Propagation characteristics of blast-induced shock waves in a jointed rock mass

The propagation characteristics of blast-induced shock waves in a jointed rock mass have been monitored and studied. Accelerometers were set up on a rock surface along three lines, at 0°, 45° and 90° with respect to the orientation of the predominant joint strikes. Cylindrical charges were detonated in a charge hole, and ground accelerations in both vertical and radial directions at various points on the rock surface were recorded. Results show that rock joints have significant effects on the propagation characteristics of blast-induced shock waves. The amplitude and principal frequency of shock waves attenuate with the increase of distance from the charge centre, and the increase of incident angle between the joint strike and the wave propagation path. The measured data were compared with the empirical equations of shock wave attenuation proposed by other authors. The mechanism of rock joint effect, the attenuation of shock waves in relation to the propagation distance, the charge weight and the incident angle, are discussed in this paper.     

断续节理岩体中地震波响应的数值与理论分析

为研究地震产生的应力波在断续节理岩体中的传播规律和应力分布趋势,首先,采用数值模拟方法分析应力波通过贯通节理的传播规律,并与已有理论研究结果进行对比,验证数值分析的准确性和适用性;然后,对应力波在断续节理岩体中的传播进行数值模拟,分析透射系数在水平方向的分布趋势以及不同节理连续性对波传播的影响,并结合波的衍射原理,给出定性的理论解释。结果表明:应力波通过断续节理时,节理的透射作用会使应力波振幅减小,引起波的衰减,岩桥的衍射作用则会使波阵面由平面变为曲面,波的传播方向发生改变,从而导致应力波振幅在水平方向的分布发生变化;应力波通过断续节理的透射系数与岩桥尺寸L_r和衍射角μ相关,当衍射角比较小时,透射系数主要受岩桥尺寸L_r的影响,当衍射角较大时,岩桥尺寸L_r和衍射角μ共同影响应力波在岩体中的传播。      

A thin-layer interface model for wave propagation through filled rock joints

The present study essentially employs a thin-layer interface model for filled rock joints to analyze wave propagation across the jointed rock masses. The thin-layer interface model treats the rough-surfaced joint and the filling material as a continuum medium with a finite thickness. The filling medium is sandwiched between the adjacent rock materials. By back analysis, the relation between the normal stress and the closure of the filled joint are derived, where the effect of joint deformation process on the wave propagation through the joint is analyzed. Analytical solutions and laboratory tests are compared to evaluate the validity of the thin-layer interface model for filled rock joints with linear and nonlinear mechanical properties. The advantages and the disadvantages of the present approach are also discussed.     

应力波作用下节理面前后电磁辐射强度的变化

从压电体中的压电本构方程出发,得到了含石英等压电介质岩体在应力波作用下产生的电场值的关系表达式．电磁辐射强度随电阻率增大而增大,随传播距离发生衰减．对于电阻率较大导电性能较差的岩石来说,压电电荷的贡献是足够引起重视的．利用所得到的表达式对实际地震电磁信号幅值进行了估算,所得结果与实测结果吻合．依据所得到的电场值的表达式及应力波在节理面处的透射解,获得了垂直入射应力波作用下产生的电磁波在线性变形节理面前后的强度关系．研究了节理参数、岩体电性参数以及入射波频率对节理面前后电磁辐射强度的影响．结果表明,电磁辐射的强度随节理初始刚度增大而增大;对于节理面两侧岩体性质不同的情形,从理论上讲,电磁辐射强度随单个参数的变化是明确的,但在多种参数的综合影响下,电磁辐射强度变化情况相对比较复杂．本文的理论计算结果与其它众多学者得出的实验结果一致．      

Progressive failure of sheeted rock slopes: the 2009–2010 Rhombus Wall rock falls in Yosemite Valley,California, USA

Progressive rock‐fall failures in natural rock slopes are common in many environments, but often elude detailed quantitative documentation and analysis. Here we present high‐resolution photography, video, and laser scanning data that document spatial and temporal patterns of a 15‐month‐long sequence of at least 14 rock falls from the Rhombus Wall, a sheeted granitic cliff in Yosemite Valley, California. The rock‐fall sequence began on 26 August 2009 with a small failure at the tip of an overhanging rock slab. Several hours later, a series of five rock falls totaling 736 m³ progressed upward along a sheeting joint behind the overhanging slab. Over the next 3 weeks, audible cracking occurred on the Rhombus Wall, suggesting crack propagation, while visual monitoring revealed opening of a sheeting joint adjacent to the previous failure surface. On 14 September 2009 a 110 m³ slab detached along this sheeting joint. Additional rock falls between 30 August and 20 November 2010, totaling 187 m³, radiated outward from the initial failure area along cliff (sub)parallel sheeting joints. We suggest that these progressive failures might have been related to stress redistributions accompanying propagation of sheeting joints behind the cliff face. Mechanical analyses indicate that tensile stresses should occur perpendicular to the cliff face and open sheeting joints, and that sheeting joints should propagate parallel to a cliff face from areas of stress concentrations. The analyses also account for how sheeting joints can propagate to lengths many times greater than their depths behind cliff faces. We posit that as a region of failure spreads across a cliff face, stress concentrations along its margin will spread with it, promoting further crack propagation and rock falls. Published in 2012. This article is a US Government work and is in the public domain in the USA.     

