DECLARATION 1: PLAGIARISM
2. CHAPTER 2: LITERATURE REVIEW
2.4 Soil Properties
After performing the investigations, Van Baars (1995) concluded that models using equilibrium equations (FEM) yielded the same results as models based on equations of motion (DEM) but only when soil is in a quasi-static state and motion is minimal. FEM provides quicker convergence but for completely dynamic applications, DEM must be used. The main limitation in modelling using DEM is the restriction on the number of particles; hence any models performed will only illustrate laboratory models of a small scale.
Where the Poisson’s ratio is 0.1 – 0.3 for loose sand and 0.3 – 0.4 for dense sand.
2.4.2 Young’s Modulus
The Young’s modulus provides as indication of the soils stiffness and the degree of settlement that a soil fill will undergo when subjected to static load. The elastic behaviour of the soil is governed by the Young’s Modulus and the Poisson’s ratio. At the onset of plastic deformation the soils behaviour is described by Mohr-Coulombs failure envelope. In previous studies performed by Mifsud (2005) and Potts (2007) the soils Young’s modulus was varied in a parametric investigation to determine the influence it had on the FEM results.
2.4.3 Mohr-Coulomb failure criterion
Mohr theory states that when failure takes place in a soil mass it is due to a combination of the shear stress and the normal stress at a critical state. The shear strength is approximated by the following equation:
R= S + tan ( ) (Mohr-Coulomb equation)
c = cohesion
= Angle of internal friction
= Normal stress on the failure plane
R = Shear strength
In the laboratory model, when the soil undergoes a loss of support it is expected that the soil behaves in a plastic manner as it will be suddenly forced into failure. The failure envelope that occurs is governed by the Mohr-Coulomb yield criterion. In the FEM program the soil elements were modelled as elastic-perfectly plastic materials with the Mohr-coulomb failure criterion.
2.4.4 Angle of internal friction
The angle of internal friction provides an indication of a soils ability to withstand shear force.
The angle of internal friction as well as the angle of dilation should have an effect on the geometry of the surface trough and the deflected shape of the geosynthetic.
2.4.5 Density of soil
Compaction increases the shear strength of the soil. In previous studies performed by Potts (2007), the behaviour of dense and loose geosynthetically reinforced soil when subjected to a subgrade void was considered. Potts (2007) concluded that denser soil tended to dilate more due to the increased angle of shearing resistance and provided an overall decrease in soil settlements. Potts (2007) also concluded that in looser fill, adding, reinforcement had a greater effect on the surface settlement than adding reinforcement to a compacted soil fill layer.
2.4.6 Soil arching
Soil arching is defined as “The transfer of forces between a yielded mass of soil and adjoining stationery members” Terzagi (1943). Classical arching theory states that when the vertical support at some part of a soil mass is lost, the soil mass will want to move downward due to self-weight. The mass that moves downward will shear along a boundary between itself and the soil that remains stationary. The shearing resistance along this boundary opposes the downward motion and results in a redistribution in some of the stresses. This has an effect in reducing the pressure on the yielding area (vertical stresses) and increases the pressure in the stationary soil (horizontal stresses) (Potts, 2007). The occurrence of soil arching is indicated by the shear strength of the soil being larger than expected, due to the soil supporting itself over a certain area.
Various factors have been identified to effect the occurrence and degree of soil arching. Giroud et al. (1990) theorises that the H/D ratio has a significant influence on whether soil arching takes place. Other factors identified were the properties of the fill material, density of the fill and the number of reinforcement layers used.
The earliest recorded occurrence of soil arching was discovered in the 1800’s (Smith, 2014).
After the construction of a silo, it was found that the forces being applied to the base of the silo was less than the anticipated weight of fill within the silo. This was due to the fact that the sidewalls of the silo carried some of the fill weight due to the transfer of forces to the sidewalls of the silo structure. The soil tends to “arch over the yielded part of the support” Terzagi (1943).
Arching theory also plays a role in the initial formation of the sinkhole. Sinkholes are generally formed due to voids in the soil-rock interface, as the void gets larger; the soil above the void is
unsupported. The soil will arch until a point where the arch across the cavity is incapable of handling the overburden, after which collapse will occur. Potts (2007) concluded that there is a correlation between soil arching and the ratio of the overburden height to the depth of soil deflection. The larger the H/D ratio, the greater the chance of soil arching taking place.
2.4.7 Soil dilation
The angle of dilation “controls an amount of plastic volumetric strain developed during plastic shearing and is assumed constant during plastic yielding” (Bartlett, 2012). When a soil undergoes deformation while in shear, and the volume of the material is preserved, the angle of dilation of the soil is said to be zero.
The dilation of the soil depends on the soil type, degree of compaction and the movement of the soil. Figure 2.2 shows the relationship between stress, strain and rate of volumetric change. The peak stress corresponds to the development of dilation in dense soil. Beyond this point the soil will continue to dilate until a critical state is reached. At the critical state the soils volume will remain constant as it shears (Bolton, 1986).
Figure 2.2 Diagrammatic representation of widely adopted concepts of the relationship between shearing and dilation as expressed in Schofield & Wroth (1986)
When constant volume deformation takes place and there’s no dilation (
UVW
UVX = 0), YH
ZH = M. When strain <
A the soil sample will contract and UVW
UVX is a positive value. The sample undergoes expansion from YH
ZH = A to YH
ZH = B, and point C represents the point where the maximum rate of dilation occurs at some point C. Atkinson (1981) thus concluded that there is a
direct link between the shape of the -: and YH
ZH : curve.
According to Bartlett (2012) the angle of dilation for sands depends on the angle of shearing resistance. In non-cohesive soils like sand and gravel, when the angle of shearing resistance is greater than 300, the angle of dilation can be estimated as equal to 300 (Bartlett, 2012). Bartlett (2012) further states that soil contraction (negative dilation) is more likely to take place in loose sands. When performing an FEA involving soil in motion, the possible dilation of the soil must be accounted for. The Strand 7 program used for the FEA analysis regarded the angle of dilation as equal to the angle of shearing resistance. The angle of soil dilation cannot be altered independently from the shearing resistance hence the Strand 7 system may overestimate the predicted angle of dilation, especially in cases where the soil is in a loose state and is more likely to contract.
Figure 2.3: Typical [H
\H vs ]^ and ]_vs ]^ relationships for a drained triaxial test on dense sand where [H
\H = stress ratio and `]_
`]^ = rate of dilation Atkinson (1981).