to the undrained shear strength Su adopted in our modelling.
A staged construction process was modelled with an initial excavation phase, followed by the slab construction and load application, and a consolidation for the cohesive soils for dissipation of the excess pore pressures due to foundation loading. The ‘seismic’ condition was not a dynamic/cyclic loading stage with advanced constitute models and application of an acceleration time history, but a rather simplified approach targeting the post-cyclic likely ‘system’ behaviour. The modelling developed to simulate, or ‘force’, the model to differential performance as anticipated due to cyclic softening, liquefaction triggering and likely ejecta or heave (volume increase) below the structure/raft.
Volume change, εv = εxx + εyy + εzz (where εzz = 0 for plane strain), applied to some modelling clysters and/or layers, with +ve for heave/expansion and -ve for contraction/shrinkage to simulate the effects of liquefaction triggering and softening. Three and four scenarios (eq1 to 4) assumed for modelling the post-cyclic response of the soft cohesive and loose to medium dense soil, as presented in Figure 2.
Figure 2: Post-cyclic modelling scenarios for the two different ground profiles; Profile A / soft cohesive silts, [ML] model & Profile B / loose silty sands, [SM] model
3. Results of the Analysis
The phase and total deformation plots at the end of the consolidation phase, where dissipation of excess pore water pressures was completed, are shown in Figure 3. This includes the performance of the ground and slab interface for the untreated subgrade, the 1.0m thick reinforced gravel raft, as well as the 1.0m and 0.6m thick Terefil rafts respectively.
Figure 3: Phase and total deformation plots at the end of consolidation phase for the soft compressible clayey silts (Profile A), and hardening soil constitutive model
In addition, Table 2 and 3 present the resulting deformations and differential settlements under the assumed static and seismic cases respectively.
Table 2: Static settlements under the assumed cases, soil profiles and constitutive models (-ve values represent heave/uplift)
Table 3: Resulting deformations and differential settlements under the assumed seismic cases, soil profiles for the hardening soil constitutive model (-ve values represent heave/uplift) across the foundation
Figure 4 is presenting the deformed mesh under the assumed [eq1] condition adopting a ‘total loss of support’ over 2.0 from the edge and 4.0m across the center of the raft at 1.0m depth.
Figure 4: Deformed mesh under eq1 for the loose – medium dense sandy soil profile A
Based on the settlement model, the predicted static settlement of the soil under the building loads over the untreated ground was between 25 – 45mm for the soft cohesive soil, and 20mm for sandy soil profile. The predicted static settlement of the soil under the building loads with a 1.0m thick lightweight raft were reduced and almost ‘balanced’ between excavation heave and foundation load settlement with few mm of calculated heave. In every calculated case, the reinforced gravel and the Terefil rafts are estimating a differential performance less than 25mm across the 10m slab.
4. Conclusions
Even though the proposed simplified procedure didn’t capture the dynamic analyses, i.e. seismic loading and development of liquefaction or cyclic softening, the overall system performance can be comparatively evaluated in terms of anticipated deformations. The analyses performed reveals, as expected, the benefits of a reinforced gravel raft below the foundations, and more importantly, that a Terefil light-weight raft have an equivalent performance while reducing the static settlements to a considerable degree.
Consequently, a Terefil raft is significantly stiffer, lighter and less deformable than the gravel raft under the same applied loads, with due consideration for the depth to ground water table which is, or should be, a critical feasibility application check. The benefit of reduced weight when compared to the traditional gravel rafts, should be evaluated for avoidance of excessive uplift pressure or heave due to excavation and depth to ground water table. A critical design and application consideration is the depth to ground water due to the light-weight nature of the Terefil, specifically for the mixes with densities < 1000 kg/m3, i.e. those in our study at 700 and 500kg/m3, due to the calculated heave/relaxation and likely buoyancy.
Based on the results of the numerical analyses, the following conclusions regarding the engineering performance of the Terefil can be drawn:
- The analyses performed reveals, as expected, the benefits of a reinforced gravel raft below the foundations, and more important that a Terefil light-weight raft have an equivalent performance reducing the static settlements to a considerable degree.
- Rafts, as expected, are reducing the total settlements by 50 to 80% for the sandy and silty soil profiles, with a more uniform response limiting the potential of differential foundation displacements.
- Use of Terefil as an alternative is estimated to further reduce the predicted settlements to less than 10% to 50% of that of the reinforced gravel raft.
- Reducing the density of the Terefil mix, the system is predicted to equally perform in a similar manner with regards to differential settlement, however increasing the uplift/heave potential.
- With regards to the system performance under the assumed post-cyclic conditions, the differential performance is reduced in all examined cases. The reinforced gravel raft estimated reduction ranges between 20% to 25% when compared to the slab on the untreated subgrade, while Terefil is between 5% to 20%.
- Eq1 is the worst case calculated for the post-cyclic scenario for the soft cohesive soil profile, where the 800mm thick Terefil raft appears to be ‘numerically’ performing better than the other configurations.
- On the other hand, eq4, is the critical scenario for the sandy, liquefiable, soil profile, where similarly the 800mm Terefil raft demonstrates better performance and limits the differential settlements between 20% to 30% of those of the reinforced gravel raft.
- Inclusion of geogrids, although beneficial for the gravel raft, do not appear to numerically demonstrate an improved performance for the Terefl rafts.
- Our work presented can be considered as a basis for comparison and for preliminary feasibility evaluation. Application and use of the Terefil as an alternative should be considered, and designed, on a case-by-case basis taking into account the site-specific conditions, foundation details and loading (or demand) from the superstructure.
- It is our opinion, based on the numerical models presented, that a 800mm thick Terefil raft is performing as a stiff subgrade reducing the differential settlements to a degree similar or better than the reinforced gravel rafts.
References
Sai Louie, A.J., Nogueira, A.M., Hnat, T., 2019. The use of Terefil rafts to control static settlement under building loads. 2019 Pacific Conference on Earthquake Engineering, 4-6 April, Auckland, NZ.
