Numerical simulation of the effects of falling rock’s shape and impact pose on impact force and response of RC slabs

Perera S., Lam N., Pathirana M., Zhang L., Ruan D., Gad E.

Impact by windborne debris can cause severe and wide spread damage to building facades and other exposed installations. There is no clear guidance on how to estimate the amount of force generated by the impact of windborne debris when design codes of practices only provide estimates of the wind pressure. The model presented in this paper enables the value of the peak contact force generated by the impact of a piece of debris to be predicted. Results of calculations employing the derived relationships have been verified by comparison with experimental results across a wide range of impact scenarios. Once the impact action has been quantified the predicted impact force can be applied to the target in a quasi-static manner for predicting damage.

Fang Q., Zhang J.

This paper presented a three-dimensional (3D) finite element analysis approach to study the projectile penetration into rock-rubble overlays considering the randomness of rock-rubble in shape and distribution. The generation algorithm of 3D rock-rubble with random size and shape was firstly proposed. The dropping and compacting algorithms for the random distribution of all particles of rock-rubble in an overlay were then developed. Thirdly, a finite element grid was formed using the mapping algorithm. An analysis approach for the 3D finite element model of the random distribution of all particles of rock-rubble in an overlay was established by employing the hydrocode LS-DYNA taking into account the different materials properties and contact effect. In order to validate the analysis approach, the numerical results were compared with the limited test data, and a good agreement was obtained. Finally, numerical studies of the projectile penetration into the grouted concrete rock-rubble overlays were presented under different impact conditions, focusing on the penetration depth, yawing angle, trajectory and projectile deformation. It is indicated that impact obliquity affects the penetration depth, terminal yawing angle and penetrator deformation greatly. In order to reveal the stopping and deflecting mechanism of rock-rubble overlays, parametric studies were carried out to analyze the effects of different impact conditions and target configurations on projectile penetration. The numerical results show that the size, strength and volume percentage of rock-rubble and grouted concrete strength are critical to penetration depth and terminal yawing angle.

Fityus S.G., Giacomini A., Buzzi O.

From a consideration of the concepts of geological weathering and structure, it can be expected that rockfall hazards should be characteristically different in different geological environments. This paper tests this idea by looking at the geometric characteristics of rock fragments formed on natural slopes in four different geological environments in Eastern Australia, where rockfall phenomena are often characterised by rolling of pre-detached debris. By measuring the three principle dimensions and making a systematic assessment of the shape characteristics of samples of rock debris in significant geological environments, it is found that the distributions of size and shape for the surface debris are statistically different. From the results, it is shown that the size and shape of debris is directly controlled by the rock type, its weathering characteristics and the structure of the parent rock mass. The severity of rockfall hazards is shown to be relatively lower in areas of Tertiary basalt, as the size of rolling fragments is limited by closely spaced fracturing inherited from its formation and the tendency to deteriorate further as it weathers deeply and rapidly. It is also lower in areas of Palaeozoic volcanics, since these tend to produce relatively angular fragments with higher proportions of fragments that are inherently more resistant to rolling. By contrast, thickly bedded sandstones form larger blocks with a larger proportion of shapes that are more prone to rolling. The size distribution of fragments is shown to be well approximated by a log-normal statistical distribution, and using the data provided in this study, it is possible to generate the size and shape data needed to undertake a stochastic assessment of rockfall trajectories in different geological environments. • In eastern Australia, rockfall hazards commonly involve pre-detached debris. • The size and shape of debris are characteristic to geological environment. • Size distribution can be approximated by a log-normal distribution. • Basalts and felsic volcanic form smaller blocks with more stable shapes. • Sandstones form larger blocks with shapes more prone to rolling.

Mignelli C., Peila D., Lo Russo S., Ratto S.M., Broccolato M.

Many kilometres of roads are close to rock slopes that are prone to rockfalls. The fulfilment of safety requirements in such situations is a multidimensional design process involving public and private technicians in the assessment and management of the problem. In this paper, a rockfall risk management approach has been applied to the road infrastructure network of the Regione Autonoma Valle D’Aosta, in order to calculate the level of risk and of its reduction using rockfall protection devices. In order to better understand the methodology, a comparative analysis of road accidents in Aosta Valley has been discussed. The road risk assessment was developed taking into account the absence of rockfall protection devices, and when they are present, different levels of efficacy have been considered.

