# Staged construction of embankment on soft soil improved with vertical drains

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Staged construction of embankment on soft soil improved with vertical drains\n\nDesign brief\nYou are requested to construct a 2 km long highway embankment of 4m height on a soft clay layer foundation soil. The clay layer is underlain by sand. At the top of the clay layer there is one metre of permeable made ground. The bearing capacity of the soil will be insufficient therefore staged construction of the embankment and improvement of the soft soil with prefabricated vertical drains (PVD) fully penetrating the clay layer (used to speed up the consolidation of the foundation soil) will be required. \nThe design requirement is that all settlement but the last 30mm must be completed within the specified total construction period, which in this case is 14 months. The dimensions of the PVDs are 95mm wide and 5mm thick and they will be laid out in a square grid.\nYou will consider the stress distribution both under the centre line of the embankment as well as the edges of the embankment.\n\nA. Embankment geometry and material properties\nThe embankment fill is free draining. The properties of the embankment soil are as follows:\n γ (kN/m3) Embankment fill angle of friction, ɸ’ c’ (kPa)\nEmbankment gravel fill* 17 37 0\n*drains will be provided\n\nThe geometry of the embankment is:\nEmbankment’s height h (m) 4\nWtop(m): embankment top width (crown) 13\nEmbankment gradient 1:2.5\n\n\n\nB. Foundation soil\nThe properties of the foundation soils are:\n\nMaterial Depth\n(m) γ (kN/m3) φcu \n\nφ’ Cuave (kPa) (average undrained shear strength)\n Top of clay clay soil mv (m2/MN)\n Decrease of mv with depth z Cv (m²/year) Ch\n(m²/year)\n\nPermeable fill 0.0-1.0 19 34 \nNormally consolidated soft clay 1-21 \n18 15 \n22 20 0.23 mv-0.0015z 2.9 6\nSand 21-25 20 35 \n\nHints for calculations\nStep 1 \nAssess the bearing capacity of the soil qbc and whether it is capable to support the full height of the embankment fill. Assume Nc=5.14 and a bearing capacity safety factor FoS of 2.5.\nqbc=cuave*Nc/FoS where Cuave is the average undrained shear strength\nIf it is not sufficient, staged loading /construction needs to be anticipated, and the soil will probably be improved by the construction of vertical drains, so that consolidation will have been completed within the period specified in the design brief.\n\nAssess whether the soil can consolidate sufficiently within the period specified in the design brief so that only the allowable settlement remains to be completed after construction.\nFor this task you will need to use consolidation settlements according to the stress distribution under the centre of a long embankment (according to the formula –not Osterberg’s chart- given in the class for long embankment loading). The foundation soil will be divided into an equal amount of sub-layers and the stresses in the mid-point of each sublayer will need to be calculated.\n\nStep 3\nConsider the total settlement at the end of consolidation to adjust the necessary height of the embankment fill layers so that, after settlement, the required embankment height is as specified in the design brief. Include the effect of undrained settlement taking a value of Eu=150*Cu (Bergado et al, 1990) but comment how important this effect was comparatively.\nFor the adjusted height of the embankment also consider that the embankment fill will also settle to some extent even if the fill is not made of a compressible soil such as normally consolidated clay. In your case the embankment is free draining (gravel) and it will be well compacted while the layers are built. An approximate long term settlement of 20% of the height of the embankment for this case of fill has been suggested (Das, 2002).\nTo adjust your height to be actually constructed, you may also consider settlement due to traffic loading using a simplified method such as the equivalent static load method by Fujikawa et al, 1996, as cited in Battacharya, 2009), p.54 (NB the method gives increase in strength, not settlement so the finale settlement will need to be calculated accordingly)\n\nStep 4\nConsider the allowable height of the first layer of the embankment based on the calculation in step one. For this layer in place, calculate the effective stress change under the middle of the embankment only (for the purposes of this coursework) at the mid-point of each sub-layer into which the foundation soil has been subdivided.\nFind the average effective stress change. \n\nAlso calculate the final consolidation settlement due to the construction of this layer.\n\nStep 5\nConsidering the average effective stress change calculated in step 3, calculate the increase in the soil’s shear strength after consolidation (speeded up with vertical drains) for this stage, after a specified waiting period (according to the brief) between construction stages.\nThis increase in the undrained shear strength can be calculated as:\n∆cu=U∆σ’tan φcu\nWhere ∆σ’ is the increase in the vertical effective stress, U is the degree of consolidation and φcu the friction angle of the foundation soil as determined from consolidated undrained triaxial tests (NB: this is not the only method to assess the increase in undrained shear strength due to consolidation and you will investigate later what differences it would make if you considered another method).\nConsider the allowable height of the next embankment layer with the new undrained shear strength of the soil.\nNote: When calculating the degree of consolidation between construction stages, ignore the time of construction of this layer, and assume consolidation starts immediately for the full height of the layer.\n\nStep 6 \nRepeat steps 3-4 until the full embankment has been constructed. \nAt the end of the iterations, when the full embankment has been constructed, check if the staged construction (together with the waiting periods) is within the period specified in the design brief and make recommendations about the drain design and waiting times accordingly.\nIn the calculations of the degree of consolidation after each construction step and respective waiting period, do not forget that some layers have been constructed earlier than others and consolidation of these layers is probably ongoing.\n\nStep 7 \nMake an engineering drawing of the final embankment together showing any other provisions (e.g. for drainage etc.)\n\nStep 8 \nFurther investigations:\n1. Compare what method would give less overall waiting times, while satisfying the design criteria for overall construction time, e.g. a method where you would build the embankment in very thin layers of say 20-30mm each and wait for 30% or so consolidation to occur or wait for 90% consolidation to happen before building a next layer of more substantial thickness?\n2. Assess the effect of smear zone \n3. (optional) Assess the effect of ramped consolidation according to Olson’s (1977) expressions (see e.g. Battacharya (2009), p. 75 but also look at pp 72-74 as Olson is to be used together with Hansbo’s formula and you need to see the symbols); incidentally these pages also apply to investigation 2.\n\nStep 9: Discussion\nDiscuss on the differences between methods and simplifying assumptions. Also, even when we considered some effects, are you happy that the calculations above gave the actual settlement of the structure and the required consolidation times, and considered (albeit in a simplified way) all aspects of short-term stability? Did we miss anything in our simplifying assumptions and how important were these omissions? Are you happy that the finalised embankment as calculated above satisfies exactly the design brief requirements? If not what can be done /should have been anticipated in the calculations? (etc.)\n

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