Technical paper: Framework for optimised design of rockfall protection embankments reinforced with geosynthetics, part 1

By Pietro Rimoldi, independent civil engineering consultant and Nicola Brusa, independent civil engineer at Tailor Engineering

In this technical article, the authors propose a framework for the optimised design method of geosynthetic reinforced soil rockfall protection embankments (RS-RPE).

Due to the variability of geometry, soil fill material, embankment construction, various reinforcement options, interactions between soil and reinforcement, and the dynamic behaviour of the soil, a consistent design procedure has not been developed yet.

At the moment, design regulations or guidelines for reinforced embankments subject to dynamic impacts are still rather vague and based on assumed data, most coming from outside the geotechnical field. There is not much specific research available on the subject, and no analytical formulation has been proven to be solid enough to provide designers with a simple and feasible design method.

The authors believe that this paper can provide a comprehensive analysis of the phenomena involved in high energy impacts on RS-RPE. The aim of this paper is to develop a framework for the optimised design of RS-RPE, applicable to all the situations of practical interest in terms of design impacts, embankment configurations and reinforcement options.

In this article, the authors will not describe the various types of impacts, types of rockfall event, the analysis of trajectories, nor the statistical definition of the impact mass, velocity and energy, but purely focus on the design of the RS-RPE for the given critical impact.

In part 1, the paper introduces a critical review of the current design methods and guidelines available for RS-RPEs, as well as an analysis of the full scale test research programs available in literature to identify the mechanisms of boulder impacts on a RS-RPE and the contribution of the uphill facing system on the performance of the structure. The paper thus presents the proposed design procedure, further illustrated through design flowcharts.

In the next issue of GE, in part 2, the authors will present an original design method for RS-RPE subject to high energy rock impacts. Considering a totally inelastic impact, it is possible to calculate the impact energy, which produces the compressive deformation (the crater) on the uphill face, and the residual energy, which propagates to the valley side and produces the extrusion of the downhill face; the residual impact energy is assumed to propagate in a diffusion cone, which diverges laterally from the impact footprint by a spreading angle α, while at top and bottom, the cone is limited by the horizontal surfaces tangent to the impact footprint. The resistance to the uphill compressive deformation, provided by the facing system, is taken into account through an empirical factor, proportional to the energy absorption capacity of the facing system itself. The resistance to downhill extrusion is provided by the direct shear resistance of the soil and by the pullout resistance of the reinforcement layers included in the diffusion cone. From the impact energy and the total deformation (uphill + downhill) it is possible to calculate the horizontal force produced by the impact on the RS-RPE structure; this force is then used to check the global, external and internal stability conditions.

In mountains and hilly regions, infrastructure and people are often threatened by quick and destructive rockfall events. While falling boulders can have extremely high speeds, up to 30m/s, these events involve a complex pattern of movement (eg detachment, fall, rolling, sliding and bouncing) of one or more rock fragments (Peila et al, 2007).

Rockfall protection embankments (RPEs) have proven to be a safe measure for protecting people, structures and infrastructure from rockfall events (Figure 1), and they are being used all around the world.

RPEs can be built as unreinforced or reinforced soil embankments and designed to absorb medium to high impact energies (1,000kJ to 30,000kJ). Depending on their characteristics, these structures could withstand multiple impacts.

RS-RPEs can be constructed in various shapes and sizes to suit the site, using a wide range of internal reinforcing elements (geogrids, geostrip, geotextiles and steel meshes) and facing systems (wrap around, gabions, geocells, sand bags, tyres and so on), some of which provide a cushioning effect on the hillside face.

Through a combination of deformation and internal compaction of the soil, as well as tensile and pull-out resistance of the geosynthetic reinforcements, RS-RPEs absorb the impact energy of the falling rock blocks.

According to Peila et al. (2002), reinforced embankments are the most appropriate solution in those areas where the falling blocks are anticipated to have volumes or velocities great enough to pass the maximum resistance of traditional wire netting rock protection barriers or when dealing with important and critical infrastructure such as mountain highways or railways, as well as populated areas.

RS-RPEs can provide important advantages compared to RPEs:

Furthermore, whenever geosynthetics, and particularly geogrids or geostrips, are used as reinforcing elements, the following advantages are also introduced:

RS-RPEs have been used for more than 50 years. Many research works (see next section) have been conducted since the 1980s with the aim of improving their design, in particular with respect to the structure's ability to withstand the impact. Some of this research was adopted by engineering practices, either through national recommendations or design methods. In particular, some recommendations have been published for defining the structure geometry (structure height and face inclination) and several engineering methods have been developed over the last two decades to predict the ability of RS-RPE to withstand impacts.