Bhatti A.Q., Kishi N., Konno H., Mikami H.

This paper focuses on an applicability of the proposed numerical analysis method to the large scale RC girder under falling-weight impact loading using effective finite element mesh size distribution by comparing with experimental results. The results obtained from this study are: (1) displacement wave can be accurately estimated with seven-division of stirrup interval. (2) The maximum impact force and reaction force can be roughly estimated by using the mesh geometry with one-division for the each interval. (3) Damping constant should be used as 1.5%. (4) Drucker-Prager yield criterion should be applied. (5) The crack patterns can be roughly estimated with seven divisions between intervals of stirrup.

Volkwein A., Schellenberg K., Labiouse V., Agliardi F., Berger F., Bourrier F., Dorren L.K., Gerber W., Jaboyedoff M.

Abstract. Rockfall is an extremely rapid process involving long travel distances. Due to these features, when an event occurs, the ability to take evasive action is practically zero and, thus, the risk of injury or loss of life is high. Damage to buildings and infrastructure is quite likely. In many cases, therefore, suitable protection measures are necessary. This contribution provides an overview of previous and current research on the main topics related to rockfall. It covers the onset of rockfall and runout modelling approaches, as well as hazard zoning and protection measures. It is the aim of this article to provide an in-depth knowledge base for researchers and practitioners involved in projects dealing with the rockfall protection of infrastructures, who may work in the fields of civil or environmental engineering, risk and safety, the earth and natural sciences.

Bhatti A.Q., Kishi N.

In order to establish a proper finite element model of prototype RC girder with sand element for impact response analysis, dynamic response analysis of RC girders with sand cushion subjected to impact force due to weight falling from the height of H = 2.5, 5, 7.5 and 10 m was performed to improve the state of the art of protective design for real scale rock-sheds by using LS-DYNA code. An applicability of proposed model was discussed comparing with experimental results (e.g. impact force, reaction force and displacement waves). From this study, dynamic characteristics of impact response can be better simulated by using the proposed model. As a result, when the sand cushion was set up, the impact force, reaction force, mid-span displacement waves, distribution of reaction force–displacement loops, and crack patterns obtained from the numerical analysis are in good agreement with those from the experimental results.

Chen Y., May I.M.

This paper describes a series of experimental studies to investigate the high-mass, low-velocity impact behaviour of reinforced concrete members including beams and slabs, and to provide high-quality input data and results to validate numerical modelling. Fourteen 2·7 m and four 1·5 m span beams, four 0·8 m square 76 mm thick and two 2·3 m square 150 mm thick slabs were tested under impact loads using a drop-weight facility. Measurements included transient impact loads, accelerations and strains in the steel reinforcement. Additionally the impact events were recorded using a high-speed video camera operated at up to 4500 frames per second. For the beam tests, the local failure pattern of a beam under the impact zone was examined by correlating the images of development of cracks, spalling and scabbing with the impact load history. For the slab tests, the imposed energy on a slab was compared with the minimum energy causing the slab to scab, which was predicted using empirical formulae. The investigations enabled a better understanding of the behaviour of reinforced concrete members subject to impact loads.

Delhomme F., Mommessin M., Mougin J.P., Perrotin P.

Rock falls can cause a lot of damage to infrastructure built along steep slopes. Recently, a 1/3 scale model of a new type of protection gallery, referred to as Structurally Dissipating Rock Shed, has been tested. The aim of this paper is to reanalyze the structural response of this protective system by a three-dimensional Finite Element model and a mass-spring system. In the numerical code (Ansys), an implicit analysis is performed and a smeared element (Solid65) is used to model the reinforced concrete slab. The model parameters are identified such that numerical results reproduce the measured structural behaviour as well as possible. The results of these two models are compared to several experimental tests and their accuracy in predicting the dynamic behaviour of the structure is assessed.

