Supplementary Problems for Chapter 7

Size: px

Start display at page:

Download "Supplementary Problems for Chapter 7"

Beverly Palmer
6 years ago
Views:

1 Supplementary Problems for Chapter 7 Problem 7.1 consolidation test has been carried out on a standard 19 mm thick clay sample. The oedometer s deflection gauge indicated 1.66 mm, just before the removal of the last load, that is, no swelling was allowed. The voids ratio was found to be 0.55 at this stage. Determine: a) The initial voids ratio of the saturated specimen b) The height of the specimen for the voids ratio of 0.62 Problem 7.2 Superficial deposits were removed some years ago from a site, to be used for housing development. The section of the ground in Figure 7.42 shows the known properties of two soil layers overlying solid rock. The overconsolidation ratio of the stiff clay layer was found to be 5. Existing surface 3m 2.5 m Gravelly sand GWL Stiff clay e = 0.62 OCR = 5 Rock e = 0.8 G s = 2.67 G s = m Centre line of the layer Figure 7.42 Estimate: a) The pressure exerted originally by the removed overburden on the top of the gravelly sand layer. b) The thickness of the superficial deposit, assuming its mass density as 1988 kg/m 3. Introduction to Soil Mechanics, First Edition. Béla Bodó and Colin Jones John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. 1 Problems_c07.INDD 1

2 2 Introduction to Soil Mechanics Problem 7.3 n oedometer test has been carried out on a clay specimen, taken from a 2.5 m thick layer. The results recorded were: Table 7.12 Swelling stage s x = pressure (kn/m 2 ) D x = dial reading (mm) The voids ratio, 24 hours after the removal of the last, 600 kn/m 2 load, was found to be 54.2%. The original effective pressure at the centre of the 2.5 m thick clay layer is 100 kn/m 2. The final effective pressure, after the construction of the structure, will be 200 kn/m 2, at the same depth. Estimate: a) The voids ratio for each load increment b) The coefficient of volume compressibility for Δs = = 100 kn/m 2 c) The settlement of the structure due to Δs = 100 kn/m 2, in millimetres Problem 7.4 Site and laboratory investigations indicate that a 2 m thick sandy gravel surface layer of 19.8 kn/m 3 density is underlain by 4.4 m thick medium clay of 20.4 kn/m 3 unit weight. The clay itself is underlain by very stiff clay. The ground water table is 2 m below the surface. It is proposed that: a) Either the entire area is covered by compacted fill, surcharging the ground by 360 kn/m 2 b) Or constructing a 6 m wide, long, rigid, concrete slab on the surface, imparting 360 kn/m 2 foundation pressure to the ground. Estimate the effective and hence the excess effective pressures, induced by the two types of loading of the centre (x x) of the layer at time: 1. t = 0, that is at the start of consolidation 2. t =, that is at the completion of consolidation. Compare the two results. Problems_c07.INDD 2

3 Supplementary Problems for Chapter 7 3 Problem 7.5 The oedometer consolidation test results, carried out on a normally consolidated clay, are given in Table Plot log s x against e x on Graph 7.4 and determine the Compression Index, hence express the voids ratio in terms of formula (7.8). Indicate the extent of validity of this expression. 0.8 s x kn/m Table log s x e x B Extent of validity e e B = = C c = Compression index e e B = = s log B s = 0.13 e x = log s x ex = Voids ratio logs B logs = log s B s = log = B log s x = log (Effective pressure) Graph 7.4 Problems_c07.INDD 3

4 4 Introduction to Soil Mechanics Problem m wide strip footing is to support part of a settlement-sensitive structure. It is proposed to be based 0.5 m below the surface in a 3.3 m thick, dense, coarse sand layer. The sand is underlain by normally consolidated clay, 4.6 m thick, below which compact gravel is found. The ground water table is 3.3 m below the surface. The footing transmits a net pressure of 250 kn/m 2, including self weight to the soil. Soil characteristics: Sand: Unit weight = 18.2 kn/m 3 Clay: Saturated density = 20.1 kn/m 3 Equation of void ratio: e x = log (s x ) Valid for: 50 s x 500 kn/m 2 Coefficient of consolidation = 4.14 mm 2 /min Coefficient of volume change = m 2 /kn Calculate the voids ratio in the unexcavated state and just after the construction of footing at: Point : Top of the clay layer Point C: Centre line of the clay layer Point B: Bottom of the clay layer Estimate the primary consolidation of the clay layer. Problem 7.7 Calculate the time taken for the structure in Problem 7.6 to settle 78 mm. C Sand Clay Flow Flow H 0 = 2.3 m H 0 u a = 0 u c = kn/m 2 The pore pressure distribution is nearly triangular, thus curve B (Chart 7.5) may be applied. B Gravel u b = kn/m 2 Figure 7.50 Problems_c07.INDD 4 6/24/2013 4:00:06 PM

5 Supplementary Problems for Chapter 7 5 Problem 7.8 The structure in Problems 7.6 and 7.7 was indicated to be sensitive to settlement. However, it was estimated that the 4.6 m thick clay layer would consolidate about 78 mm in 2.1 years. In order to prevent, or at least minimize settlement, the ground is proposed to be pre-loaded by metal kentledge of 43 kn/m 3 unit weight, for one year. Calculate the height of kentledge layer required to consolidate the clay by 78 mm, using the time-consolidation curve on Graph 7.5 for the pressure range kn/m 2 at m v = m 2 /kn Problem 7.9 The magnitude of consolidation of the clay layer in Problem 7.6 was estimated to be 87 mm, by using the maximum pressure below the centre of the footing (See Figure 7.49). Show that the result would not be much more different, should the settlement be determined by means of the average induced pressure. Problem 7.10 Δh Starting from formula (7.11), show that m v= h Δ σ 1 Problem 7.11 long 4 m wide concrete slab is constructed in an 11 m thick, homogeneous clay layer, one metre below the ground surface to minimize seasonal effects. There is no evidence of ground water table. Oedometer test results indicate that the coefficient of volume change may be taken as m 2 /kn for the pressure range kn/m 2. It is specified that the slab should not settle more than 250 mm. Determine: the required net and total bearing pressures to produce consolidation of this magnitude. Check, whether the bearing capacity of the clay is exceeded by the estimated bearing pressure. dopt 2.5 as thefactor of safety. Problems_c07.INDD 5 6/24/2013 4:00:06 PM

Chapter (5) Allowable Bearing Capacity and Settlement

Chapter (5) Allowable Bearing Capacity and Settlement Introduction As we discussed previously in Chapter 3, foundations should be designed for both shear failure and allowable settlement. So the allowable