Runout of the Socompa volcanic debris avalanche, Chile: a mechanical explanation for low basal shear resistance

We propose a mechanical explanation for the low basal shear resistance (about 50 kPa) previously used to simulate successfully the complex, well-documented deposit morphology and lithological distribution produced by emplacement of the 25 km³ Socompa volcanic debris avalanche deposit, Chile. Stratigraphic evidence for intense basal comminution indicates the occurrence of dynamic rock fragmentation in the basal region of this large granular mass flow, and we show that such fragmentation generates a basal shear stress, retarding motion of the avalanche, that is a function of the flow thickness and intact rock strength. The topography of the Socompa deposit is realistically simulated using this fragmentation-derived resistance function. Basal fragmentation is also compatible with the evidence from the deposit that reflection of the avalanche from topography caused a secondary wave that interacted with the primary flow.     

Obliquely incident wave propagation across rock joints with virtual wave source method

Due to the presence of joints, waves are greatly attenuated when propagating across rock masses. Zhu et al. (2011) (Normally incident wave propagation across a joint set with virtual wave source method. J. Appl. Geophys.73, 283–288.) studied normally incident wave propagation across a joint set with the virtual wave source method (VWSM). The introduced VWSM has merits in some aspects, especially the capability of separating differently arriving transmitted waves. However, normal wave incidence is only the special case for wave incidence with arbitrary incident angles. Obliquely incident wave propagation across a joint set is more complicated than normally incident wave propagation due to wave transformation at the joints. As a continuation of the previous paper, this work is extended to analytically study obliquely incident wave propagation across joints with VWSM. Complete theoretical reflection and transmission coefficients across single joint described by displacement discontinuity model are derived through plane wave analysis. The superposition of P wave and S wave is for the first time mathematically expressed and studied. The VWSM is verified through comparison with the propagation matrix method. Through extensive parametric studies on wave transmission across single and multiple parallel joints, it is shown that transmitted wave energy is mainly constrained in the transmitted wave of the same type as the incident wave. And with increasing joint stiffness, the transmission coefficients across single joint increases except those whose wave type is different from the incident wave. The amplitude of superposed transmitted wave for P wave incidence increases with incident angle, which is coincident with field observations. Both joint spacing and number of joints have significant effects on transmission coefficients. We find that when joint spacing is sufficiently large, the transmission coefficient is no longer a constant as the normally incident wave propagation case (Zhu et al., 2011). And when joints are very closely spaced, wave attenuation depends little on the number of joints, which is different from the conclusions from equivalent medium method.     

Air ionization at rock surfaces and pre-earthquake signals

Pre-earthquake signals have been widely reported, including perturbations in the ionosphere. These precursory signals, though highly diverse, may be caused by just one underlying physical process: activation of highly mobile electronic charge carriers in rocks that are subjected to ever increasing levels of stress. The charge carriers are defect electrons associated with O^? in a matrix of O^2?. Known as positive holes or pholes h, they flow out of the stressed rock into the unstressed rock volume, traveling meters in the laboratory, probably kilometers in the field. At the rock–air interface they cause: (i) positive surface potential, (ii) field-ionization of air molecules, (iii) corona discharges. The rate of formation of airborne ions can exceed 10⁹ cm^?2 s^?1. Massive air ionization prior to major earthquakes increases the electrical conductivity in the air column and may cause ionospheric perturbations, earthquake lights, and unusual animal behavior as well as infrared emission.     