Pichler B., Hellmich C., Mang H.A.

Layers of gravel represent an energy-absorbing system for structures subjected to rockfall. To support the design of such structures, relations between the penetration depth, the impact duration, and the impact force, respectively, and the rock boulder mass, the height of fall, and the indentation resistance of the gravel are presented. Knowledge about projectiles impacting onto concrete and soil is incorporated in these relations. They can be simplified by dimensional analysis. This is the basis for the design of rockfall experiments comprising heights of fall up to 20 m , and a rock boulder mass up to 20 000 kg . From these experiments, the indentation resistance of gravel is obtained by back-analysis and evaluated statistically. This permits estimation of penetration depths caused by rockfall events which are beyond the experimental means of the current study. Finally, a model for the impact kinematics is deduced from experimental acceleration measurements. It yields design diagrams for impact duration and impact forces, supporting probability-based engineering design of rockfall protection systems with gravel as an energy-absorbing component.

Mougin J., Perrotin P., Mommessin M., Tonnelo J., Agbossou A.

This paper concerns the protective structures against rock fall. We propose a new concept of rock-shed protection. The proposed rock-shed protection is made of reinforced concrete slabs held up by specially designed supports that act as a type of expendable fuse to absorb high rock-fall energy especially when shock occurs on the side of the slab. Thus, by a simple change of damaged supports and local restoration of concrete in the impact area, the structure can continue to be used. We present also an experimental method to characterize and analyze shock absorption effected by this type of reinforced concrete slab. The analyzed slab is a 1/3 scale reproduction of an actual structure.

Malvar L.J., Crawford J.E., Wesevich J.W., Simons D.

Lagrangian finite element codes with explicit time integration are extensively used for the analysis of structures subjected to explosive loading. Within these codes, numerous material models have been implemented. However, the development of a realistic but efficient concrete material model has proven complex and challenging. The plasticity concrete material model in the Lagrangian finite element code DYNA3D was assessed and enhanced. The main modifications include the implementation of a third, independent yield failure surface; removal of the tensile cutoff and extension of the plasticity model in tension; shift of the pressure cutoff; implementation of a three invariant formulation for the failure surfaces; determination of the triaxial extension to triaxial compression ratio as a function of pressure; shear modulus correction; and implementation of a radial path strain rate enhancement. These modifications insure that the response follows experimental observations for standard uniaxial, biaxial and triaxial tests in both tension and compression, as shown via single element analyses. The radial path strain rate enhancement insures constant enhancement for all those tests. As a full scale example, a standard dividing wall subjected to a blast load is analyzed and the effects of the modifications assessed.

Labiouse V., Descoeudres F., Montani S.

Note: Roches Reference LMR-ARTICLE-1996-001 Record created on 2006-11-09, modified on 2016-08-08

Li R.W., Meng S.B., Chen Y., Wu H., Zhou Y.D.

Peilin Z., jinghe W., Songhong Y., Junshun W.

Meree H., Wang D., Yan S., Li M., Lu S., Lovati M., Liu F.

This study investigates the effectiveness of Lightweight Expanded Clay Aggregate (LECA) as a novel cushion material mitigating repeated rockfall impacts on reinforced concrete (RC) slabs in rock sheds. Small-scale impact tests and finite element simulations analyze LECA particle size, cushioning material, block shape, and impact energy level influence on the dynamic response and damage. Results show LECA outperforms sand in attenuating impact forces and transmitted loads under successive impacts, which indicates a better protection effect on the substructure. Smaller LECA particles lead to wider stress distribution angles, longer impact durations, and lower peak forces. Block shape significantly influences impact force, with higher unified nose factors increasing forces. LECA cushions exhibit a dynamic amplification factor less than 1, indicating reduced transmitted loads compared to sand. Under high-impact energy conditions, the LECA cushion limits RC slab deflection within the elastic limit across all block shapes, while sand exceeds the elastic limit, potentially leading to structural failure. LECA mitigates flexural cracking and redistributes loads more uniformly, reducing overall RC slab damage compared to sand. However, localized failure modes require further optimization. This study highlights LECA's potential for enhancing rock shed structural safety and resilience against severe rockfall events, providing insights for optimal mitigation strategies.

