4.4 Results of the close-ended pipe pile
4.4.2 Wave matching analysis of the DLT
57
58
n
E
E
ref v cref c
'
(4.1)
where ref is the reference value of the vertical stress (100 kPa is used in this case), Ecref
is thevalue of Ec at ref, and n is an index number.
Figure 4.8. Relationship between the confined modulus, Ec, with overburden stress,v' . The mean values of Ec are closely approximated using Ecref = 37.5 MPa and n = 0.5 as shown in Fig. 4.8. The shear modulus, G, of the soil is estimated using the following equation of elasticity:
) c
1 ( 2
) 2 1
( E
G
(4.2)
where is Poisson's ratio of the soil, and assumed to be 0.3.
The first assumptions about the soil properties are shown in Fig. 4.9. The distribution of the shear modulus, G, with depth was estimated using Eqs. (4.1) and (4.2) with Ecref = 37.5 MPa and n = 0.5. The distribution of the outer shaft resistance was estimated from Fig. 4.6.
Although the model ground was divided into 5 layers, the pile was divided into 55 elements in the analyses.
The measured pile force at SG1 (50 mm from the pile head) in the fifth blow (Fig. 4.10) was used as the input force in the WMA. Hence, the pile section below the level of SG1 was modelled in the analysis.
0 100 200 300 400 500
0 20 40 60 80 100
Approx., Ec = Eref ( v' / ref)n, n = 0.5 E
ref = 42.0 MPa (upper bound) Eref = 33.0 MPa (lower bound) E
ref = 37.5 MPa (average) Experimental data, D
r = 70%
Test 1 Test 2 Test 3
Stiffness, E c (MPa)
Stress, (kPa)
59
In the first WMA with the soil properties shown in Fig. 4.9, a good matching was not obtained. The soil properties were then changed until a good matching between the calculated and the measured responses was obtained.
Figure 4.9. Soil properties used in the first WMA of the CP.
Figure 4.10. Measured axial force at SG1 of blow 5 of the CP.
Figure 4.11 shows the results of the final WMA. The calculated changes in the axial pile forces over time are compared with the measured values at SG3, SG4 and SG5. At every level, the calculated axial forces were in close agreement with the measured forces. It is seen from Fig. 4.11, that both of the calculated and measured pile axial forces returned to zero after
0.5 0.4 0.3 0.2 0.1 0.0
0.5 0.4 0.3 0.2 0.1
0.00 1 2 3
0.5 0.4 0.3 0.2 0.1
0.00 5 10 15 20
Layer 5 Layer 1
Layer 2
Layer 3
Layer 4
Depth from ground surface, z (m)
Soil profile
from OED modelling Shear modulus
G (MPa)
Outer shear resist.
max_out (kPa)
60
about 9 ms, indicating that residual axial forces are negligible in this driving. It also can be seen from the calculated results in Fig. 4.12 that the driving event terminates at 9 ms.
Figure 4.11. Results of the final WMA of the CP for the axial forces.
(a) at SG3. (b) at SG4. (c) at SG5.
It should be noted that oscillation axial forces are found in the calculated results and the magnitude of the oscillation decreases over time without divergence. The period of the oscillation corresponds to the return travelling time, 2L/c = 0.22 ms, of the stress wave in the pile. This means that the proposed numerical method is capable of calculating the wave propagation in a pile. Oscillation with a period of 0.22 ms is not seen in the measured forces.
A possible reason for this might be due to the low frequency response of the amplifier used for the strain measurement. The oscillation of the calculated pile forces seems to be reduced for longer piles. Analyses of the case histories of longer piles would be useful for a more detailed discussion in a future study.
