Solution
The seepage flow can be determined using the spreadsheet tool on the Companion Website.
Repeating the calculations for different lengths, Lw, of cut-off wall (Figure 2.25(a)) and separately for different lengths of impermeable blanket, Lb, as shown in Figure 2.25(b), the results shown in Figure 2.25(c) can be determined. By comparing the two methods, it can be seen that for thin layers such as in this problem, cut-off walls are generally more effec- tive at reducing seepage and typically require a lower volume of material (and therefore lower cost) to achieve the same reduction in seepage flow.
Seepage D15≤0 5. mm
Care must be taken to avoid segregation of the component particles of the filter during construction.
To ensure that the permeability of the filter is high enough to allow free drainage, it is recom- mended that
( ) ( )
D D s
15 15
f >5 (2.42)
Graded filters comprising two (or more) layers with different gradings can also be used, the finer layer being on the upstream side. The above criterion (Equation 2.41) would also be applied to the component layers of the filter.
Summary
1 The permeability of soil is strongly affected by the size of the voids. As a result, the permeability of fine soils may be many orders of magnitude smaller than those for coarse soils. Falling head tests are commonly used to measure perme- ability in fine soils, and constant head tests are used for coarse soils. These may be conducted in the laboratory on undisturbed samples removed from the ground (see Chapter 6) or in-situ.
2 Groundwater will flow wherever a hydraulic gradient exists. For flow in two dimensions, a flow net may be used to determine the distribution of total head, pore pressure and seepage quantity. This technique can also account for soils which are layered or anisotropic in permeability, both of which parameters sig- nificantly affect seepage.
3 Complex or large seepage problems, for which flow net sketching would prove impractical, can be accurately and efficiently solved using the Finite Difference Method. A spreadsheet implementation of this method is available on the Companion Website.
4 Seepage through earth dams is more complex as it is unconfined. The conformal transformation provides a straightforward and efficient method for determining flow quantities and developing the flow net for such a case (if required). Seepage through and beneath earth dams, which may affect their stability, may be con- trolled using a range of techniques, including a low permeability core, cut-off walls, or impermeable blankets. The efficacy of these methods may be quantified using the techniques outlined in the chapter.
Problems
2.1 In a falling-head permeability test, the initial head of 1.00 m dropped to 0.35 m in 3 h, the diameter of the standpipe being 5 mm. The soil specimen was 200 mm long by 100 mm in diameter. Calculate the coefficient of permeability of the soil.
2.2 The section through part of a cofferdam is shown in Figure 2.26, the coefficient of permeabil-
2.3 The section through a long cofferdam is shown in Figure 2.27, the coefficient of permeabil- ity of the soil being 4.0 × 10–7 m/s. Draw the flow net and determine the quantity of seepage entering the cofferdam.
2.4 The section through a sheet pile wall along a tidal estuary is given in Figure 2.28. At low tide the depth of water in front of the wall is 4.00 m; the water table behind the wall lags 2.50 m behind tidal level. Plot the net distribution of water pressure on the piling.
2.5 Details of an excavation adjacent to a canal are shown in Figure 2.29. Determine the quantity of seepage into the excavation if the coefficient of permeability is 4.5 × 10–5 m/s.
2.6 The dam shown in section in Figure 2.30 is located on anisotropic soil. The coefficients of permeability in the x and z directions are 5.0 × 10–7 and 1.8 × 10–7 m/s, respectively. Determine the quantity of seepage under the dam.
Figure 2.26 Problem 2.2.
Figure 2.27 Problem 2.3.
Seepage
Figure 2.28 Problem 2.4.
Figure 2.29 Problem 2.5.
Figure 2.30 Problem 2.6.
2.7 Determine the quantity of seepage under the dam shown in section in Figure 2.31. Both lay- ers of soil are isotropic, the coefficients of permeability of the upper and lower layers being 2.0 × 10–6 and 1.6 × 10–5 m/s, respectively.
2.8 An embankment dam is shown in section in Figure 2.32, the coefficients of permeability in the horizontal and vertical directions being 7.5 × 10–6 and 2.7 × 10–6 m/s, respectively.
Construct the top flow line and determine the quantity of seepage through the dam.
References
ASTM D4043-17 (2017) Standard Guide for Selection of Aquifer Test Method in Determining Hydraulic Properties by Well Techniques, American Society for Testing and Materials, West Conshohocken, PA.
