EFFECT OF REINFORCEMENT DENSITY ON THE BEHAVIOUR OF REINFORCED SAND UNDER A SQUARE FOOTING

In this study, the behaviour of reinforced sand under a square footing has been investigated. A series of bearing capacity tests were performed on a small-scale laboratory model, filled with a poorly-graded homogenous bed of sand, which was placed in a medium dense state using sand raining technique. The sand was reinforced with 40 mm wide household Aluminium foil strips. The aim was to study the load-settlement behaviour, bearing capacity ratio and settlement reduction factor, considering the effect of reinforcing strip length, with various linear density of reinforcement, number of reinforcement layers and depth of top layer of reinforcement below the footing. Generally the relation of load-settlement showed similar trend in all the tests. The failure was defined as the settlement equal to 10% of the footing width. The recommended optimum reinforcing strip length, linear density of reinforcement, number of reinforcement layers and depth of top layer of reinforcing strips, that give the maximum bearing capacity improvement and minimum settlement reduction factor were presented and discussed. Both bearing capacity and settlement reduction factor versus length of the reinforcing strips relation at failure have showed an improvement of the bearing capacity ratio by a factor of 3.82 and a reduction of the settlement reduction factor by a factor of 0.813. The optimum length of the reinforcement was found to be 7.5 times the footing width.


L
Length of the reinforcing strips.
LDR Linear density of the reinforcement. The footing resting on weak soils (i.e. soils having low bearing capacity) exhibits large settlements even under small loads, which can cause serious engineering problems leading to instability of the foundation and severe damage to the superstructure. Because of the population growth and increasing demand for extending the urban outspread, the reinforced soil is becoming a growing concern for geotechnical engineers dealing with foundation stability issues, especially above soft ground beds.
The modern concept of sand reinforcement was introduced by the French architect engineer Henry Vidal in 1966. Reinforced earth is defined as a construction material composed of granular materials and reinforcements placed in it. The reinforcing action requires frictional bond between the reinforcing strips and the soil particles with interlocking and adhesion properties. Hence free drainage granular soils were considered. The reinforcement can usually be any material possessing a substantial friction coefficient with the soil mass and capable of withstanding the tension force and deformation induced in the fill [7]. The resulting stable mass behaves monolithically, and can be used as earth retention and load supporting structures.
The main advantages of this technique are the low cost and rapid construction.
Therefore it is an attractive and economical answer to many earth retention problems, such as retaining walls, bridge abutments, platform supporting structures, foundation slabs and dams [7]. The main purpose of sand reinforcement technique in load supporting structures is to increase the bearing capacity and reduce the settlement (i.e. improvement of the load bearing capacity and stiffness of the sand).
After the pioneer Henry Vidal studied the reinforced earth, much works have been conducted by several researchers on the analysis, field test and construction of reinforced sand models. During the past five decades, results of several studies have been performed that relate the evaluation of the ultimate and allowable bearing  [8].
In this study the results of laboratory model tests with square footing resting on homogenous reinforced sand bed were studied. The studied parameters were the effect of length of reinforcing strips on the load-settlement, bearing capacity ratio and settlement reduction factor using different linear density of the reinforcing strips, number of reinforcing strip layers and depth of the top layer of the reinforcing strips below the footing.  [10]. The corresponding values of the minimum and maximum void ratios were 0.567 and 0.858 respectively.
Sand raining technique was used to calibrate the density of the sand. The sand was rained through a mesh of 2.87 x 2.87 mm opening using different height of drops, which provides different values of placing density [10]. Fig. 2 shows the relation between height of drops, density and percentage relative density of the sand. It was decided to use medium dense state with density of 15.80 kN/m 3 throughout the investigation. This was obtained by 350 mm height of raining, which yielded in to a relative density of 60%.

Box tank
The tests were all conducted in a well-stiffened wooden box of 450 mm deep x 550 mm wide x 1,350 mm length as internal dimensions, with 16.5 mm side and base thickness, supported by a rigid frame work 1,166 mm height to support the box as shown in Fig. 3. The box tank was strengthened in horizontal directions using a channel shaped steel section to avoid lateral deformation / bulging of tank walls during filling of the sand bed and loading conditions. The footing dimension (B) was 160 mm square side rigid steel plate 10 mm thick as shown in Fig. 3. The base of the model footing was roughened by covering it with epoxy glue and rolling it in sand [3]. In order to provide vertical loading alignment, a small hemi-spherical indentation was made at the centre of the footing model to accommodate a ball bearing through which vertical loads were applied to the footing uniformly. Such arrangement produced a hinge, which allows the footing to rotate freely as it approaches the failure and eliminates any potential moment transfer from the loading fixture to the footing.