Although embankment design methods for how to assess trajectory control and impact stability have improved, a number of limitations have been identified, as explained below.

RS-RPE design should consider the dynamic complex mechanisms occurring during the impact, which depends on the impact energy, the embankment materials and geometrical characteristics, reinforcement properties and layout (ie spacing and longitudinal/transversal distribution). As a consequence, the available analytical models are not yet satisfactory for this purpose. They fail to give good estimates of impact forces, block penetration and downhill extrusion, as well as energy dissipation forces.

Numerical models and finite element method (FEM) analyses were developed in those years, but these methods require validation, which most of the time is based on costly real-scale experiments involving high impact energies to simulate the real impact. Numerical models in this instance could be used for research purposes, jointly with full scale experiments, to improve the analytical models for different loading cases.

Numerical models can be useful to evaluate the effects of block impacts on RS-RPEs, even if often such models represent the reinforced soil embankment as a soil mass with increased rigidity, without considering the reinforcement type and performance, which are still not addressed. In addition, satisfactorily modelling the impact response of RPEs requires the definition of constitutive laws and mechanical characteristics, which is generally difficult when considering the impulsive and dynamic nature of the impact loads.

Therefore, RPE design has been based, so far, on simplistic approaches, considering dynamics only to a minor extent. In addition, there are no precise guidelines for the performance of RS-RPEs.

The most comprehensive guidelines available worldwide for RPEs are the Italian (UNI 11211-4:2018) and the Austrian (ONR 24810:2020) ones, both cross-referenced also by the New Zealand Geotechnical Society (NZGS)/Ministry of Business Innovation & Employment (MBIE) guidance (MBIE, 2016). In these guidelines, RPEs can be reinforced either with steel elements or geosynthetics and it is clear in these documents that reinforcement layers significantly improve the ability of an embankment to withstand impacts.

The Italian standard UNI 11211-4:2018 provides recommendations for the input data required for the design of RPEs. But it does not specify how to use the input data for verifying the structure response to a given impact; it is only indicated how the block penetration should be compared with the RPE cross-sectional width. In addition, these guidelines refer to the case of a given single block volume in a given release area. The design of the RPE needs to define the impact height, the block velocity and the kinetic energy of the design block, as obtained from statistical elaboration of trajectory simulations, as the 95% percentile of the statistical distribution of these parameters. The standard recommends that all the blocks from a given release scenario are stopped. The main limitation in this standard is that no indication is given for the RPE design with respect to the block impact.

The present available analytical methods developed over the years are based on block penetration or impact force to provide design engineers with easy-to-use tools. However, their applicability can be limited due to the uncertainty associated with their assumptions and calculations, which are not necessarily related to geotechnics or rock mechanics.

As mentioned by Lambert & Kister (2017):

Moreover, by comparing the experimental data and the results obtained with the available analytical methods and with the available numerical models, the following main results were obtained (Peila et al, 2007):

To summarise, the analytical and theoretical evaluation of the effect of the impact of blocks with high kinetic energy against a reinforced soil embankment is very difficult, due to the plastic behaviour of the ground and the large deformations that occur during the dynamic event.

Historically, the design of a RS-RPE was based on calculations derived from tests on the effect of the impact of a projectile against the embankment or from the studies of the impact of falling blocks on rock sheds covered with a soil cushion. Only a limited number of full scale tests have been carried out (see next section) to fully understand the behaviour of a RS-RPE under the real conditions of the impact of a rock block.

Since RS-RPEs have generally trapezoidal cross sections, 3m to 8m thick at the centre of impact, usually made of frictional non-cohesive soil, reinforced with several layers of geosynthetic with tensile strengths in the range of 50kN/m to 300kN/m, and subject to impacts of blocks with different shapes (more often cubic or spherical), travelling at 1m/s to 30m/s, which generate impact energy in the order of 1,000kJ to 30,000kJ, it is clear that the above mentioned models are hardly applicable to real RS-RPEs.

Results of full scale tests are important for understanding the behaviour of RS-RPEs under high energy impacts of rock blocks, as explained below.

Peila et al (2002) performed full scale tests with impacts produced by concrete smooth-edged cubic boulders, weighing 5t to 10t, having speed at the point of impact of approximately 31.7m/s, and kinetic energy of up to 4,354kJ. FEM models of the impact tests were developed to improve the understanding of the dynamic phenomena.