ASTM D5084-16a (2016) Standard Test Methods for Measurement of Hydraulic Conductivity of Saturated Porous Materials Using a Flexible Wall Permeameter, American Society for Testing and Materials, West Conshohocken, PA.
ASTM D6391-11 (2011) Standard Test Methods for Field Measurement of Hydraulic Conductivity Using Borehole Infiltration, American Society for Testing and Materials, West Conshohocken, PA.
Figure 2.31 Problem 2.7.
Figure 2.32 Problem 2.8.
Seepage British Standard BS EN ISO 17892-11 (2019) Geotechnical Investigation and Testing – Laboratory
Testing of Soil: Permeability Tests (ISO 17892-11: 2019), British Standards Institution, London.
British Standard BS EN ISO 22282-2 (2012) Geotechnical Investigation and Testing – Geohydraulic Testing: Water Permeability Tests in a Borehole Using Open Systems (ISO 22282-2: 2012), British Standards Institution, London.
British Standard BS EN ISO 22282-4 (2012) Geotechnical Investigation and Testing – Geohydraulic Testing: Pumping Tests (ISO 22282-4: 2012), British Standards Institution, London.
CEN ISO/TS 17892-11 (2019) Geotechnical Investigation and Testing—Laboratory Testing of Soil: Permeability Tests, International Organisation for Standardisation, Geneva.
CEN ISO/TS 22282 (2004) Geotechnical Investigation and Testing—Geohydraulic Testing, International Organisation for Standardisation, Geneva.
Casagrande, A. (1940) Seepage through dams, in Contributions to Soil Mechanics 1925–1940, Boston Society of Civil Engineers, Boston, MA, pp. 295–336.
Cedergren, H.R. (1989) Seepage, Drainage and Flow Nets (3rd edn), John Wiley & Sons, New York, NY.
Clayton, C.R.I., Matthews, M.C. and Simons, N.E. (1995) Site Investigation (2nd edn), Blackwell, London.
Hazen, A. (1911) Discussion: Dams on sand foundations, Transactions of the ASCE, 73, 199.
Hvorslev, M.J. (1951) Time Lag and Soil Permeability in Ground-Water Observations, Bulletin No. 36, Waterways Experimental Station, US Corps of Engineers, Vicksburg, MS.
Sherard, J.L., Dunnigan, L.P. and Talbot, J.R. (1984a) Basic properties of sand and gravel filters, Journal of the ASCE, 110(GT6), 684–700.
Sherard, J.L., Dunnigan, L.P. and Talbot, J.R. (1984b) Filters for silts and clays, Journal of the ASCE, 110(GT6), 701–718.
Vreedenburgh, C.G.F. (1936) On the steady flow of water percolating through soils with homo- geneous- anisotropic permeability, in Proceedings of the 1st International Conference on SMFE, Cambridge, MA, Vol. 1.
Williams, B.P., Smyrell, A.G. and Lewis, P.J. (1993) Flownet diagrams—the use of finite differ- ences and a spreadsheet to determine potential heads, Ground Engineering, 26(5), 32–38.
Further reading
Cedergren, H.R. (1989) Seepage, Drainage and Flow Nets (3rd edn), John Wiley & Sons, New York, NY.
This is still the definitive text on seepage, particularly regarding flow net construction. The book also includes case histories showing the application of flow net techniques to real problems.
Preene, M., Roberts, T.O.L., Powrie, W. and Dyer, M.R. (2000) Groundwater Control—Design and Practice, CIRIA Publication C515, CIRIA, London.
This text covers groundwater control in more detail (it has only been touched on here). Also a valuable source of practical guidance.
For further student and instructor resources for this chapter, please visit the Companion Website at www.routledge.com/cw/craig
Effective stress
Chapter 3
Effective stress
Learning outcomes
After working through the material in this chapter, you should be able to:
1 Understand how total stress, pore water pressure and effective stress are related and the importance of effective stress in soil mechanics (Section 3.1, 3.2, 3.4 and 3.5);
2 Determine the effective stress state within the ground, both under hydrostatic conditions and when seepage is occurring (Section 3.3 and 3.6);
3 Describe the phenomenon of liquefaction, which arises due to a reduction in effective stress, and determine the hydraulic conditions within the groundwater under which liquefaction will occur (Section 3.7).