The key features of the Eighth Edition are retained, including threads on limit analysis for ULS design, finite difference approaches to solving complex problems, expanded case studies (updated to reflect new material), and an expanded companion website (also updated). 3 Determine the basic physical properties of a soil continuum (i.e. at the level of the macrosubstance, Section 1.6).
The origin of soils
1 Understand how soil deposits form and the basic composition and structure of soils at the micro-fabric level (Sections 1.1 and 1.2); The material, which is typically highly variable in particle size from clay to boulder-sized particles, is carried to the base of the glacier and deposited as the ice melts; the resulting material is known as (glacial) till.
The nature of soils
Chemical processes result in changes in the mineral form of the parent rock due to the action of water (especially if it contains traces of acid or alkali), oxygen and carbon dioxide. An example of the structure of a natural clay, in diagrammatic form, is shown in Figure 1.9(e).
Plasticity of fine-grained soils
A little more of the soil paste is added to the cup and the test is repeated until a consistent value of penetration is obtained. This water content (to the nearest whole number) is defined as the plastic limit of the soil.
Particle size analysis
If samples are pipetted at a specified depth at times corresponding to other selected particle sizes, the particle size distribution can be determined from the residue mass. The size at which 10% of the particles are smaller than this size is marked with D10.
Soil description and classification
1.4) The higher the value of the uniformity coefficient, the greater the range of particle sizes in the soil. The plasticity of fine soil can be assessed by means of the toughness and dilatancy tests, which are described below.
Phase relationships
Water content (w), or moisture content (m), is the ratio of the mass of water to the mass of solids in the soil, i.e. 1.6) Water content is determined by weighing a soil sample and then drying the sample in an oven at 105–110°C and reweighing. The void ratio (e) is the ratio of the volume of voids to the volume of solids, i.e. 1.8) Porosity (n) is the ratio of the volume of voids to the total volume of the soil, i.e.
Soil water
Above the water table (known as the vadose zone), the soil may remain saturated, with pore water held at negative pressure by capillary tension; the smaller the pore size, the higher the water can rise above the water table. The height of the suction zone above the water table can then be estimated by zs = uc/γw (Figure 2.1).
Permeability and testing
An unconfined layer of uniform thickness with a (relatively) impermeable lower boundary is shown in Figure 2.3(a), where the water table is below the upper surface of the layer. The test enables the determination of the average coefficient of permeability of the soil mass under the cone of depression.
Seepage theory
Thus, if the function ϕ(x, z) is given a constant value, equal to ϕ1 (for example), it will represent a curve along which the value of the total head (h1) is constant. Referring to Figure 2.6, the current per unit time between two streamlines for which the values of the current function are ψ1 and ψ2 is given by.
Flow nets
Curved squares must be square - in Figure 2.8(c), the 'squareness' of the flow mesh is controlled by drawing a circle inside each square. In the flow network in Figure 2.8(c), the number of flow channels is three and the number of equipotential points is eight; so the Nf/Nd ratio is 0.375.
Anisotropic soil conditions
The validity of equation 2.28 can be demonstrated by considering an elementary flow grid field through which flow occurs in the permeability ellipse of Figure 2.11. The discharge rate vx can be expressed in terms of k′ (transformed section) or kx (natural section), i.e.
Non-homogeneous soil conditions
For one-dimensional seepage in the horizontal direction, the equipotentials in each layer are vertical. Similar expressions for kx and kz apply in the case of any number of soil layers.
Transfer condition
If h1 and h2 represent total head at any point in the respective layers, then for a common point on the boundary h1 = h2. For one-dimensional percolation in the vertical direction, the discharge rates in each layer, and in the equivalent single layer, must be equal if the requirement of continuity is to be met.
Numerical solution using the Finite Difference Method
A more detailed description of the boundary conditions that can be used and their formulation is given in the User's Manual, which can also be found on the companion website. The appropriate formulas are then entered into the cells representing each node, as shown in User's Manual Figure 2.16 Example 2.3.
