Design of unreinforced and reinforced working platforms
Figure 1: Computational Limit Analysis of working platform problem from BR470 (load bearing on 0.6m working platform of granular material over soft clay), clearly illustrating punching failure and also showing full extent of the failure mechanism. Predicted bearing pressure = 213 kPa, compared to 205 kPa from BR470.
Working platform design requires consideration of a range of practical and analytical issues. These are covered, for example by the UK guidance document BRE470. In September 2011 LimitState published an article in theGeotechnica magazine describing the use of computational limit analysis (CLA) to undertake rapid analysis and design of unreinforced working platforms. However, in this brief note platforms reinforced via the addition of geosynthetics are also considered.
Working platform design
Current industry guidance for working platforms is available, for example in the good practice guide ‘Working platforms for tracked plant’, BR470 (Skinner, 2004, BRE). This provides a straightforward semi-empirical design method for determining platform strength and thickness.
As illustrated in Figure 1, computational limit analysis (CLA) software, such as LimitState:GEO, allows a quick check of any design to be performed. LimitState:GEO shows the extent of the failure mechanism and also frees users from many of the restrictions of semi-empirical methods, for example allowing the following to be considered:
- sloped platforms;
- platform edge stability;
- variable strength or multilayer subgrades;
- track interaction;
as well as providing scope for straightforward sensitivity studies.
Comparison with widely-used examples
Figure 2 compares the results of LimitState:GEO analysis with the examples given in the widely-used guidance document BR470 for clay subgrade. It can be seen that a good match (typically less than 4% difference) is obtained between the two approaches for plane strain (2D) analysis. Obtaining the results using LimitState:GEO requires only a few minutes to set up the model. Analyses typically solve in seconds or minutes.
Figure 2: Comparison of BR470 and CLA plane strain results for a range of subgrade undrained shear strength (cu) values.
However, LimitState:GEO really comes into its own when non-standard design situations are involved, e.g. when considering stability on a sloped platform (Figure 3a), a multi-layered subgrade (3b), or when checking how close plant can be taken to a platform edge (3c). In this latter case, the available bearing capacity was reduced by 26% (the same strength of platform material was assumed throughout. In practice reduced strength may be found at the edges, a situation which is easily modelled in LimitState:GEO).
Figure 3: Different working platform configurations, analysed using LimitState:GEO. a) Sloped platform; b) Multi-layered subgrade and c) Collapse mechanism at platform edge
Modelling geosynthetic reinforcement
Geosynthetics (geogrids or geotextiles) are able to reduce the transmission of shear stresses induced at the base of a working platform to the underlying soil, thus increasing the capacity of the system to resist loading. Furthermore, as the mechanism of failure moves upwards through the soil it is resisted by further shearing against the geosynthetic, again increasing the capacity of the system.
Geosythetics are easily incorporated into a CLA analysis. For example, this can be done in LimitState:GEO through the use of a 1-dimensional ‘Engineered Element’ material.. Consider the problem shown in Figure 4, where a geosynthetic material has been added at the interface of the platform and the underlying soil. When compared to the similar, non-reinforced problem of Figure 1 It is clear that the extents of the associated failure mechanism in the lower layer are increased and the calculated resistance of the construction is greater as a result.
Figure 4: Computational Limit Analysis of working platform problem from Figure 1 but with the inclusion of a geosynthetic layer. Note the increased extent of failure mechanism in the lower soil layer.
As with any numerical method, engineering judgement should be applied when considering the parameter inputs and results of a CLA model, but its use helps engineers to rapidly and accurately assess non-standard situations, without the need to resort to modified hand-calculations or more complex procedures such as FEA.
The original article published in theGeotechnica in September 2011 can be found at theGeotechnica online.
Additionally, working platform analysis using computational limit analysis was the subject of a recent webinar presented by Dr Colin Smith. If you would like to watch a recording of the webinar, please visit the LimitState YouTube channel.