Impact tests on soil material Measurement of deceleration
Werner Gerber1, Axel Volkwein1 and Perry Bartelt2 1: Swiss Federal Research Institute WSL, Zürcherstr. 111, 8903 Birmensdorf, Switzerland (
[email protected]) 2: WSL Institute for Snow and Avalanche Research SLF, Flüelastr. 11, 7260 Davos Dorf, Switzerland
Introduction
Material and Methods
In the mountainous regions of Switzerland, many earth dams protect against rockfall and thereby reduce the risk of damage (Fig. 1). To stop falling rocks and boulders in this kind very high forces in the dam body are required. These forces are largely unknown and there is no universal formula with which such forces can be calculated. Fore these reasons we made falling weight tests on soil material.
12 m3
2 m3
3 m3
Fig. 1: Impact in a protective embankment of a block of 12 m3 (32’000 kg). The impact-velocity was 22 m/s, the kinetic energy 7’700 kJ and the penetration depth arround 50 cm.
In the WSL test side Walenstadt nearly 100 drop tests with cube-shaped concrete bodies have been carried out. During the experiments the deceleration of the test bodies have been measured using fix attached acceleration sensors (Fig. 2). With the measured values, the dynamic penetration and the brake-time is determined. From these results a brake-model was developed, which can also be used for general brake processes on soil material. Fig. 2: 4’000 kg test block shortly before falling testation
Tests carried out
Results of deceleration
Three cube-shaped concrete bodies with different masses (800 kg, 4000 kg and 8000 kg) fell from different heights (2.5 m, 5 m, 10 m and 15 m) on soil material with varying thicknesses (0.5 m, 1 m 1.5 m and 2 meter). A total of 96 tests were carried out (Tab.1).
The maximum decelerations are in a range of 280-1880 m/s2. The results show a strong dependence of the drop height and a low dependence of the falling mass. The strength of the soil layer has practically no influence on the size of the maximum deceleration (Fig. 3).
Tab. 1: Enumeration of experiments with corresponding masses, soil thicknesses and falling heights. Thickness of soil layer
Falling height
2.5 m
5m
10 m
15 m
800 kg
0.5 m 1.5 m 2m
1, 2, 3 13, 14, 15 25, 26, 27
4, 5, 6 16, 17, 18 28, 29, 30
7, 8, 9 19, 20, 21 31, 32, 33
10, 11, 12 22, 23, 24 34, 35, 36
4‘000 kg
1m 1.5 m 2m
37, 38, 39 49, 50, 51 61, 62, 63
40, 41, 42 52, 53, 54 64, 65, 66
43, 44, 45 55, 56, 57 67, 68, 69
46, 47, 48 58, 59, 60 70, 71, 72
8‘000 kg
1.5 m 2m
73, 74, 75 85, 86, 87
76, 77, 78 88, 89, 90
79, 80, 81 91, 92, 93
82, 83, 84 94, 95, 96
2400 800 kg
800 kg
800 kg
0.5 m
1.5 m
2.0 m
4'000 kg
4'000 kg
4'000 kg
8'000 kg
8'000 kg
1.5 m
2.0 m
1.5 m
2.0 m
2200 2000 Verzögerung amax (m/s2)
Mass of body
0.5 m
1800 1600 1400 1200 1000 800
Impact-model
600 400
The course of a delay do to the penetration depth to a maximum value at 40% of the deceleration. After falling from the delay to a third of the maximum value (at 70% of the deceleration time) and remains constant for the remainder. The rise and fall of the delay are functions of the second degree (Fig. 4a). The mathematical functions of the velocity and the penetration depth are third and fourth degree in this time interval (Fig. 4b). 120
80
20
60
40
40
60
33
20
80
0
100
0
-20 0
20
40 60 Braking time (%)
80
100
12
24
36
48 Versuchs Nr.
60
72
84
96
Fig. 3: Maximum deceleration amax of single impact tests
Comparison of measurements and model
0
Eindringtiefe z
Penetration depth z (%)
Velocity v (%)
Deceleration a/amax. (%)
100 Verzögerung a
67
0
-20 Geschwindigkeit v
100
200
The multiple linear regression with the calculated penetration depths were used together with the model to calculate the maximum deceleration. The results of the model calculations shows values which are higher of about a factor of 1.35 and a standard deviation of 0.15 (Fig. 5). This fact has been made aware, because we want to calculate a maximum value and not an average of the deceleration. 2000
120 0
20
40
60
80
100
800 kg 4'000 kg 8'000 kg Modell
1800
Braking time (%)
1600
Example for calculating the deceleration and braking force m3
In this example, the deceleration of the rock with a volume of 12 (Fig.1) is analyzed. The block has a mass of m = 32000 kg and impacted at a speed of v = 22 m / s (Falling height h = 25 m) is almost perpendicular to the slope. With these two values a penetration depth z can be calculated using the following formula: z = 7.63 ·10-3 · h + 4.57 · 10-6 · m + 0.05 = 0.4 m (z measured = 0.5 m) Using the penetration depth z and the falling height h the maximum deceleration amax and the braking force Fmax ca be calculated:
Deceleration amax (m/s^2)
Fig. 4: Abbremsmodell der Verzögerung (a) mit Geschwindigkeitsverlauf und Eindringkurve (b)
1400 1200 h = 15 m v = 17 m/s
1000 h = 10 m v = 14 m/s
800 600 h=5m v = 10 m/s
400
h = 2.5 m v = 7 m/s
200 0
0.05
0.1
0.15
0.2
Penetration depth z (m)
Maximum deceleration a max = v 2 / z = 1‘250 m/s 2 Maximum brake force Fmax = m · a max = 400‘000 kN
Fig. 5: Comparison of measured and calculated maximum deceleration
0.25
0.3