Seepage through embankment dams
The resulting total head distribution is shown in Figure 2.16 and applying equation 2.1 the pore water pressure distribution around the tunnel can be plotted. For positive values of z the parabolas for the specified values of n are shown in figure 2.19(b).
Filter design
For flow in two dimensions, a flow grid can be used to determine the distribution of total head, pore pressure, and drainage amount. On the steady flow of water infiltrating through soils of homogeneous-anisotropic permeability, in Proceedings of the 1st International Conference on SMFE, Cambridge, MA, Vol. 1993).
Introduction
1 Understand how total stress, pore water pressure and effective stress are interrelated and the importance of effective stress in soil mechanics (section and 3.5); 2 Determine the effective stress state in the soil, both under hydrostatic conditions and when seepage occurs (Sections 3.3 and 3.6);
The Principle of Effective Stress
The pore water pressure acting equally in each direction will act on the entire surface of any particle, but it is assumed that it does not change the volume of the particle (ie the soil particles themselves are incompressible); nor does the pore water pressure cause particles to be compressed. The total vertical stress (i.e. the total normal stress on a horizontal plane) σv at depth z is equal to the weight of all material (solids + water) per unit area above that depth, i.e.
Numerical solution using the Finite Difference Method
Pore water pressure is the hydrostatic pressure corresponding to the depth below the water table. From Section 2.1, the water table is the level at which the pore water pressure is atmospheric (ie u = 0).
Response of effective stress to a change in total stress
The spring represents the compressible soil skeleton, the water in the cylinder the pore water, and the valve bore diameter the soil permeability. The initial stresses and pore water pressure in the center of the clay layer are.
Effective stress in partially saturated soils
Above the water table the pore water pressure will be negative (0 >uw> -γwzs). The soil can then be considered a fully saturated soil, but with the pore water having some compressibility due to its presence.
Influence of seepage on effective stress
Therefore, the force on BC due to pore water pressure acting on the boundaries of the element, called the boundary water force, is given by. Total weight of the element = γsat L2 = vector ab Boundary water force on CD = γw L2cosθ = vector bd.
Liquefaction
The flow network for drainage under a sheet pile wall is shown in Figure 3.9, the saturated soil unit weight is 20 kN/m3. Using the flow net in Figure 3.9(a), determine the factor of safety against failure rising adjacent to the bottom face of the column.
Introduction
On the other hand, if an excavation (reduction in total stress) is made in saturated clay, uplift (upward movement) will cause the bottom of the excavation to swell due to swelling of the clay. This chapter deals with the prediction of the extent and rate of consolidation settlement under one-dimensional conditions (ie, where the soil deforms only in the vertical direction).
The oedometer test
The relationship between void ratio and effective stress depends on the stress history of the soil. 3 The compression index (Cc) is the slope of the 1DCL, which is a straight line on the e–log σ′.
Estimating compression and swelling parameters from index tests
Note that Cc will be the same for any voltage range on the linear part of the e–log σ′ curve; A further advantage of equation 4.9 over 4.8 is that it can be derived from considering the fundamental mechanics of the soil (e.g. Wood, 1991), rather than as a purely empirical correlation.
Consolidation settlement
Therefore, the settlement of the layer with thickness dz will be given by. The variations of the initial effective vertical stress (s0¢) and the effective vertical stress increment (Δσ′) over the depth of the layer are represented in Figure 4.9(a); the variation of mv is represented in Figure 4.9(b).
Degree of consolidation
For one-dimensional consolidation, Δσ′=Δσ, where the stress increases in the center of each layer are indicated in Figure 4.10. Referring to Figure 4.12, immediately after the increase has occurred, although the total stress has increased to σ1, the effective vertical stress will still be s0¢ (unrained conditions); only after the completion of consolidation will the effective stress arise.