0 2 4 6 8 10 12
0.0 1.0 2.0 3.0 4.0 5.0 6.0
0.22 ms
(a) Calculated Measured at SG3
Axial force,F (kN)
Time, t (ms)
0 2 4 6 8 10 12
0.0 1.0 2.0 3.0 4.0 5.0 6.0
0.22 ms
(b)
Time, t (ms)
Axial force,F (kN)
Calculated Measured at SG4
0 2 4 6 8 10 12
0.0 1.0 2.0 3.0 4.0 5.0 6.0
0.22 ms
(c)
Time, t (ms)
Axial force,F (kN) Calculated
Measured at SG5
61
Furthermore, a reasonable agreement in the final settlements between the calculated and the measured values was obtained as indicated in Fig. 4.12.
Figure 4.12. Pile head displacement calculated from the final WMA of the CP.
Figure 4.13. Distribution of the shear moduli and shear resistances.
(a) Shear moduli. (b) Shear resistances
The soil properties identified from the final WMA are shown in Fig. 4.13. The soil properties used in the first assumption are also indicated for comparison. The other soil properties identified from the final WMA are; = 0 (refer to Eqs. (3.13) and (3.14) in Chapter 3), Rfs = 0.3 (refer to Eq. (3.17) in Chapter 3), Rfb = 0.9 (refer to Eq. (3.18) in Chapter 3), end-bearing resistance at the pile tip = 1410 kPa, and shear modulus of the soil beneath the pile tip
0 2 4 6 8 10 12
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Calculated
Measured final set
Time, t (ms) Pile head disp., w h (mm)
0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05
0.00 1 2 3
0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05
0.000 10 20 30
(a) (b)
1st assump.
Final WMA From SLT Outer shear moduli
G (MPa)
Outer shear resist.
max (kPa)
Distance from ground surface, z (m)
1st assump.
Final WMA
62
= 3000 kPa. Note that (refer to Eqs. (3.13) and (3.14) in Chapter 3) has no influence on the WMA results when = 0. The identified non-linearity coefficients of the soil at the pile shaft, Rfs, and at the pile tip, Rfb, are consistent with the soil responses as mentioned earlier in Figs.
4.6a and 4.6b. The maximum negative shear resistances,maxneg, were 30 % of the maximum positive shear resistance,maxcomp,and qmaxtens was set to zero in the final WMA.
Figure 4.13a shows that the values of the shear modulus, G, of the soil layers identified from the final WMA are smaller than those used in the first WMA. It should be noted that the effective overburden pressures, v', in the model ground were less than 10 kPa. Estimation of the G of soil subjected to such small effective overburden pressures from the OED test results (Fig. 4.8) using Eqs. (4.1) and (4.2) may not be so reliable. Hence, the shear moduli were estimated from the static load test results in Fig. 4.6a. The spring stiffness, ks(static), was obtained from the initial stiffness of each curve in Fig. 4.6a, and then G was estimated using the relations in Eqs. (4) and (5). Thus, the estimated values of G are also indicated by circles in Fig. 4.13a. The values of G identified from the final WMA are comparable with those from the SLT.
Figure 4.14. Derived and measured static load-displacement curves of the CP.
Figure 4.14 shows the static load-displacement curve derived from the soil properties identified in the final WMA when compared with the static load test results. Although the derived curve overestimates the pile displacement for applied loads greater than 0.5 kN, an overall agreement between the derived and the measured results was obtained. The overesti-mation of the pile displacement in the derived curve is attributed to the underestioveresti-mation of G
4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5
0.00.0 0.2 0.4 0.6 0.8 1.0 1.2
SLT from WMA
Head force, Fh (kN)
Pile head displacement,w h (mm)
63
in the final WMA compared to that in SLT2 (see Fig. 4.13a). It should be noted that the load-displacement curve could be calculated until the pile head force reached 1.2 kN, because the set per blow, S, was about 3.3 mm in the pile driving test, and the identified pile tip resistance during pile driving was used in the calculation of the static response.
Figure 4.15. Derived and measured distributions of the axial forces of the CP.
Figure 4.15 shows the derived axial force distributions of the pile at different pile head loads, together with the SLT results. Fairly good agreements between the derived and the measured results were obtained.