The determination of rockfall impact force is crucial in designing protection measures. In the present study, laboratory tests are carried out by testing the weight and shape of the falling rock fragments, drop height, incident angle, platform on the slideway, and cushion layer on the protection measures to investigate their influences on the impact force. The test results indicate that the impact force is positively exponential to the weight of rockfall and the instantaneous impact velocity of the rockfall approaching the protection measures. The impact velocity is found to be dominated not only by the drop height but also by the shape of rockfall and the length of the platform on the slideway. A great drop height and/or a short platform produces a fast impact velocity. Spherical rockfalls experience a greater impact velocity than cubes and elongated cuboids. A layer of cushion on the protection measures may reduce the impact force to a greater extent. The reduction effects are dominated by the cushion material and the thickness of the cushion layer. The thicker the cushion layer, the greater the reduction effect and the less the impact force. The stiffer the buffer material, the lower the buffering effect and the greater the impact force. The present study indicates that the current standard in China for designing protection measures may overestimate the impact force by not taking into consideration the rockfall shape, platform, and cushion layer.

The protection measures for rockfalls are mostly designed to avoid direct
exposure of the protected buildings or structures to falling rock fragments.
Protective flexible wire net and embankment are typical in such design
(Giani et al., 2004; Labiouse, 1996; Peila et al., 1998). There is normally a strong
collision behaviour when the rockfall impacts the protection measures. The
maximum impact force (

The present study carries out laboratory tests by using the weight and shape of rockfalls, drop height, incident angle, cushion on the protected measures, and platform on the slideway as factors. The aim is to investigate and depict their influences on impact force of rockfalls.

The rockfall devices:

The protection device:

The test system developed in this study consists of three parts: rockfall device, protection device, and measuring unit. As shown in Fig. 1a, the rockfall device takes a bracket structure to withstand the slideway, which is a smooth steel U-shaped channel 7 m long and 30 cm wide inside. Both ends of the slideway are placed on scaffolding brackets. An alternative device (Fig. 1b) is composed of an upper slideway, lower slideway, and a platform in-between. The length of the platform is adjustable. During tests the inner sides of the slideway and the platform were fully lubricated with a mineral oil to minimize the friction.

Physical and mechanical parameters of the cushion materials.

The protection device, being about 1.4 m high, consists of a baffle plate, a bottom plate, and four lifting outriggers (Fig. 2a). The baffle plate is made of steel and is 1.2 m long, 0.8 m wide, and 15 mm thick. The bottom plate is a 1.3 m long, 0.9 m wide, and 10 mm thick steel plate. The inclining angle of the baffle plate can be adjusted by lifting/lowering the outriggers to mold different incident angles. The measuring device includes four force transducers seated on the bottom plate and passing through the holes in corners of the baffle (Fig. 2a and b). During the test, the falling fragments were directed by the slideway to impact one of the transducers. As the tips of the force transducers were clear of the baffle by 5 mm (Fig. 2b), the transducer could grasp the full impact force without participation by the baffle. The impact forces collected by the transducer were then transmitted and stored in a data log system. In the cases where buffering effects of cushion layer were considered, the cushion materials were evenly placed on the baffle plate at a certain thickness. The test set-up simulated the impaction of rockfall on a protection measure, as shown in Fig. 3.

Schematic diagram of rockfall impacts.

Three types (sphere, cube, and rectangular cuboid in shape) of samples were adopted in the experiments (Fig. 4). Each type of samples had three specimens with the weight of 4, 5, and 6 kg.

Points A, B, and C marked on the slideway were the starting points to slide
(Fig. 1), representing different drop heights, i.e. 4.0, 3.5, and 3.0 m
respectively. The impact incident angles were set to be 30, 60, and 90

In total, 109 tests were conducted for encompassing the possible permutation
and combination of factors listed in Table 2. A test with the identifier of
S-6-4-90 denotes a spherical sample with the weight of 6 kg falling from 4 m
and impacting the baffle plate at an incident angle of 90

Shapes and sizes of the falling specimens.

Test conditions.

In the experiment, each test was repeated three times and therefore had three test results. The standard deviation of the three results ranges from 0.86 to 2.43, which is less than 5 % of the average. This indicates a good repeatability of the tests. The average value of the three results for each test was then taken for the following discussion.

Measured impact force vs. incident angle for samples of different
weights: sample weight

Impact force vs. drop height for samples of different shapes:

Impact force vs. drop height for samples with different weights:
sample weight

The maximum impact force (47.7 kN) occurred in the case where a 6 kg weight
spherical sample falling from 4.0 m height impacts the baffle plate at the
incident angle (

As shown in Fig. 6, the impact force increases with sample weight. The average impact force for 6 kg weight samples is about 10 % greater than that for 5 kg weight samples, which in turn is about 16 % greater than that for samples of 4 kg weight. However, sample shape is found to impose strong effects on the measured impact forces. The spherical block had a higher rotation rate in its motion and less energy dissipated during its impact (Labiouse and Heidenreich, 2009). As shown in Fig. 7, spherical samples generate greater impact forces than cubes and elongated cuboids.

