4. SIMULATION OF A RAM IMPACT WITH A DRILLED DEEP FOUNDATION 1 Overview
4.9 Uneven impact (tilted ram) .1 Surface conditions
T = 5.0 ms T = 6.0 ms T = 7.0 ms T = 8.0 ms T = 9.0 ms T = 10 .0 ms
-15708 0 15708 31416 47124
Equivalent Force ( kN )
Figure 61. Calculated Normal Stress for Elements on Concrete Surface in FE Model with Ram Diameter
= 1.0m and Tilt Angle =0° for d = -0.5 to 0.5m.
To obtain a better feel for this variation, isometric 3-D images were prepared, detailing the contact stresses at the pile’s surface with time and are presented in Figure 62 (a to l). The obtained images show high stresses around the external rim of the contact between the ram, striking plate, wood and the pile’s top.
4.8.2 One meter below the surface
Figure 63 (a to l) describes the normal stresses across the pile at a location 1.0m (0.5 diameter) below the surface, for various times of the stress passing along the pile. The obtained images clearly show a well-distributed stress across the pile’s section. It should be noted that the stress is uniform and what seem to be a stress increase at the circumference is only a result of the isometric presentation of the data.
Additional presentation of the stress at the depth of 2m (1 diameter from the surface had shown similar results shifted only in time.
4.9 Uneven impact (tilted ram) 4.9.1 Surface conditions
The stress and velocity with time at eight points across the pile’s surface (see Figure 32) are presented in Figures 64 and 65 with further details on a smaller time scale presented in Figures 66 and 67 respectively.
65 60 55 50 45 40 35 30 25 20 15 10 7.5 5 2.5 0 -5 -10 -15 MPa
Figure 62. Calculated Normal Stress for Elements on Concrete Surface in FE Model with Ram Diameter
= 1.0m and Tilt Angle = 0° for Time equal to; (a) 1.8ms, (b) 2.0ms, (c) 2.5ms, (d) 3.0ms, (e) 3.5ms, (f) 4.0ms (g) 4.5ms, (h) 5.0ms, (i) 6.0ms, (j) 7.0ms, (k) 8.0ms, and (l) 9.0ms.
e
a b
c d
f
g h
i j
k l
65 60 55 50 45 40 35 30 25 20 15 10 7.5 5 2.5 0 -5 -10 -15 MPa
Figure 63. Calculated Normal Stress for Elements 1m Below Concrete Surface in FE Model with Ram Diameter = 1.0m and Tilt Angle = 0° for Time equal to; (a) 1.8ms, (b) 2.0ms, (c) 2.5ms, (d) 3.0ms, (e)
3.5ms, (f) 4.0ms (g) 4.5ms, (h) 5.0ms, (i) 6.0ms, (j) 7.0ms, (k) 8.0ms, and (l) 9.0ms.
e
a b
c d
f
g h
i j
k l
0 10 20 30 40 Time ( ms )
-40000 0 40000 80000
Axial Stress ( kN/m2 )
Element Distance Measured from Centerline
-0.4460 m -0.4040 m -0.2160 m -0.0307 m 0.0307 m 0.2160 m 0.4040 m 0.4460 m
Figure 64. Calculated Normal Stress for Elements on the Concrete Surface in the FE Model with Ram Diameter = 1.0m and Tilt Angle = 1° for Time = 0ms – 40ms.
0 10 20 30 40
Time ( ms ) -12000
-8000 -4000 0 4000 8000 12000
Velocity ( mm/s )
Node Distance Measured from Centerline
-0.500 m -0.437 m -0.250 m -0.062 m 0.062 m 0.250 m 0.437 m 0.500 m
Figure 65. Calculated Velocity for Nodes on the Concrete Surface in the FE Model with Ram Diameter
= 1.0m and Tilt Angle = 1° for Time = 0ms – 40ms.
0 2 4 6 8 10 Time ( ms )
-20000 0 20000 40000 60000 80000
Axial Stress ( kN/m2 )
Element Distance Measured from Centerline
-0.4460 m -0.4040 m -0.2160 m -0.0307 m 0.0307 m 0.2160 m 0.4040 m 0.4460 m
Figure 66. Calculated Normal Stress for Elements on the Concrete Surface in the FE Model with Ram Diameter = 1.0m and Tilt Angle = 1° for Time = 0ms – 10ms.
0 2 4 6 8 10
Time ( ms ) -2000
0 2000 4000 6000 8000 10000
Velocity ( mm/s )
Node Distance Measured from Centerline
-0.500 m -0.437 m -0.250 m -0.062 m 0.062 m 0.250 m 0.437 m 0.500 m
Figure 67. Calculated Velocity for Nodes on the Concrete Surface in the FE Model with Ram Diameter
= 1.0m and Tilt Angle = 1° for Time = 0ms – 10ms.
A complementary graph describes the stress as a function of the location at the pile’s surface for various times, and is presented in Figure 68. The obtained results suggest a very large variation in the normal stresses and velocities across the surface of the pile and moreover this variation seem to last for a significant time
length in relation to the time required for the stress wave to travel to the pile’s tip and back (see Figure 64). A detailed investigation is, therefore, required in order to assess the significance of an inclined impact, even though such an incline is considered in most cases very small (1°).
-0.4 -0.2 0 0.2 0.4
Element Distance Measured from Centerline ( m ) -2000
Axial Stress ( kN/m2 )
Time Step
Element Distance Measured from Centerline ( m ) -20000
Axial Stress ( kN/m2 )
Time Step
Figure 68. Calculated Normal Stress for Elements on the Concrete Surface in the FE Model with Ram Diameter = 1.0m and Tilt Angle = 1° for d = -0.5 to 0.5m and time equal to (a) 1.8 to 2.2ms, and (b) 2.0 to
4.5ms.
