Soil experiences irrecoverable (plastic) deformation even at low stress levels and shows nonlinear behavior very early in the stress-strain curve. The deformation characteristics of both the unreinforced and glass fibre-reinforced clayey soil specimens can be quantified through a deformation modulus, as a measure of its resistance against deformation in response to any external applied load.
The soil modulus of the soil at any deformation level can be determined from the stress-strain curve by drawing a secant line from the origin to the point considered on the stress-strain curve, and is the ratio of deviator stress level to its corresponding strain level.
The stress-strain curves of reinforced soil, and therefore the soil modulus, are influenced by fibre parameters (content and length), moulding state factors (moisture content and dry unit weight) and and confining pressure. The secant modulus has been calculated at different axial strain values (0.5, 1, 2.5, 5, 10 and 20%).
For soil specimens of Series 1, with varying fibre content of 20 mm length, the secant modulus values at 2.5, 5, 10 and 20% axial strain are tabulated in Table 6.6. For any specimen, the secant modulus is higher at small axial strain and decreases with increasing
axial strain. The secant modulus values of the unreinforced soil at 2.5% axial strain are 8.08, 9.10, 11.94 and 14.84 MPa under 100, 200, 300 and 400 kPa confining pressures, respectively. The corresponding values decrease to 1.13, 1.61, 2.17 and 2.52 MPa at 20%
axial strain.
Typical effect of fibre content on secant modulus variation under 100 kPa confining pressure, for specimens of Series 1 reinforced with 20 mm fibres, is shown in Fig. 6.14. At any axial strain level, the secant modulus increases with fibre content up to 0.75% and then decreases with 1% fibres. Under 100 kPa confining pressure, the secant modulus is the maximum with 0.75% fibres of 20 mm length (Table 6.6). The corresponding maximum value is 12.15 MPa at 2.5% axial strain which decreases to the minimum value of 1.93 MPa at 20% axial strain.
Typical effect of fibre length on secant modulus variation under 100 kPa confining pressure, for specimens of Series 1 reinforced with 0.75% fibres, is shown in Fig. 6.15. At any strain level, the secant modulus increases with fibre length to reach maximum value with 20 mm fibres, and then decreases with 30 mm fibres. However the secant modulus values with 30 mm fibres is higher than that of with 10 mm fibres. Under 100 kPa confining pressure, the maximum values of secant modulus with 0.75% fibres are 10.26, 12.15 and 11.48 MPa at 2.5% axial strain with 10, 20 and 30 mm fibres, respectively (Table 6.6).
Table 6.6 Summary of secant modulus values under different confining pressures for specimens reinforced with fibres of 20 mm length and moulded at OMC and MDU (Series 1)
Axial strain (%)
fc (%) Secant modulus (MPa)
L = 10 mm L = 20 mm L = 30 mm
100 kPa
200 kPa
300 kPa
400 kPa
100 kPa
200 kPa
300 kPa
400 kPa
100 kPa
200 kPa
300 kPa
400 kPa
2.5
0 8.08 9.10 11.94 14.84 8.08 9.10 11.94 14.84 8.08 9.10 11.94 14.84
0.25 8.81 11.37 14.06 15.58 9.11 11.72 14.76 17.04 8.31 10.83 13.32 15.95 0.5 8.87 12.68 15.10 17.54 12.05 12.72 16.44 20.49 9.91 12.31 14.58 18.89 0.75 10.96 13.83 16.77 19.90 12.15 14.12 17.20 20.58 10.85 13.24 16.92 19.86
1 8.63 11.78 15.86 19.56 10.51 12.32 15.64 18.12 9.96 13.03 15.86 19.71
5
0 4.38 5.17 6.51 8.22 4.38 5.17 6.51 8.22 4.38 5.17 6.51 8.22
0.25 4.70 6.68 7.81 8.94 5.42 7.19 9.45 10.16 5.69 6.71 8.29 9.24
0.5 5.02 7.72 9.39 10.83 5.93 8.34 10.03 12.89 5.95 7.74 9.56 11.41
0.75 5.81 8.55 9.88 12.45 7.02 8.87 10.48 13.31 6.19 8.01 9.99 12.58
1 5.26 7.49 9.41 11.93 6.05 8.49 10.12 13.18 5.91 7.70 9.74 11.93