The impact on the RS-RPE, showed in Figure 2(a) on the left, reinforced with extruded geogrids and wrap-around facing, produced a crater on the hillside with a maximum depth of about 1m while on the valley side a large displacement of about 0.9m was observed. The maximum measured displacement on the valley side was concentrated or rather confined by the reinforcements on the two reinforcing layers involved in the impact. After the test, the reinforced embankment was dug, and a tension crack was observed (Figure 2(b)); this tension crack was 0.6m below the top and then spreading inside downward almost following the shape of the boulder. The tension crack was about 140mm wide. The tension crack practically separated the soil mass into two parts.

Figure 2 (a) (top) Cross-sections of the tested RS-RPE; Figure 2 (b) (bottom) the tension crack as observed after the first test (from Peila et al, 2002). The tension crack practically separated the soil mass into two parts.

After the other two impact tests, each one developing about 4,300kJ, it was shown that such a barrier can stop up to three high energy boulders before collapsing. The collapse was due to failure of reinforcing layers and loss of compaction in the soil medium.

Another impact test was carried out to evaluate the behaviour of a steep-sided, unreinforced embankment having the same shape and geometry of the reinforced one; the whole structure collapsed right after the impact, yet the block was arrested by the embankment, stopping its flight after penetrating inside the front face for about 1.5m. Deformation measurement on the valley side was impossible due to the collapse of the fill. It is important to note that the unreinforced embankment failed along two surfaces perpendicular to the face, hence with no lateral spreading of the impact load.

An additional test was performed to evaluate the influence of the steel mesh facing formwork (Figure 2(a) right) on embankment global behaviour. After the impact, a crater with a maximum depth of 0.9m was measured, while the valley side deformation showed displacements of about 1m, due to the fact that geogrids wrapping of layers three and four (from the top) were pulled out, thus allowing large deformations to take place.

A test with a slightly weaker soil fill was used for the reinforced embankment construction, in order to evaluate the role of soil plasticity and resilience in the impact and post-impact phase. The boulder produced a large crater with a maximum depth of about 2m, involving four soil layers. On the valley side a maximum displacement of 0.8m was measured.

These tests clearly showed that the depth of the crater on the hillside and the extrusion on the valley side depend, at equal geometry of the RS-RPE, on the reinforcement property and layout, the fill properties, and the type of facing on the hillside. The fact that geogrids did not break during tests validates the hypothesis of perfectly elastic behaviour of the reinforcement and of increased dynamic strength and modulus under impulsive loads.

Other full scale tests are available in literature, and these publications basically confirm the above analysis, while providing additional results related to different type of facing systems on the hillside of the RS-RPE.

Yoshida and Nomura (as reported by Yoshida, 1999) carried out nine tests, with impact energy ranging between 58kJ and 2,700kJ, on an RS-RPE with a facing system including two types of sand filled bags (Figure 3). These tests showed that a cushioning system on the hillside can reduce the depth of the crater and can simplify the post-impact maintenance of the hillside structure; even if the extrusion on the valley side face was just slightly reduced by such a double bag system.

Figure 3. Tests carried out by Yoshida and Nomura on a RS-RPE with a facing system including two types of sand filled bags: (a) sketch of boulder impact on the RS-RPE; (b) cross-section of the RS-RPE showing the facing system (after Yoshida, 1999).

Lambert et al (2009) carried out tests on a structure consisting of a sandwich wall leaned against a reinforced soil embankment (Figure 4). The gabion cages were made up of a hexagonal wire mesh with an 80mm by 120mm mesh. Gabion cages are parallelepiped in shape, subdivided into three or two 1m3 parts. The fill materials were coarse or fine granular non-cohesive materials. The latter consisted of sand alone or as a mixture containing 30% by mass of scrapped tyres. Lambert et al (2009) report that, during the impact, the kinetic energy of the boulder is transferred to the embankment via the compression wave. It has been shown that the compression wave progressively travels from the impact point to the entire structure, within a cone. When approaching the facing opposite the impacted face, the energy wave resulted in increased soil displacement. These results suggest that the mechanical characteristics of the materials near the front facing govern the boulder–structure interaction and consequently the impact force, with consequences for the stress transmitted within the structure, while the characteristics of the whole structure govern its response and ability to survive the impact load. Lambert et al (2009) added that relevant design methods should be able to account for the boulder–structure–facing interaction, and for the so-called buttress effect of the rest of the structure.