Terzaghi’s Theory of One-Dimensional Consolidation
Such curves are called isochrones, and their shape will depend on the initial distribution of excess pore water pressure and the drainage conditions at the boundaries of the soil layer. In part (a) of the figure, the initial distribution of ui is constant and for an open layer of thickness 2d the isochrone is symmetrical about the center line.
Determination of coefficient of consolidation
The point (D) corresponding to Uv = 0 is obtained by extrapolating the linear part of the curve to the ordinate at time zero. The intersection of the line DE with the experimental curve locates the point (a90) corresponding to Uv = 90% and the corresponding value t90 can be obtained.
Secondary compression
For some highly plastic clays and organic clays, the secondary compression portion of the compression-log time curve can completely mask the primary consolidation portion. For a small number of normally consolidated clays, secondary compression has been found to account for the greater part of the total compression under applied pressure.
Numerical solution using the Finite Difference Method
Any point on the grid can be identified by the subscripts i and j, the depth position of the point is indicated by i (0 ≤i≤m) and the passage of time by j (0 ≤j≤n). It has been shown that for convergence the value of the operator may not exceed 1/2.
Correction for construction period
Draw the time-settlement curve due to consolidation of the clay for a period of five years from the start of pumping. The clay layer is open and two-way drainage can occur due to the high permeability of the sand above and below the clay: therefore d = 4 m.
Vertical drains
The solution of the consolidation equation for radial drainage only can be found in Barron (1948); a simplified version suitable for design is given by Hansbo (1981) as. Construction of the embankment will increase the total vertical stress in the clay layer by 65 kPa.
Pre-loading
Determine the values of the consolidation coefficient and the compression ratios from (a) the root-time plot and (b) the log-time plot. Also determine the values of the coefficient of volume compressibility and the coefficient of permeability.
An introduction to continuum mechanics
A third idealization is the elastic-strain-hardening plastic model, shown in Figure 5.3(d) by OY′P (solid line), in which plastic deformation beyond the yield point necessitates further stress increase, i.e. A further idealization is the elastic-stretch-softening plastic model, represented by OY′P′ (chain-dotted line) in Figure 5.3(d), in which plastic deformation beyond the yield point is accompanied by stress reduction or softening of the material.
Simple models of soil elasticity
The Coulomb criterion, which will be described in Section 5.3, is a possible (simple) yield function if perfectly plastic behavior is assumed. From equation 5.4 it can be seen that the behavior of soil under pure shear is independent of normal stresses and is therefore not affected by pore water (water cannot sustain shear stresses).
Simple models of soil plasticity
As described in section 5.1, the state of stress in a soil element is defined based on the normal and shear stresses applied to the boundaries of the soil element. Soil behavior in shear in total stress (due to construction operations) is applied in relation to the rate of dissipation of excess pore water pressure (consolidation), which in turn is related to soil permeability as described in Chapter 4.
Laboratory shear tests – the direct shear test
In addition, the cross-sectional area of the specimen under shear and vertical loads does not remain constant during the test. The advantages of the test are simplicity and, in the case of coarse-grained soils, easy sample preparation.
Laboratory shear tests – the triaxial test
Non-uniform deformation of the specimen can be largely eliminated by lubrication of the end surfaces. Pore water pressure measurements can be taken during the undrained part of the test to determine strength parameters in terms of effective stresses.
Shear strength of coarse-grained soils
Stresses at the critical state define a straight line (Mohr–Coulomb) Figure 5.17 Shear strength properties of coarse-grained soils. In direct shear tests, the pore water pressure is approximately zero so that the TSP and ESP lie on the same line, as shown in Figure 5.19(c).
Shear strength of saturated fine-grained soils
Typical test results for samples of normally consolidated and overconsolidated clay are shown in Figure 5.24. Error envelopes for normally consolidated and overconsolidated clay are of the shapes shown in Figure 5.25.
