6- STRAINS COMPUTATION 
The strains are calculated from the values 
of the vertical and horizontal 
displacement at the nodes of the grid. 
Each element of the grid is considered to 
be a square element (12.5mm X 12.5mm). 
The vertical and horizontal strains are 
calculated through the centre of the 
element. The following assumptions 
(James, 1972) apply: 
1- displacements vary linearly across each 
element which in turn assumes that the 
sand in every element strains uniformely. 
2- changes in the geometry of the system 
during testing have a negligible effect on 
the caleulated strains. 
3- compressive strains are assumed to be 
positive. 
The shear strain is defined as the angular 
distortion at the centre of the element 
taken from the top right hand quarter of 
the element and is calculated from the 
appropriate vertical and horizontal 
displacements of the four corners of the 
element. All the strain values are 
assigned to the centres of the elements 
and the coordinates of the nodes of the 
grid containing the strains are redefined 
to these positions. The nodal points of 
each element are numbered proceeding in a 
counterclockwise direction around the 
element in the order 1,2,3 and 4 (fig. 2). 
y Va Vv 
T 
u42 > u 
4 3 3 
- WwW 
  
  
  
  
  
Fig.2 Numbering convention for 
the nodal points. 
The following equations were derived : 
  
  
e UE (u, ;4.u,) - (Cu, v u) 
x 2x 
. (v tV = (Va i Va) 
y 2y 
Yxy7 [((v;-v9)*(v,-v,))72x] * 
FCCuzzu, 90 (u,7u,))72y] 
Where, ‘x , ‘> and Y:;y are the axial strains 
and shear strain respectively. u and wv 
represent the horizontal and vertical 
displacement. 
7- TESTING PROCEDURE 
The apparatus consisted of a wooden box, 
600 om by 300 cm in plan and 400 cm depth. 
The front viewing face of the box was 
designated to allow a 6 mm thick glass to 
slide in and out. Sufficiently stiff 
bracing for this glass face was obtained 
on the bottom and sides of the tank by the 
use of thin U metal plates. It was 
restrained against the frame by bolts 
screwed through tapped holes in the front 
of the box. 
with 5 mm inside diameter was fixed in the 
base at the centre of the box immediately 
behind the glass face. À semi circular 
brass disc 50 mm diameter and 13 mm thick 
was welded to the upper end of 5 mm 
diameter shaft to make the anchor unit. 
The shaft was 400 mm long, its diameter 
having been reduced to 5 mm from the 
middle to the upper end in order to be 
pushed through the bush. The bottom end 
of the shaft was fixed to a load cell 
which in turn was fixed to the base plate 
of a 1 ton Whykeham Farrance multispeed 
machine. À Sangamo transducer was 
also fixed to the base plate to record the 
displacement of the plate anchor. The 
load cell and the LVDT were connected to a 
data logger and a plotter in order to 
monitor the different stages of the test. 
The sand was placed in layers of 30 mm 
thickness until the required depth was 
reached , a rectangular hopper, 650 mm by 
300 mm in plan and 300 mm in depth, being 
used to produce a rain of sand grains and 
therefore achieve the required densities. 
Details of the technique have already been 
given in Bouazza (1990) and Bouazza & 
Finlay (1990). 
120 
I00 r 
Push out load P (N) 
  
  
1 1 J 1 — 
0 I 2 3 4 5 6 
Displacement ¢ (mm) 
FIG.3: TYPICAL LOAD VS DISPLACEMENT CURVE. 
A semi circular brass bush.