Figure 4. Tests carried out by Lambert et al. (2009) on a RS-RPE with a facing system including gabions filled with coarse and fine fills.

Maegawa et al (2011) conducted rockfall tests on full scale embankments reinforced with geogrids and protected by a 800mm thick cushioning layer made of geocells, with a cell height of 150mm, filled with crushed stones of 5mm to 13mm diameter (Figure 5). Under an impact energy of 2.71MJ the crater had a maximum depth of 1,900mm, while the maximum protrusion was 441mm. Hence, according to Maegawa et al (2011), the cushion layer is indeed damaged in exchange for playing the role of an absorber for the embankment, but it can be rebuilt easily. On the contrary, it is not so easy to repair the embankment damaged by the direct impact of a boulder. Therefore, a cushion layer is effective not only in protecting embankments but also in reducing life cycle costs.

Figure 5. The RS-RPE tested by Maegawa et al. (2011), with facing system made up of geocells: (a) (top) cross-section showing the geocell facing system; (b) (bottom) dimensions of the tested RS-RPEs

Green (2019) carried out tests where impact energies were delivered to the RPE via a rolling bogey fitted with a spherical impacting head. The impacting head consisted of a 1m diameter concrete-filled, steel-reinforced spherical steel dome. The tested RPE (Figure 6) utilised a modified configuration of seawall blocks together with an upslope energy-dissipating layer consisting of sand-filled and rock-filled gabion baskets. The concrete blocks were 2m by 1m by 1m, with a weight of about 5,000kg. The gabion baskets were 2m by 0.5m by 0.5m. Even if the tested structure is an unreinforced RPE, it is interesting because both faces are vertical, hence there is no variation of the cross-section with the height. Test results showed that, when the impact occurs closer to the base or to the top, the higher or lower vertical stresses on the sliding plane (which is the same at any elevation) increase or decrease the resistant shear stresses.

Hence it can be inferred that horizontal displacements are resisted by direct shear on the top and bottom surfaces of the sliding cone if there is no reinforcement. If there is reinforcement, horizontal displacements are resisted by pullout of the reinforcement layers within the cone. Both for direct shear and pullout, the resistance decreases if the impact is closer to the top because lower vertical stresses are produced. Hence the resistance to downside extrusion occurs by direct shear in case of no reinforcement, and by both direct shear and pullout in case of reinforced embankment.

Figure 6. (a) (top) Cross-Section of Modular Rockfall Protection Wall; (b) (bottom) Test Wall A following Test 3 (sliding, 750 kJ) (from Green, 2019)

As reported by Lambert & Kister (2017), the response of the RPE to impact, until collapse, may be described as a four phase process, as proposed by Lambert and Bourrier (2013) (Figure 7).

Figure 7. A 4-phases schematic description of the RPE response to impact, until collapse (after Lambert & Bourrier, 2013). From left to right: (a) Rock impact footprint; (b) The energy wave produces compression in the soil mass adjacent to the rock impact footprint; (c) after a certain distance the residual energy produces the acceleration of the soil mass beyond the crater and an outward horizontal movement; (d) at the limit between the compressed and the "tensioned" zone, cracks are formed and the soil mass is separated into two parts.

It is clear that the behaviour of the different mechanisms mentioned above depends on the impact energy in proportion to the embankment's capacity to absorb energy. For low impact energies, the penetration required to stop the block and the stress generated within the embankment are small. The residual downhill face deformation is small compared to the block penetration. The impact energy is dissipated by compaction and soil crushing in the vicinity of the impact area while only a small part propagates by elastic waves.

Of course, in case of higher impact energy, the block penetration and stress within the embankment increase. The downhill face displacement increases and, for slender structures, the displacement may progressively tend towards the value of the uphill face displacement. And, the thicker the embankment, the lower the downhill face displacement.

It is also clear that dissipative mechanisms occur by soil compaction close to the impact point, and by frictional dissipation along shear planes beyond the impact crater.

Overall energy dissipation through soil compaction remains predominant during the impact process, with an estimated proportion of about 75% to 80% of the block's kinetic energy. The influence of parameters associated with the compressive response, friction angle and unit mass on the whole structure's behaviour depends on the impact energy, the structure's dimensions and the structure's boundary conditions. This influence increases with the block kinetic energy.

The behaviour of an embankment subject to a rockfall event strongly depends on the impact height, the closer the impact to the crest, the higher the penetration, with detrimental effects on the structure stability.