Ullah A., Khan A., Tariq M., Waqas H.A., Khan A.

Xue J., Cao C., Yan J., Ji Y., Chen J.

Rock shed is an effective protection measure against rockfall. To investigate the influences of falling rock's shape and impact angle on the impact effect of the cushioned rock shed, a modeling approach for a rock shed with a cushion layer using PFC-FLAC. The granular cushion is modeled as an aggregate of discrete non-cohesion particles, while the concrete plate and the beam are modeled as zones. The falling rock with different sphericities and impact angles is modeled as a rigid assembly. The numerical model is validated by comparing the simulation results with experimental and numerical results from previous literature. This model is applied to analyze the effects of rock shape and impact angle on the dynamic interaction effects between falling rock and cushioned rock shed, including the impact force, transmitted bottom force, penetration depth, and plate deflection. The numerical results show that the variation in the falling rock's shape has different effects on the falling rock with different impact angles. These findings could support rock shed design by revealing the limitations of the assumptions in the past research, which may result in unsafe rock sheds for some rockfall cases.

Wang C., Cui Y., Nie J., Hu B., Fang J., Cao Z.

Particle shape plays a crucial role in determining the mobility and impact characteristics of granular flows, yet analyses of the effects of particle shape are rare. In this study, three-dimensional (3D) printing technology is used to create rock-like materials with varying shapes. This approach enables the precise control of mechanical properties other than particle shape, eliminating potential confounding factors. Then, we construct particle flow samples with distinct shape characteristics, quantitatively assessing their shape variations according to their overall regularity (OR). Flume experiments are conducted, with the findings used to calibrate a discrete element numerical model. By integrating the numerical simulations and experimental data, we systematically investigate the flow, impact, and deposition behaviours of granular flows under diverse flume inclinations considering the influence of particle shape. The results demonstrate that the mobility and destructiveness of granular flows increases with higher OR values and steeper flume inclinations. The transition from pile-up to runup deposition is primarily controlled by the flume inclination, while within specific inclination ranges, changes in OR can also induce deposition mechanism transition. This study provides substantial insights into interactions between granular flows and protection structures, emphasizing the significance of particle shape and terrain characteristics within a source area.

Mei X., Wu J., Wang T., Wang T., Liang X., Wang Y., Li B., Su T., Xu L.

Abstract In the rockfall prevention and control project, the reinforced concrete (RC) slab and sand (gravel soil) soil cushion layer are commonly used to form the protection structure, thereby resisting the rockfall impact. Considering that the oversized deformation of the cushion layer under impact load using the finite element simulation cannot converge, this article establishes a numerical calculation model using smoothed particle hydrodynamics–finite-element method coupling (SPH–FEM). First, the standard Lagrange finite-element mesh is established for the whole model using ABAQUS, and then the finite-element mesh of the soil cushion layer is converted to SPH particle at the initial moment of the calculation, and finally the calculation results are solved and outputted. The results indicate that, compared with the results of the outdoor rockfall impact test, the relative errors of the rockfall impact force and the displacement of the RC slab are within 10%, which proves the rationality of the coupling algorithm; moreover, in terms of the numerical simulation, the SPH–FEM coupling algorithm is more practical than the finite element for reproducing the mobility of the rockfall impacting the sand and soil particles. In addition, at an impact speed of less than 12 m·s−1, the cushion layer is able to absorb more than 85% of the impact energy, which effectively ensures that the RC slab is in an elastic working state under small impact energy and does not undergo destructive damage under large impact energy; the peak impact force of the rockfall is approximately linear with the velocity, and the simulated value of the peak impact force is basically the same as that of the theoretical value of Hertz theory; the numerical simulation is good for reproducing the damage process of the RC slab in accordance with the actual situation. The SPH–FEM coupling algorithm is more justified than the FEM in simulating the large deformation problem, and it can provide a new calculation method for the design and calculation of the rockfall protection structure.

Bian M., Peng J., Qin S., Zhang X., Li J.