现场大尺度摩擦实验中观测到的断层泥中的塑性变形波

本文介绍了在断层区的岩体中进行的现场大尺度摩擦实验。实验的目的是探索地壳中变形波的存在。实验结果表明,在加载时断层泥屈服时间不一致,加载一端的断层泥先屈服,然后屈服范围逐步扩大,此过程相应于塑性变形波在断层泥中的传播。实验测得试件中塑性变形波波速约为2—3 cm/min,实际相当于10—16km/year。     

Dynamic stress concentration in pre-stressed poroelastic media due to moving punch influenced by shear wave

During the occurrence of earthquake, the shear wave propagates in the rocks present inside/at the Earth’s crust. The propagation of shear wave may lead to the progression of punch present inside the rock medium. As a result of this, substantial stress accumulated at the vicinity of propagating punch inside rock medium which significantly affects the stability of various geological and human-made structure and, hence, may cause failure of structure. Therefore, the analysis of stress concentration at the vicinity of punch moving due to shear wave propagation has become prominent in the area of seismology. In the present paper, an analytical perspective has been employed to discuss the influence of velocity of moving punch associated with the propagation of shear wave on developed dynamic stress concentration (DSC) in three types of pre-stressed vertical transversely isotropic (VTI) poroelastic media viz. granite (an igneous rock); sandstone (a sedimentary rock); and marble (a metamorphic rock). The closed form expression of DSC for the force of constant intensity has been derived with the aid of Weiner-Hopf technique along with Galilean and two-sided Fourier integral transformations. The noticeable influence of different affecting parameters (viz. velocity of moving punch associated with the shear wave propagation, horizontal compressive/tensile initial stresses, vertical compressive/tensile initial stress, porosity, and anisotropy parameter) on dynamic stress concentration has also been reported. Numerical computation and graphical illustrations have been carried out for the aforementioned three different types of porous rocks to investigate the profound impact of affecting parameters on DSC. Moreover, some noteworthy peculiarities have also been derived from the obtained expression of dynamic stress concentration.     

长应力波对于深部隧道衬砌的作用

应力波与隧道衬砌的相互作用问题为岩石力学的一个十分复杂的问题,到目前为止还没有得到圆满的解决。对于考虑介质与结构弹塑性性质的课题,解析解更难以求得。研究表明长波与深地下硐室的作用问题可以用拟静法解答。本文用拟静法研究了考虑岩体塑性性质时长纵波与地下硐室的相互作用问题。并获得了确定长应力波对于隧道支护作用的解析解。     

Controls on the stability and inclinations of hillslopes formed on hard rock

In identifying controls on rock slope form a distinction is made between: (1) rock slopes with joints which dip steeply out of a cliff and hence are subject to mass failure of the rock mass above a critical joint; and (2) rock slopes with inclinations which are either in equilibrium with the mass strength of their rocks, or have profiles which will develop towards strength equilibrium as cross joints open. In the first class of slope, stability results not just from the basic frictional resistance of the rock but also from the frictional roughness along the critical joint and from the normal stress acting across that joint. Stability may be reduced by weathering and loss of strength of the joint wall rock. As a result of normal stress variations with depth, induced by overburdens, high cliffs which are not undercut have a concave profile. The second group of slopes includes those with inclinations controlled at the scale of individual joint blocks, buttressed slopes and those on unjointed rock masses. Buttressed and unjointed rock masses develop towards a condition of mass strength equilibrium as cross joints open. Strength equilibrium slopes may be recognized by application of a rock mass strength classification proposed for geomorphic purposes. Eleven propositions are formulated which identify controls on rock slope development and some consequences of these controls.     

Generation of baroclinic topographic waves by a tropical cyclone impacting a low-latitude continental shelf

Numerical model experiments have been performed to analyze the low-latitude baroclinic continental shelf response to a tropical cyclone. The theory of coastally trapped waves suggests that, provided appropriate slope, latitude, stratification and wind stress, bottom-intensified topographic Rossby waves can be generated by the storm. Based on a scale analysis, the Nicaragua Shelf is chosen to study propagating topographic waves excited by a storm, and a model domain is configured with simplified but similar geometry. The model is forced with wind stress representative of a hurricane translating slowly over the region at 6 km h⁻¹. Scale analysis leads to the assumption that baroclinic Kelvin wave modes have minimal effect on the low-frequency wave motions along the slope, and coastal-trapped waves are restricted to topographic Rossby waves. Analysis of the simulated motions suggests that the shallow part of the continental slope is under the influence of barotropic topographic wave motions and at the deeper part of the slope baroclinic topographic Rossby waves dominate the low-frequency motions. Numerical solutions are in a good agreement with theoretical scale analysis. Characteristics of the simulated baroclinic waves are calculated based on linear theory of bottom-intensified topographic Rossby waves. Simulated waves have periods ranging from 153 to 203 h. The length scale of the waves is from 59 to 87 km. Analysis of energy fluxes for a fixed volume on the slope reveals predominantly along-isobath energy propagation in the direction of the group velocity of a topographic Rossby wave. Another model experiment forced with a faster translating hurricane demonstrates that fast moving tropical cyclones do not excite energetic baroclinic topographic Rossby waves. Instead, robust inertial oscillations are identified over the slope.     