Influence of cushion layer on the impact force:

Influence of platform length on the impact force by different shapes
of rockfalls:

The embankment is often used as a protective measure against rockfalls,
and it is commonly composed of a core wall and cushion layer made of buffer
material. In this study, gravel, sand, and clay are chosen as cushion
materials and were evenly placed on the baffle with a thickness (

In the case of right collision (

For simulating the reduction effects by a platform on natural slope, a set
of tests were conducted with platform lengths of 30, 60, and 90 cm (see Fig. 1b for test set-up). Samples of different shapes and
weights fell from a certain drop height

As shown in Fig. 9, a platform of 30 cm long may reduce the impact force by about 10 %. The 60 and 90 cm platforms can even reduce the impact force by 18 and 30 % respectively. The longer the platform, the less the impact force measured. Another observation is that the reduction effect of platform is more obvious for rockfalls of cube and elongated cuboid than cubic ones, as the gradient of the trend line for cubic samples is the least in Fig. 9.

Based on the test results, several findings can be drawn: (1) the incident angle and drop height positively affect the impact force; (2) spherical rockfalls introduce higher impact force than cubes and elongated cuboids; (3) the impact force increases with weight of rockfall; (4) the cushion layer made of gravel, sand, or clay may significantly reduce the impact force, and the thicker the cushion layer, the greater the extent of reduction; and (5) a flat platform on the slideway can lead to a reduction of impact force, and the longer the platform, the more the impact force is reduced.

According to the theorem of momentum, the rockfall impact force can come out
from the following equation (Johnson, 1985; Han et al., 2004):

The instantaneous velocity (

The above equations indicate a positive exponential correlation between drop
height and impact velocity of rockfalls, which is consistent with the
theoretical formula deriving falling velocity (

Positive exponential correlation between impact velocity (

Normalized velocity (

Figure 11 shows the normalized velocity (

Influence of platform length on the impact velocity of rockfalls of
different shapes and weights:

Change of rockfall velocity along a slideway with a platform (length of the vector indicates the absolute velocity values).

Nonetheless, the instantaneous impact velocity is significantly
reduced by a buffer platform on the slideway. The impact velocity of 6 kg
spherical rockfalls falling form 4.0 m height was 5.19, 4.68, and 4.11 m s

Figure 13 demonstrates the change process of rockfall velocity during the
falling process. At point O (the start point), the velocity (

Regression analysis taking the measured impact velocity (

The above exponential equation indicates that the impact force is positive to weight and impact velocity of rockfall. Thus, the impact velocity is dependent not only upon the drop height but also upon the shape of rockfall and the platform length. However, in the present engineering practice, both rockfall shape and the platform are not taken into account during designing of protection measures; instead an equivalent spherical object is normally used. This is thought to overestimate the impact force.

According to the law of energy conservation, the kinetic energy (

According to the Green formula,

Considering

The total strain energy (Eq. 5) of the cushion layer therefore can be
expressed as Eq. (10):

Combining Eqs. (5) and (10) gives

According to Eq. (11), for a certain impaction a thick cushion layer made of material with low elastic modulus would introduce a relatively low stress in the cushion layer. The above derivation explains the greater buffering effect by a layer of clay than that by gravel and explains the contribution of cushion layer thickness (Fig. 8). However, the contact area changes with the shape of rockfall. A spherical rockfall minimizes the contact area, which maximizes the stress and therefore the measured impact force.

According to the foregoing discussion, main conclusions can be drawn as follows.

The impact force is positively exponential to the weight of rockfall and instantaneous impact velocity of the rockfall approaching the protective measures. The impact velocity is in turn dominated not only by the drop height but also by the shape of rockfall as well as platform on the slideway. A platform reduces the impact velocity by eliminating the vertical component of falling velocity and minimizing the horizontal component. A spherical rockfall may introduce an impact velocity close to that from theoretical calculation.

A layer of cushion material on the protection measures may reduce the impact force to a greater extent. The reduction effects are dominated by the cushion material and the thickness of the cushion layer. The thicker the cushion layer, the greater the reduction effect and therefore the less the impact force. The stiffer the cushion material, the less the reduction effect and the greater the impact force.

The determination of impact force is crucial in designing protection measures for rockfalls. The present study depicts the influences of drop height and weight of rockfall, platform on the slideway, and buffer layer on the protection measures, which indicate that the impact force may be misestimated by taking no consideration for rockfall shape, platform, and buffer layer. Due to the limitation of the experiments, the bouncing and rolling behaviour of rockfalls was not considered in this study. Further investigation is desired to verify and improve the relationships derived from this study in order to cover a broader natural situation.

This study was supported by the National Natural Science Foundation of China (nos. 51309176 and 40972195), Science and Technology Innovation Team of Sichuan Province (no. 2011JTD012), Ministry of Land and Resources of China (no. 201211055), and independent research of the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (no. HGY-2012-08). Edited by: T. Glade Reviewed by: J. Huo and one anonymous referee