Transmission tower structures support high-voltage power lines that carry electricity over long distance and rockfall is one of critical disasters during its safe operation. This paper presented a simplified analytical methodology for lateral dynamic responses of a transmission tower structure due to rockfall impact. At first, the lateral dynamic displacement of a lattice transmission tower structure can be represented by a second-order partial differential equation and half sine wave was used for rockfall impact. Then, the solution can be approximated by a set of specified shape functions multiplied by time-dependent generalized coordinates. And the partial differential equation is discretized into a set of single degree of freedom system. And then the shape function can be determined by solved an eigenvalue function and the fundamental frequency of a transmission tower can was derived based on the energy method and combination synthesis method. Finally, the lateral dynamic displacements can be approximately obtained. A numerical study of a transmission tower was conducted. Parametric study of the effect of impact location height, impact duration, peak impact force, as well as the distribution of cross-arms on dynamic responses were also carried out. And the results show that the discrepancy between the analytical and the computed of fundamental frequency is less than 3%, the error of dynamic displacement is within 10%, and the fundamental frequency of the structure decreases with the increase of the tower top additional mass ratio.

Dattola G., di Prisco C., Crosta G.B.

AbstractIn this paper, an advanced rheological model for impacts of ellipsoidal blocks on deformable ground surfaces, introducing the effects of block eccentricity and orientation at impact, is presented. This allows us to assess impact penetration and force, restitution coefficients, and block trajectories. A parametric analysis was carried out by considering different block aspect ratios, impact angles and initial block orientations at impact. The results are presented in terms of restitution coefficients, penetration and force time histories, maximum penetration depth, maximum force and rotational/total kinetic ratios. Impacts along the major block axis, versus those along minor axis, are characterized by larger penetrations (ranging from 3.3 to 50%), shorter impact durations (ca 50%) and very slightly larger vertical forces (ranging from 0.3 to 60%) according to the model parameter used. In contrast, the impact angle is shown to strongly affect maximum penetration and force values, and markedly increase rotation at impact. Analogously, normal restitution coefficient is severely dependent on impact angle, with a variation of more than two orders of magnitude. A mathematical expression for computing the energetic restitution coefficient from the normal and tangential apparent restitution coefficients and the ratio between the rotation and total kinetic energy is proposed. This overcomes the drawback of classical restitution coefficients greater than one when a change in block rotation occurs allowing us to bracket the coefficient of restitutions values to support and improve classical rock fall simulations also highlighting their intrinsic limitations. Finally, the effects of block geometry and initial angular velocity on rockfall simulations were analyzed by implementing the approach in the HyStone simulation code. The simulated frequencies of the maximum height during each ballistic trajectory follow an exponential distribution, whereas those for normal and tangential apparent restitution coefficients follow normal distributions.

Jin L., Zheng M., Zhang R., Du X.

Zhao P., Liu J., Zhang Y.

Geofoam with good buffer performance and low density is proposed to replace part of the sand, forming a composite cushion to resist rockfall impact. On the other hand, falling rock is usually variable and irregular in shape. In this study, laboratory tests and numerical research are conducted to study the buffer performance of geofoam, as well as the effect of the rock shape. When the rock shape changes from the flat form to the cone form, more time is needed to undergo the impact process and the maximum impact force decreases. Thicker geofoam is advantageous for reducing the impact force. However, the decrease degree is affected by the rock shape. Both the geofoam thickness and the rock shape have an obvious effect on the maximum deformation and the vertical stress in the geofoam. Thicker geofoam can amplify the influence of the rock shape on the stress in the beam. Accordingly, in the design of an effective composite cushion in a rock-shed, the geofoam thickness necessarily requires appropriate determination to meet both the buffer performance and the cushion deformation. Furthermore, the rock shape plays a crucial role in evaluating the buffer performance of the composite cushion.

Bilal A., Sadique M.R., Iqbal M.A.

