Dynamic response of flexible rockfall barriers under different loading geometries

Flexible steel barriers are commonly constructed on steep hillsides to mitigate rockfall. The evaluation of the dynamic response of proprietary flexible barriers is conventionally performed using full-scale field tests by dropping a weight onto the barriers in accordance with the European test standard ETAG 27. The weight typically has a spherical or polyhedral shape and cannot reproduce more complex rockfall scenarios encountered in the field. A rigid slab may load a barrier over a larger area and its effect has not been investigated. In this study, a calibrated three-dimensional finite-element model was developed to study the performance of vertically and horizontally orientated rockfall barriers under concentrated areal impact loads. A new bilinear force-displacement model was incorporated into the model to simulate the behavior of the energy-dissipating devices on the barriers. The effect of different weight geometries was studied by considering impacts by a rigid single spherical boulder and a rigid slab. Results reveal that areal loading induced by a rigid slab increases the loading on the barrier foundation by up to 40 % in both horizontally and vertically positioned barriers when compared to a concentrated load scenario with a single boulder. This indicates that barriers tested under the current test standard does not give the worst-case scenario in terms of foundation loads, and barrier designers should take into account the possible effect of increased foundation loads by reinforcing the barrier posts and/or increasing their spacing.     

Landslide susceptibility mapping based on Support Vector Machine: A case study on natural slopes of Hong Kong, China

The Support Vector Machine (SVM) is an increasingly popular learning procedure based on statistical learning theory, and involves a training phase in which the model is trained by a training dataset of associated input and target output values. The trained model is then used to evaluate a separate set of testing data. There are two main ideas underlying the SVM for discriminant-type problems. The first is an optimum linear separating hyperplane that separates the data patterns. The second is the use of kernel functions to convert the original non-linear data patterns into the format that is linearly separable in a high-dimensional feature space. In this paper, an overview of the SVM, both one-class and two-class SVM methods, is first presented followed by its use in landslide susceptibility mapping. A study area was selected from the natural terrain of Hong Kong, and slope angle, slope aspect, elevation, profile curvature of slope, lithology, vegetation cover and topographic wetness index (TWI) were used as environmental parameters which influence the occurrence of landslides. One-class and two-class SVM models were trained and then used to map landslide susceptibility respectively. The resulting susceptibility maps obtained by the methods were compared to that obtained by the logistic regression (LR) method. It is concluded that two-class SVM possesses better prediction efficiency than logistic regression and one-class SVM. However, one-class SVM, which only requires failed cases, has an advantage over the other two methods as only “failed” case information is usually available in landslide susceptibility mapping.     

Inclusion of higher modes in the analysis of non-classically damped systems

A time-integration procedure for dynamic analysis of non-classically damped systems, in which high-frequency modes play a significant role, is suggested. This procedure is an extension of Clough and Mojtahedi's¹ method. Clough and Mojtahedi suggested integration of the transformed coupled equations of motion where the transformation is done using a truncated set of undamped mode-shapes. The proposed extension consists in adding the response of all the higher modes through a quasistatic analysis. Approximations involved in using such a procedure are examined. Numerical results presented indicate that the proposed extension leads to a significant improvement over Clough and Mojtahedi's method.     

Frame transformation of spherical-harmonic coefficients of differential particle intensity

We present a general second-order-correct frame transformation on spherical-harmonic coefficients of differential particle intensity. The transformation, valid for relativistic particles as well, provides a clear view of the Compton-Getting effect. It shows explicitly how each transformed harmonic coefficient depends on a subset of the original harmonic coefficients. The general expression for the first-order Compton-Getting vector anisotropy is derived and interpreted. In addition, we show how the new transformation allows one to simplify a current procedure for determining the directional intensity in a comoving frame. This involves the directional particle data measured on a spacecraft.     

Geophysical flows impacting a flexible barrier: effects of solid-fluid interaction

Flexible barriers undergo large deformation to extend the impact duration, and thereby reduce the impact load of geophysical flows. The performance of flexible barriers remains a crucial challenge because there currently lacks a comprehensive criterion for estimating impact load. In this study, a series of centrifuge tests were carried out to investigate different geophysical flow types impacting an instrumented flexible barrier. The geophysical flows modelled include covered in this study include flood, hyperconcentrated flow, debris flow, and dry debris avalanche. Results reveal that the relationship between the Froude number, Fr, and the pressure coefficient α strongly depends on the formation of static deposits called dead zones which induce static loads and whether a run-up or pile-up impact mechanism develops. Test results demonstrate that flexible barriers can attenuate peak impact loads of flood, hyperconcentrated flow, and debris flow by up to 50% compared to rigid barriers. Furthermore, flexible barriers attenuate the impact load of dry debris avalanche by enabling the dry debris to reach an active failure state through large deformation. Examination of the state of static debris deposits behind the barriers indicates that hyperconcentrated and debris flows are strongly influenced by whether excessive pore water pressures regulate the depositional process of particles during the impact process. This results in significant particle rearrangement and similar state of static debris behind rigid barrier and the deformed full-retention flexible barrier, and thus the static loads on both barriers converge.     