Reinforcement layers significantly improve the ability of an embankment to withstand the impact. Such reinforcement layers, made of geogrids, geostrips or geotextiles, spread the impact load along the embankment axis. The impact load is thus distributed to soil masses at a distance on both sides of the impacted area. In the impact vicinity, the resulting confining effect by the reinforcing layers increases the penetration resistance of the embankment. Moreover, if reinforcement also concerns the downhill face of the RPE, the layer restrains the displacement of this face and thus increases the ability to withstand the impact.

Finally, it is important to note that all tests show that the reinforcement produces an increase of the load spreading angle.

The proposed framework for design of RS-RPEs, presented in the next sections, is consistent with all the evidence of mechanisms and behaviour from the full scale tests, as explained above.

The authors suggest that the design of an RS-RPE should be carried out following these steps (see Figures 8 and 9):

1.Perform risk analysis to define the design block size, shape and mass (guidelines can be found in ONR 24810 and UNI 11211)

2. Define the position of the RS-RPE, considering its longitudinal extension and height in relation to the potential trajectories of the design blocks and the objects or infrastructures to be protected (guidelines can be found in ONR 24810 and UNI 11211)

3. Perform statistical calculation of block trajectories to define the block speed, bounce height and kinetic energy at the impact point with the RS-RPE (specific software packages are available, eg Rocscience Rocfall 3, Geo Stru Geo Rock 3D, etctera)

4. In case trajectories do not match with the embankment position and/or height, go back to point 2 and correct the position and/or height of the RS-RPE

5. Based on the design impact data calculated at point 3, make a preliminary design of the RS-RPE, including the geometry, type and layout of reinforcement, type of fill and facing system

6. Perform global, external and internal stability analyses considering the RS-RPE and the slope on which it is built, in static conditions and, if required, in seismic conditions (before any impact). Check that ultimate limit states (ULS) are not reached (collapse of the structure shall not occur); all the factors of safety shall be larger than the minimum values required by geotechnical norms for ULS analyses in static or seismic conditions.

7. Perform dynamic analyses of the design impact, with the evaluation of the penetration depth on the hillside and the extrusion length on the valley side, following the framework presented in the next section. Check that serviceability limit states (SLS) are not reached (deformations should not affect other structures and should permit an easy rehabilitation and repair of the RS-RPE); note that only the horizontal component of the impact velocity is relevant for the design of reinforcement. The following SLS conditions should be checked:

8. Perform global, external and internal stability analyses considering the RS-RPE and the slope on which it is built, under the dynamic forces generated by the impact, which can be defined following the framework presented in the next section. Check that ULS (collapse of the structure) are not reached; all the factors of safety shall be larger than the minimum values required by geotechnical norms for ULS analyses under transient/impulsive loading conditions.

9. If one or more analyses (ULS and/or SLS) are not verified, repeat the procedure from point 5 and modify the design of the RS-RPE by trials and errors.

Note that:

When making the preliminary as well as the final design of the RS-RPE, the following should be considered:

Figure 8: Flow chart of passive RPS (Rockfall Protection System) design process (modified from MBIE, 2016). For the design of the RS-RPE follow the flow chart in Figure 9.

Green, R (2019). Development and Testing of a Modular Rockfall Protection Wall to Mitigate Earthquake-Induced Slope Hazards. NZ Geomechanics News, Issue 98 – December 2019.

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Lambert, S and Bourrier, F (2013). Design of rockfall protection embankments: A review, Engineering Geology, 154, pp 77 to 88, 2013.

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Mayne, PW and Jones, SJ (1983). Impact stresses during dynamic compaction. Journal of Geotechnical Engineering 109, pp1342 to 1346.

MBIE (2016). Rockfall: Design considerations for passive protection structures. Ministry of Business, Innovation & Employment, Building System Performance branch. Wellington, New Zealand.

Kar, AK (1978). Projectile penetration into buried structures. Journal of Structural Division, ASCE 104 (1), pp125 to 139.

ONR. (2020). ONR 24810: Technischer Steinschlagschutz: Begriffe, Einwirkungen, Bemessung und konstruktive Durchbildung, Überwachung und Instandhaltung (Technical rockfall protection: terms, effects, dimensioning and structural development, monitoring and maintenance). Austrian Standards Institute. Vienna, Austria (in German).

UNI 11211-4 (2018). Opere di difesa dalla caduta massi – Parte 4: Progetto definitivo ed esecutivo (Rockfall protection works – Part 4: Definitive and executive design). UNI – Ente Italiano di Normazione, Milano, Italy (in Italian).

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