Rockfall is a major problem in hilly areas. Falling rocks pose a great threat to human life and engineering structures lying in these areas. To mitigate the hazard of rockfall, broadly two types of techniques are used, namely active protection and passive protection techniques. Active protection measures are those which prevent the rockfall from occurring, whereas the passive protection measures reduce the damage caused by the falling rocks. Rock-sheds have been considered as important passive protection structures for protection of roads or railway lines in the areas which are prone to rockfall. Rock-sheds are made up of reinforced concrete with a cushion layer on the top. The cushion layer can be of soil or a composite layer having soil and some other energy absorbing material which can dissipate the impact energy of rockfall and protect the rock-shed. In this paper, the work done by various researchers in the field of rockfall hazard has been discussed. Various active and passive protection measures to mitigate the rockfall hazard along with the benefits and limitations of each measure have been highlighted. The paper focuses on the importance and design of rock-sheds. Therefore, this paper discusses the design of rock-shed, the thickness of cushion layer, the various energy absorbing materials which can be used as cushion layer, and the research carried out in this area so far, and exhaustive conclusion has been made in this regard.

Anas S.M., Shariq M., Alam M., Yosri A.M., Mohamed A., AbdelMongy M.

Structural members with low-flexural stiffness, such as slabs, are more susceptible to impulsive loadings induced by falling machines/tools during construction and installation, and also from rolling boulders/rocks triggered by wind/earthquake, especially in mountainous areas. The impact resistance of reinforced concrete (RC) slabs supported on two opposite edges (often called the one-way slab) and on all four edges (i.e., two-way slab) has been adequately studied experimentally as well as computationally, and is available in the literature. However, the slabs supported on three edges have not been studied under low-velocity impact for their impact response. For this purpose, a computational study is performed through finite elements by implementing ABAQUS software on the validated model, resulting in the slab, which is supported on (i) three edges and (ii) two opposite edges, to be subjected to low-velocity impact, induced by dropping a 105 kg non-deformable steel mass from a height of 2500 mm onto the slab centroid. Furthermore, the role of the material strength of the concrete of the slab is investigated via replacing the ultra-high performance concrete (UHPC) for standard or normal-strength concrete (NSC). The impact load is modeled by considering the explicit module of the software. Failure mechanism, stress/strain contour, displacement distribution, and crack pattern of the slabs are compared and discussed.

Dong L.

Flow-like landslides and debris flow disasters pose great threats to the human living environment. Disaster risk control largely relies on good knowledge of the mechanism of disaster evolution. To better understand debris propagation and develop a run-out model, this paper conducts a detailed analysis of the coupled effect of slope angle and particle shape based on energy consumption, which is still lacking in the literature. A series of DEM simulation tests considering five types of particle shapes are conducted. The results indicate that particle shape exerts a great influence on granular mobility, and the mobility is ranked from high to low as sphere-like particles, pyramid-like particles, slab-like particles, cube-like particles and rod-like particles. Such a particle shape effect is also dependent on the flow inertia properties, and more inertial granular flow shows a less significant particle shape effect on its mobility. Particle shape effect on granular mobility is mainly through affecting the energy loss caused by tangential collision and rolling friction, and this conclusion is independent of slope angle. In addition, we found that the lower energy loss of the granular flow surging downslope with steep terrain is also an important mechanism of its high-speed nature.

Tariq M., Khan A., Ullah A.

For structures and load-bearing beams under extreme impact loading, the prediction of the transmitted peak impact force is the most challenging task. Available numerical and soft computing-based methods for finding peak impact force are not very accurate. Therefore, a simple and user-friendly predictive model is constructed from a database containing 126 impact force experiments of the simply supported RC beams. The proposed model is developed using gene expression programming (GEP) that includes the effect of the impact velocity and the impactor weight. Also identified are other influencing factors that have been overlooked in the existing soft computing models, such as concrete compressive strength, the shear span to depth ratio, and the tensile reinforcement quantity and strength. This allows the proposed model to overcome several inconsistencies and difficulties residing in the existing models. A statistical study has been conducted to examine the adequacy of the proposed model compared to existing models. Additionally, a numerical confirmation of the empirical model of the peak impact force is obtained by reference to 3D finite element simulation in ABAQUS. Finally, the proposed model is employed to predict the dynamic shear force and bending moment diagrams, thus rendering it ideal for practical application.