Performance of ethylene-vinyl acetate foam as cushioning material for rigid debris-resisting barriers

This paper reports an investigation on the performance of ethylene-vinyl acetate (EVA) foam when used as a cushion layer for rigid barriers used to resist debris flow. Large-scale pendulum impact tests were conducted to study the effects of layer thickness on cushion performance under six successive impacts. Results show that for the first impact at 70 kJ, the peak contact force with the EVA foam thickness of 500 mm is about twice larger compared to that of 1000 mm. Results also reveal that the cushion mechanism of elastic collapse of cell walls in the EVA foam results in peak contact forces and maximum transmitted loads that are up to 30 and 50% lower compared to gabions for the first impact at 70 kJ, respectively. The elastic behavior of EVA foam provides consistent cushioning efficiency. Furthermore, EVA foam is found to be susceptible to degradation by ultraviolet light so that a suitable coating layer is required for outdoor use. Polyurea was identified as a suitable coating material and a small-scale coating trial was performed to confirm this. Findings presented in this paper will have direct implications on the future design of cushion layers for rigid barriers used to intercept debris flows.     

Scaling Behavior of Gravel Surfaces

Roughness of successively developed gravel surfaces in flume experiments is investigated using laser scanned elevation fields. Scaling behavior of these surfaces is studied using structure functions. The results show that all surfaces exhibit good scaling behavior for two scaling regions. Multifractal analysis based on singular measures is then conducted for the two scaling regions, respectively. The relatively smaller scaling region characterizing subgrain scale roughness exhibits evident nonstationarity and intermittency. In contrary, the measures for the larger scaling region characterizing the spatial distribution of grains are more stationary and less intermittent than the measures for the subgrain scaling region.     

The dilatant behaviour of sand–pile interface subjected to loading and stress relief

Property and behaviour of sand–pile interface are crucial to shaft resistance of piles. Dilation or contraction of the interface soil induces change in normal stress, which in turn influences the shear stress mobilised at the interface. Although previous studies have demonstrated this mechanism by laboratory tests and numerical simulations, the interface responses are not analysed systematically in terms of soil state (i.e. density and stress level). The objective of this study is to understand and quantify any increase in normal stress of different pile–soil interfaces when they are subjected to loading and stress relief. Distinct element modelling was carried out. Input parameters and modelling procedure were verified by experimental data from laboratory element tests. Parametric simulations of shearbox tests were conducted under the constant normal stiffness, constant normal load and constant volume boundary conditions. Key parameters including initial normal stress ( $ \sigma_{{{\text{n}}0}}^{\prime } $ ), initial void ratio (e ₀), normal stiffness constraining the interface and loading–unloading stress history were investigated. It is shown that mobilised stress ratio ( $ \tau /\sigma_{\text{n}}^{\prime } $ ) and normal stress increment ( $ \Updelta \sigma_{\text{n}}^{\prime } $ ) on a given interface are governed by $ \sigma_{{{\text{n}}0}}^{\prime } $ and e ₀. An increase in $ \sigma_{{{\text{n}}0}}^{\prime } $ from 100 to 400 kPa leads to a 30 % reduction in $ \Updelta \sigma_{\text{n}}^{\prime } $ . An increase in e ₀ from 0.18 to 0.30 reduces $ \Updelta \sigma_{\text{n}}^{\prime } $ by more than 90 %, and therefore, shaft resistance is much lower for piles in loose sands. A unique relationship between $ \Updelta \sigma_{\text{n}}^{\prime } $ and normal stiffness is established for different soil states. It can be applied to assess the shaft resistance of piles in soils with different densities and subjected to loading and stress relief. Fairly good agreement is obtained between the calculated shaft resistance based on the proposed relationship and the measured results in centrifuge model tests.     

Spatial Distribution of Solar Energetic Particles in the Inner Heliosphere

We study the spatial distribution of solar energetic particles (SEPs) throughout the inner heliosphere during six large SEP events from the period 1977 through 1979, as deduced from observations on the Helios 1 and 2, IMP 7 and 8, ISEE 3, and Voyager 1 and 2 spacecraft. Evidence of intensity maxima associated with the expanding shock wave is commonly seen along its central and western flanks, although the region of peak acceleration or “nose” of the shock is sometimes highly localized in longitude. In one event (1 January 1978) a sharp peak in 20?–?30 MeV proton intensities is seen more strongly by Voyager at ～?2 AU than it is by spacecraft at nearby longitudes at ～?1 AU. Large spatial regions, or “reservoirs,” often exist behind the shocks with spatially uniform SEP intensities and invariant spectra that decrease adiabatically with time as their containment volume expands. Reservoirs are seen to sweep past 0.3 AU and can extend out many AU. Boundaries of the reservoirs can vary with time and with particle velocity, rather than rigidity. In one case, a second shock wave from the Sun reaccelerates protons that retain the same hard spectrum as protons in the reservoir from the preceding SEP event. Thus reservoirs can provide not only seed particles but also a “seed spectrum” with a spectral shape that is unchanged by a weaker second shock.     

香港花岗岩风化分级化学指标体系与风化壳分带

火成岩的化学风化过程实质上就是碱、碱土金属组分水解淋失与脱硅富铁铝化的地球化学过程。不同风化程度的岩石处于整个化学风化过程的不同阶段,因而具有不同的化学成分和风化度指标。笔者在对香港九龙两个地方5个钻孔共计150件不同深度、不同风化程度的样品化学全分析结果与岩土风化程度宏观判别结果的相互对比、选择和确认的基础上,建立了香港地区花岗岩风化岩土风化程度工程分级的化学指标体系。这一研究成果的提出不仅有利于提高花岗岩风化岩土工程分类的科。学性、可靠性和实用性,而且可以为风化岩土工程特性与风化作用关系研究提供理论依据。