Isometric 3-D images of the normal stress at the pile’s surface with time are presented in Figure 69 (a to k).
The images clearly show a stress concentration at the point of initial contact between the ram-striking plate-wood and pile. This concentration remains high throughout the time of impact
4.9.2 One meter below the surface
Figure 70 describes the normal stresses across the pile at a location 1.0m (1 diameter) below the surface, for various times of the stress passing along the pile. Within the distance of half a diameter, the sharp stress peaks that appear at the surface are muted but a large variation exists between the stresses at one side of the cross-section to the other.
4.9.3 Two meter below the surface
Figure 71 describes the normal stresses across the pile at a location 2.0m (2 diameter) below the surface, for various times of the stress passing along the pile. The stresses remain markedly uneven across the section throughout the passing of the wave.
4.9.4 Three and four meters below the surface
Further attempts to elucidate the changes in the normal stress distribution across the pile at a large distance from the surface are presented in Figure 72 and 73 for distances of 3m and 4m (3 and 4 diameters) from the pile top, respectively. Both figures show a more evenly stress distribution with increase in the distance from the impact, but even at four diameters away from the pile top the stresses seem to be highly uneven across the pile.
65 60 55 50 45 40 35 30 25 20 15 10 7.5 5 2.5 0 -5 -10 -15 MPa
Figure 69. Calculated Normal Stress for Elements on Concrete Surface in FE Model with Ram Diameter
= 1.0m and Tilt Angle = 1° for Time equal to; (a) 2.0ms, (b) 2.5ms, (c) 3.0ms, (d) 3.5ms, (e) 4.0ms, (f) 5.0ms (g) 6.0ms, (h) 7.0ms, (i) 8.0ms, (j) 9.0ms, and (k) 10.0ms.
e
a b
c d
f
g h
i j
k
65 60 55 50 45 40 35 30 25 20 15 10 7.5 5 2.5 0 -5 -10 -15 MPa
Figure 70. Calculated Normal Stress for Elements 1m Below Concrete Surface in FE Model with Ram Diameter = 1.0m and Tilt Angle = 1° for Time equal to; (a) 2.0ms, (b) 2.5ms, (c) 3.0ms, (d) 3.5ms, (e)
4.0ms, (f) 4.5ms, (g) 5.0ms (h) 6.0ms, (i) 7.0ms, (j) 8.0ms, (k) 9.0ms, and (l) 10.0ms.
e
a b
c d
f
g h
i j
k l
65 60 55 50 45 40 35 30 25 20 15 10 7.5 5 2.5 0 -5 -10 -15 MPa
Figure 71. Calculated Normal Stress for Elements 2m Below Concrete Surface in FE Model with Ram Diameter = 1.0m and Tilt Angle = 1° for Time equal to; (a) 2.0ms, (b) 3.0ms, (c) 4.0ms, (d) 5.0ms, (e)
6.0ms, (f) 7.0ms, (g) 8.0ms, (h) 9.0ms, (i) 10.0ms, (j) 11.0ms, and (k) 12.0ms.
e
a b
c d
f
g h
i j
k
Figure 72. Calculated Normal Stress for Elements 3m Below the Concrete Surface in the FE Model with Ram Diameter = 1.0m and Tilt Angle = 1° for Time Equal to (a) 6.0ms, (b) 7.0ms, (c) 8.0ms and (d)
9.0ms.
Figure 73. Calculated Normal Stress for Elements 4m Below the Concrete Surface in the FE Model with Ram Diameter = 1.0m and Tilt Angle = 1° for Time Equal to (a) 6.0ms, (b) 7.0ms, (c) 8.0ms and (d)
9.0ms.
MPa
65 60 55 50 45 40 35 30 25 20 15 10 7.5 5 2.5 0 -5 -10 -15 -20
MPa
65 60 55 50 45 40 35 30 25 20 15 10 7.5 5 2.5 0 -5 -10 -15 -20
a b
c d
a b
c d
-20 -15 -10 -5 0 2.5 5 7.5 10 15 20 25 30 35 40 45 50 55 60 65
MPa 4.10 The use of soft cushion to mitigate uneven impact (tilted ram)
The analyzed cases presented in the previous section suggest a troublesome situation in which a ram impact in a small inclination will result with uneven stress distribution across a shaft for a large distance (over four diameters) away from the surface of the shaft. In an attempt to examine mitigating solution, an analysis has been carried out for which the cushion was assumed to be two order of magnitude “softer” than the realistic value used in stage II of the analysis (E=7x107Pa vs. 7x109Pa). The results of this analysis, describing the normal stress distribution across the shaft at a distance 2m (two diameters) away from the shaft’s surface are depicted in Figure 74.
Figure 74. Calculated Normal Stress for Elements 2m Below the concrete Surface in the FE Model with Ram Diameter = 1.0m and Tilt Angle = 1° with a Soft Cushion for Time Equal to (a) 3ms, (b) 6ms, (c) 8ms, (d)
10ms, (e) 12ms, and (f) 14ms.
The obtained results clearly show improved stress distribution across the shaft in comparison with the one with a more realistic “harder” cushion presented in Figure 71. However, the duration of the stress wave had significantly increased (in time) and decreased in magnitude. So while an improvement is made in the distribution of the stress, its quality for analysis in signal match or in amount of energy arriving to the shaft had significantly diminished.
Figure 75 illustrates the difference between the two cases. The average force across the shaft’s section at the surface, 1m and 2m below the surface are plotted against time for the two cushions discussed above. The
“softer” cushion is clearly seen to reduce the peak average force/stress by about half while doubling the wave duration.
e
a b
c d
f
0 10 20 30 40 50 Time ( ms )
0