10
0 2.32 3.18 3.95 4.78 2.32 3.18 3.95 4.78 2.32 3.18 3.95 4.78
0.25 2.62 3.81 4.58 5.20 2.96 4.11 5.33 6.03 2.85 3.77 4.86 5.32
0.5 3.01 4.48 5.31 6.42 3.35 4.75 6.06 7.19 3.16 4.45 5.81 6.56
0.75 3.24 4.82 5.70 6.96 3.81 5.27 6.39 7.65 3.47 4.56 6.61 7.06
1 3.08 4.44 5.49 6.56 3.54 4.78 6.22 7.19 3.35 4.39 5.69 6.78
20
0 1.13 1.61 2.17 2.52 1.13 1.61 2.17 2.52 1.13 1.61 2.17 2.52
0.25 1.41 2.07 2.52 2.88 1.48 2.16 2.73 3.36 1.46 1.99 2.70 2.87
0.5 1.54 2.27 2.82 3.53 1.75 2.46 3.22 3.68 1.62 2.41 3.08 3.16
0.75 1.72 2.52 2.99 3.63 1.93 2.78 3.55 3.94 1.89 2.53 3.19 3.76
1 1.61 2.45 2.92 3.30 1.84 2.44 3.19 3.59 1.71 2.45 2.92 3.62
0 5 10 15 20 0
3 6 9 12 15 18 21 24
fc = 1%
fc = 0.75%
fc = 0.5%
fc = 0.25%
No fibre
Secant modulus (MPa)
Axial strain (%) L = 20 mm
d = 16.8 kN/m3
3 = 100 kPa
Fig. 6.14 Effect of fibre content on secant modulus variation under 100 kPa confining pressure for specimens reinforced with 20 mm fibres and moulded at OMC and MDU
(Series 1)
0 5 10 15 20
0 3 6 9 12 15 18 21 24
Secant modulus (kPa)
Axial strain (%)
L = 30 mm L = 20 mm L = 10 mm No fibre
d = 16.8 kN/m3 fc = 0.75%
3 = 100 kPa
Fig. 6.15 Effect of fibre length on secant modulus variation under 100 kPa confining pressure for specimens reinforced with 0.75% fibres and moulded at OMC and MDU (Series 1)
Typical effect of confining pressure on secant modulus variation for specimens of Series 1, reinforced with 0.75% fibres of 20 mm length, is presented in Fig. 6.16. At any axial strain level, the secant modulus is greater with increasing confining pressure. The maximum secant modulus values at 2.5% axial strain are 12.15, 14.12, 17.20 and 20.58 MPa under 100, 200, 300 and 400 kPa confining pressures, respectively (Table 6.6).
The secant modulus values for specimens of Series 1 & 2, with fibres of 20 mm length and different dry unit weights, under the four confining pressures (100 to 400 kPa) are presented in Tables 6.7 & 6.8. The secant modulus is observed to increase with increasing confining pressure at any dry unit weight. At any dry unit weight, secant modulus values increase with fibre content up to 0.75% fibre and decreases with 1% fibres.
At 100 kPa confining pressure, secant modulus values of the unreinforced soil at 2.5%
axial strain are 4.45, 5.14, 6.00 and 8.08 MPa for dry unit weights of 14.3, 15.1, 16.0 and 16.8 kN/m3, respectively (Table 6.7). The corresponding values increase with confining pressure to reach maximum values of 9.16, 11.04, 14.21 and 14.84 MPa at 400 kPa confining pressure (Table 6.8). For the reinforced specimens, secant modulus values are the maximum with 0.75% fibres of 20 mm length, and the secant modulus variation under 400 kPa confining pressure is shown in Fig. 6.17. The corresponding maximum secant modulus values at 2.5% axial strain are 11.93, 15.41, 18.29 and 20.58 MPa for dry unit weights of 14.3, 15.1, 16.0 and 16.8 kN/m3, respectively.
0 5 10 15 20 0
5 10 15 20 25 30
Secant modulus (MPa)
Axial strain (%)
3 = 400 kPa
3 = 300 kPa
3 = 200 kPa
3 = 100 kPa
d = 16.8 kN/m3 L = 20 mm fc = 0.75%
Fig. 6.16 Effect of confining pressure on secant modulus variation for specimens reinforced with 0.75% fibres of 20 mm length and moulded at OMC and MDU (Series 1)
0 5 10 15 20
0 3 6 9 12 15 18 21 24 27 30
Secant modulus (MPa)
Axial strain (%)
d = 16.8 kN/m3
d = 16.0 kN/m3
d = 15.1 kN/m3
d = 14.3 kN/m3 L = 20 mm
fc = 0.75%
3 = 400 kPa
Fig. 6.17 Effect of dry unit weight on secant modulus variation under 400 kPa confining pressure for specimens reinforced with 0.75% fibres of 20 mm length and moulded at OMC
(Series 1 & 2)
Table 6.7 Secant modulus values under 100 and 200 kPa confining pressures for specimens reinforced with 20 mm fibres and moulded at OMC with varying dry unit weight (Series 1 & 2)
