13 Why Soil Mechanics
Soil mechanics has become a distinct and separate branch of engineering mechanics because soils have a number of special properties, which distinguish the material from other materials. Its development has also been stimulated, of course, by the wide range of applications of soil engineering in civil engineering, as all structures require a sound foundation and should transfer its loads to the soil. The most important special properties of soils will be described briefly in this chapter. In...
141 Confined compression test
In the confined compression test, or oedometer test a cylindrical soil sample is enclosed in a very stiff steel ring, and loaded through a porous plate at the top, see Figure 14.1. The equipment is usually placed in a somewhat larger container, filled with water. Pore water may be drained from the sample through porous stones at the bottom and the top of the sample. The load is usually applied by a dead weight pressing on the top of the sample. This load can be increased in steps, by adding...
202 Mohrs circle
From the theory of stresses see Appendix A it is known that the stresses acting in a certain point on different planes can be related by analytical formulas, based upon the equilibrium equations. In these formulas the basic variable is the angle of rotation of the plane with respect to the principal directions. These principal directions are the directions in which the shear stress is zero, and in which the normal stresses are maximal or minimal. It is assumed here that the maximum principal...
Vertical Slope In Cohesive Material
A well known and important problem of soil mechanics is the case of a vertical cutoff in a purely cohesive material 0 0 , as occurs when making a vertical excavation, or a vertical slope, see Figure 44.1. The problem to be considered in this chapter is the determination of a lower bound or an upper bound for the maximum possible height hc of the slope, for a material having a constant cohesive strength c, and a constant volumetric weight 7.
462 Fellenius
In Fellenius' method, the oldest method for the analysis of slope stability, it is assumed that there are no forces between the slices. The only remaining forces acting on a slice, see Figure 46.2, then are the weight Yhb, a normal stress lt r and a shear stress t at the bottom of the slice. The normal stress lt r can most conveniently be expressed into the known weight by considering the equilibrium of the slice in the direction perpendicular to the slip surface. This gives Substitution into...
Problems 1
13.1 A colleague in a foreign country reports that the Young's modulus of a certain layer has been back-calculated from the deformations of a stress increase due to a surcharge, from 20 kPa to 40 kPa. This modulus is given as E 2000 kPa. A new surcharge is being planned, from 40 kPa to 60 kPa, and your colleague wants your advice on the value of E to be used then. What is your suggestion 13.2 A soil sample is being tested in the laboratory by cyclic shear stresses. In each cycle there are...
122 Unloading and reloading
Because the deformations of soils are mostly due to changes in the particle assembly, by sliding and rolling of particles, it can be expected that after unloading a soil will not return to its original state. Sliding of particles with respect to each other is an irreversible process, in which mechanical energy is dissipated, into heat. It is to be expected that after a full cycle of loading and unloading of a soil a permanent deformation is observed. Tests indeed confirm this. When reloading a...
442 Upper bound
A simple upper bound can be found by considering a mechanism consisting of a single straight slip surface, at an angle a with the vertical direction, see Figure 44.3. The weight of the sliding wedge is W 2 h2 tan a, and it follows from the condition of equilibrium in the direction of sliding that is equivalent with the virtual work principle for the deformation mode of the mechanism that Because the length of the slip plane is h cos a it follows that Figure 44.3 Mechanism with straight slip...
Boussinesq
In 1885 the French scientist Boussinesq obtained a solution for the stresses and strains in a homogeneous isotropic linear elastic half space, loaded by a vertical point force on the surface, see Figure 28.1. A derivation of this solution is given in Appendix B, see also any textbook on the theory of elasticity for instance S.P. Timoshenko, Theory P of Elasticity, paragraph 123 . The stresses are found to be Figure 28.1 Point load on half space. In these equations r is the cylindrical...
35 Water content
The water content is another useful parameter, especially for clays. It has been used in the previous chapter. By definition the water content w is the ratio of the weight or mass of the water and the solids, It may be noted that this is not a new independent parameter, because For a completely saturated soil S 1 and assuming that pp pw 2.65, it follows that void ratio e is about 2.65 times the water content. A normal value for the porosity is n 0.40. Assuming that pk 2650 kg m3 it then follows...
334 Neutral earth pressure
It has been found that the possible states of stress in a soil may vary between fairly wide limits, especially if the friction angle is large. For a normal sand, with 30 , the smallest value of the horizontal stress is 3 of the vertical stress which usually is known from the surcharge and the weight of the overlying soil , and the largest Hi value is 3 times the vertical stress. In case of a rigid retaining wall, the lateral stress against the wall is unknown, at least from a strictly...
Blum
In the previous chapter a procedure has been presented for the determination of the minimum length of a sheet pile wall, needed to ensure equilibrium. This method is such that whenever the wall is shorter than that minimum length, no equilibrium is possible, and the wall will certainly fail. This suggests that it is advisable to choose the length of the wall somewhat larger than the minimum length, as a total failure of the wall would be disastrous. If the length is taken somewhat larger than...
Flamant
In 1892 Flamant obtained the solution for a vertical line load on a homogeneous isotropic linear elastic half space, see Figure 30.1. This is the two dimensional equivalent of Boussinesq's basic problem. It can be considered as the superposition of an infinite number of point loads, uniformly distributed along the y-axis. A derivation is given in Appendix B. . . . . . . . .v. . . . . . . In this case the stresses in the x, z-plane are In these equations r x2 z2. The quantity F has the dimension...
252 Undrained shear strength
For the comparison of drained and undrained calculations, and for the actual calculation in an undrained analysis, it is often necessary to determine the undrained shear strength su of a soil, from the basic shear strength parameters c and 0. This can be done by noting that in a saturated soil there can be practically no volume change in undrained conditions, so that the isotropic effective stress remains constant. Thus the average effective stress remains constant, and this means that the...
432 Inclination factors
loading by a vertical force and a horizontal load, see Figure 43.2, the bearing capacity is considerably reduced. This can be understood by noting that sliding would occur if the horizontal force approaches the maximum possible shear force on the foundation surface, The formulas should be such that for this limiting value of the shear stress t with respect to the constant value of the vertical stress p the bearing capacity reduces to zero. For cases in which the shear force is smaller than its...
A3 Mohrs circle
The formulas derived above can be represented in a simple graphical form, using Mohr's circle. For this purpose it is most convenient to use the transformation formulas in the form A.4 , but expressed into the principal stresses. The orientation of the x-axis with respect to the direction of the major principal stress is denoted by y, see Figure A.4. The directions of the major and the minor principal stresses are indicated by 1 and 2. The transformation formulas for the transition from the...
44 Archimedes and Terzaghi
The concept of effective stress is so important for soil mechanics that it deserves careful consideration. It may be illuminating, for instance, to note that the concept of effective stress is in agreement with the principle of Archimedes for the upward force on a submerged body. Consider a volume of soil of magnitude V, having a porosity n. The total weight of the particles in that volume is 1 n YPV, in which yp is the volumetric weight of the particle material, which is about 26.5 kN m3....
12 History
Soil mechanics has been developed in the beginning of the 20th century. The need for the analysis of the behavior of soils arose in many countries, often as a result of spectacular accidents, such as landslides and failures of foundations. In the Netherlands the slide of a railway embankment near Weesp, in 1918 see Figure 1.1 gave rise to the first systematic investigation in the field of soil mechanics, by a special commission set up by the government. Many of the basic principles of soil...