Loading and deformation system
Vertical loads were applied by means of a motorised 3 tones capacity handoperated hydraulic jack at a constant rate of 15 mm/hr and by using a pre-calibrated load ring as shown in Fig. 3. The settlement of the footing was measured by means of two dial gauges placed on the footing surface.

Raining hopper tank
The sand raining hopper box tank was 550 x 1000 mm in plain view and 250 mm in depth and it was made of wood. The outlet of the hopper was connected to a flexible raining hose to control the sand raining easily. The raining hose was of the sliding type. It consists of two aluminium pipes, one slides inside the other, to control the raining height. A stainless steel mesh of 2.87 x 2.87 mm square opening was attached to the end of the hose in order to control the rate of flowing sand as shown in   The main parameters concerned in this study were the effect of length of the reinforcing strips on the load-settlement, bearing capacity ratio and settlement reduction factor relationships, using the following cases:

Kirkuk University Journal /Scientific Studies (KUJSS)
a. Different linear density of the reinforcing strips (LDR %).
b. Different number of the reinforcing layers (N).
c. Different depth of the top layer of the reinforcing strips below the footing (U).
While the other parameters such as the size of the footing, reinforcement properties and the relative density of the fill were kept constants.
The testing program was divided into two groups as follows: Group II: Thirty two tests were done on reinforced sand, which divided into three main series as presented in Table 2.  were placed on the opposite sides of the footing surface to measure the settlement [7].

Kirkuk University Journal /Scientific Studies (KUJSS)
The load was applied in small increments until reaching failure using a hydraulic jack.
Each load increment was maintained constant until the footing settlement had stabilized. The failure load was defined as the settlement of the footing equal to 10% of the footing width. The vertical movement was recorded and the entire load settlement curve at failure was obtained.

RESULTS AND DISCUSSION
A series of laboratory model tests were conducted to study the effect of reinforcing strip length on the behaviour of the load-settlement curve and to find the optimum reinforcing strip length required to obtain the maximum bearing capacity.  Where P and P 0 are the ultimate bearing load for reinforced and un-reinforced sand tests respectively, at any desired settlement.
The improvement due to the inclusion of the reinforcement layers in sand, in terms of reduction in footing settlement, can be known using the settlement reduction factor (SRF) parameter, which is defined as: Where S r and S 0 are the settlement of reinforced and un-reinforced sand bed respectively, at the same pressure of S 0 .
The test results of the laboratory model are presented with a discussion highlighting the effects of different parameters according to the test program as shown in Table 3.
The calculation of the bearing capacity ratio for LDR=40%, N=4 layers, U=50 mm and L=1,300 mm gives: The calculation of the settlement reduction factor for LDR=40%, N=4 layers, U=50 mm and L=1,300 mm gives: SRF = (16 -3.0) / 16 = 0.813 The presentation of all results details would make the paper lengthy. Therefore, only a calculation of one result is presented. For the tests with low density of reinforcements (i.e. L=400 and 700 mm, and U=25 mm, LDR=20% and N=2 layers), failure had occurred due to ties pulling out for the upper layer after overcoming the soil-tie friction resistance.

4.1: Effect of the studied parameters
The effect of reinforcing strip length on the BCR and SRF was divided into three main series as follows:   However, the rate of increase for L greater than 1,200 mm was very low. With increasing length of the reinforcing strips, the change in the footing settlement reduction factor SRF are insignificant and this number may be due to the optimum length of the reinforcement.

Series I: Different LDR%
As generally, the test results shows that the models with low number of reinforcement layers (N=2 layers) leads to reduction in the load carrying capacity of the footing indicated by softening in the slope of load-settlement curve. The behaviour of the load-settlement was similar to that of unreinforced sand with no noticeable changes in BCR an SRF. The results also shows that the load bearing pressure with high number of reinforcement layers increased with long strip lengths. This is due to the frictional resistance at the interface of the sand and the reinforcement, which would have prevented the soil mass from shearing under vertical applied load.

CONCLUSIONS
Based on the results discussed in this study, the following conclusions are gained: 1. The results indicated that substantial improvement in the footing system performance can be achieved with the provision of reinforcement .The reinforced sand system behaves much stiffer and causes less settlement than the unreinforced sand system.
2. The load versus footing deformation response of the reinforced sand bed was much better than the unreinforced case. This was due to the frictional resistance at the interface of the sand and the reinforcement, which would have prevented the soil mass from shearing under vertical applied load.

RECOMMENDATION
The following recommendations are suggested: 1. It is recommended to use circular footing.
2. It is recommended to use different types of reinforcement.