Axial strain (%)
fc (%) Secant modulus (MPa)
γd = 14.3 kN/m3 γd = 15.1 kN/m3 γd = 16.0 kN/m3 γd = 16.8 kN/m3 100 kPa 200 kPa 100 kPa 200 kPa 100 kPa 200 kPa 100 kPa 200 kPa
2.5
0 4.45 6.08 5.14 7.25 6.00 9.18 8.08 9.10
0.25 5.85 7.41 6.32 8.64 8.72 11.21 9.11 11.72
0.5 6.18 7.96 8.54 10.28 9.54 12.05 12.05 12.72
0.75 6.61 8.54 8.73 11.45 10.40 13.45 12.15 14.12
1 5.75 7.21 7.46 8.85 10.12 11.8 10.51 12.32
5
0 2.81 3.65 3.27 4.38 3.77 5.45 4.38 5.17
0.25 3.59 5.26 4.11 5.45 5.30 6.71 5.42 7.19
0.5 4.08 5.6 5.19 6.99 5.58 7.47 5.93 8.34
0.75 4.63 6.06 5.21 7.16 6.08 7.98 7.02 8.87
1 3.63 5.79 4.91 6.55 5.98 7.58 6.05 8.49
10
0 1.63 2.31 1.94 2.62 2.16 2.99 2.32 3.18
0.25 2.18 3.11 2.49 3.31 2.85 3.84 2.96 4.11
0.5 2.72 3.81 3.09 4.11 3.31 4.50 3.35 4.75
0.75 3.01 4.35 3.31 4.49 3.65 4.73 3.81 5.27
1 2.92 3.95 3.24 4.33 3.45 4.65 3.54 4.78
20
0 0.86 1.37 1.03 1.44 1.11 1.54 1.13 1.61
0.25 1.16 1.61 1.42 1.96 1.48 1.99 1.48 2.16
0.5 1.44 2.13 1.76 2.37 1.73 2.37 1.75 2.46
0.75 1.83 2.55 1.86 2.64 1.93 2.66 1.93 2.78
1 1.31 2.07 1.79 2.53 1.73 2.41 1.84 2.44
Table 6.8 Secant modulus values under 300 and 400 kPa confining pressures for specimens reinforced with 20 mm fibres and moulded at OMC with varying dry unit weight (Series 1 & 2)
Axial strain (%)
fc (%) Secant modulus (MPa)
γd = 14.3 kN/m3 γd = 15.1 kN/m3 γd = 16.0 kN/m3 γd = 16.8 kN/m3 300 kPa 400 kPa 300 kPa 400 kPa 300 kPa 400 kPa 300 kPa 400 kPa
2.5
0 7.86 9.16 8.09 11.04 10.85 14.21 11.94 14.84
0.25 8.43 10.25 10.61 13.42 13.85 16.35 14.76 17.04
0.5 10.17 11.78 12.16 14.06 15.15 18.07 16.44 20.49
0.75 10.35 11.93 12.75 15.41 17.02 18.29 17.20 20.58
1 9.26 11.06 11.43 14.21 14.30 15.72 15.64 18.12
5
0 4.92 5.69 5.16 5.91 6.87 8.09 6.51 8.22
0.25 6.07 7.29 6.58 8.25 8.55 9.75 9.45 10.16
0.5 7.19 8.03 8.31 9.59 9.98 11.31 10.03 12.89
0.75 7.41 8.91 8.39 10.44 10.26 12.12 10.48 13.31
1 6.81 7.32 7.96 10.16 8.95 10.56 10.12 13.18
10
0 3.01 3.47 3.32 3.91 3.75 4.56 3.95 4.78
0.25 3.81 4.39 4.06 4.91 4.81 5.57 5.33 6.03
0.5 4.67 5.43 5.12 6.19 5.58 6.67 6.06 7.19
0.75 5.27 6.09 5.58 6.57 5.81 6.98 6.39 7.65
1 5.06 4.63 5.42 6.43 5.47 6.55 6.22 7.19
20
0 1.75 2.06 1.89 2.26 1.99 2.45 2.17 2.52
0.25 2.09 2.46 2.44 2.92 2.41 2.85 2.73 3.36
0.5 2.61 2.91 2.96 3.69 2.93 3.41 3.22 3.68
0.75 3.09 3.52 3.31 3.87 3.25 3.88 3.55 3.94
1 2.58 3.01 3.14 3.60 2.84 3.59 3.19 3.59
With the optimum reinforcement (0.75% fibres of 20 mm length), the relative effects of the ranges of moulded dry unit weight and confining pressure on secant modulus improvement can be compared at the considered failure axial strain level of 10%. At the considered failure axial strain level of 10%, the relative effects of the optimum reinforcement (0.75% glass fibres of 20 mm length), dry unit weight and confining pressure on secant modulus improvement can be compared. At 16.8 kN/m3 dry unit weight and under 100 kPa confining pressure, the failure secant modulus of the unreinforced specimen which is 2.32 MPa has increased to a maximum value of 3.81 MPa (i.e. 1.49 MPa improvement).
At 100 kPa confining pressure, the failure secant modulus of the reinforced specimen is found to increase from 3.01 to 3.81 MPa (i.e. 0.80 MPa improvement) when dry unit weight is increased from 14.3 kN/m3 to 16.8 kN/m3. Further, at 16.8 kN/m3 dry unit weight, the failure secant modulus of the reinforced specimen is noted to increase from 3.81 MPa to 5.27 MPa (1.46 MPa improvement) as confining pressure is increased from 100 kPa to 400 kPa. Comparing the stiffness improvement at failure strain, it can be concluded that the effect of confining pressure is higher than that of dry unit weight or fibre content.