Influence of source region properties on scaling relations forM<0 events

Excavation induced seismic events with moment magnitudesM<0 are examined in an attempt to determine the role geology, excavation geometry, and stress have on scaling relations. Correlations are established based on accurate measurements of excavation geometry and methodology, stress regime, rock mass structure, local tectonics, and seismic locations. Scaling relations incorporated seismic moments and source radii obtained by spectral analysis, accounting for source, propagation, and site effects, and using Madariaga's dynamic circular fault model. Observations suggest that the interaction of stresses with pre-existing fractures, fracture complexity and depth of events are the main factors influencing source characteristics and scaling behaviour. Self-similar relationships were found for events at similar depths or for weakly structured rock masses with reduced clamping stresses, whereas a non-similar behaviour was found for events with increasing depth or for heavily fractured zones under stress confinement. Additionally, the scaling behaviour for combined data sets tended to mask the non-similar trends. Overall, depth and fracture complexity, initially thought as second order effects, appear to significantly influence source characteristics of seismic events withM<0 and consequently favour a non-similar earthquake generation process.     

SOME EXPERIMENTS CONCERNING THE PRIMARY SEISMIC PULSE*

Recordings were made with three types of detector of the primary compressional (P) and shear (S) wave pulses generated by explosions in boreholes. Charge weights varied from 0.08 kg to 9.5 kg and detector distances varied from about 3 m to about 80 m. Scaling by the simple factor W^1/3 where W is the charge weight, enabled observations from different sized charges to be fitted to a single expression. Experiments were carried out in the Bunter sandstone and the London clay and both fluid and solid tamping were used. This variation in tamping had no significant effect on the P-waves but it may have affected the generation of SV-waves. In both media the P-wave energy carried at 30 m from the shot by frequencies less than 100 Hz decreased rapidly with depth and was usually 1–2 % of the available chemical energy for a shot depth of 15 m. The S-wave energy was much less than this, but was highly directional. The P-wave pulse had the appearance of a damped sinusoid in very good agreement with the predictions of the ‘equivalent radiator’ hypothesis. However, the surface of this radiator should be identified not with the blown cavity but with the surface at which the tensile stresses associated with the stress wave become less than the tensile strength of the rock. The predominant frequency for a 1 kg charge at a depth of 15 m was 24 Hz in the clay and 52 Hz in the sandstone. In these and similar media, therefore, an effort should be made to keep individual charges less than 1 kg in reflection shooting and less than 10 kg in refraction shooting. The value of Q was about 50 in clay and about 25 in the sandstone. These estimates are rather uncertain because of the small distances over which the pulses were observed. The Z-transforms of the sampled pulses indicated that they were all of minimum phase, or very near to it.     

准噶尔盆地岩石品质因子与速度分析

为研究准噶尔盆地南缘地区地层中地震波的衰减机制及该区地震波传播、衰减规律，采用实验室测定的方法，对该区岩石的吸收特笥进行了测试和研究。根据实验观测结果，该区地震波速度与介质品质因子具有较好的对数线性关系；该区品质因子受岩石所处环境条件及岩石性质的影响比较大，其中岩石饱和度和介质所受的应力大小对品质因子的影响尤为突出。     

The ~4-ka Rungwe Pumice (South-Western Tanzania): a wind-still Plinian eruption

The ~4-ka trachytic Rungwe Pumice (RP) deposit from Rungwe Volcano in South-Western Tanzania is the first Plinian-style deposit from an African volcano to be closely documented focusing on its physical characterization. The RP is a mostly massive fall deposit with an inversely graded base. Empirical models suggest a maximum eruption column height H _T of 30.5–35 km with an associated peak mass discharge rate of 2.8–4.8 × 10⁸ kg/s. Analytical calculations result in H _T values of 33 ± 4 km (inversion of TEPHRA2 model on grain size data) corresponding to mass discharge ranging from 2.3 to 6.0 × 10⁸ kg/s. Lake-core data allow extrapolation of the deposit thinning trend far beyond onland exposures. Empirical fitting of thickness data yields volume estimates between 3.2 and 5.8 km³ (corresponding to an erupted mass of 1.1–2.0 × 10¹² kg), whereas analytical derivation yields an erupted mass of 1.1 × 10¹² kg (inversion of TEPHRA2 model). Modelling and dispersal maps are consistent with nearly no-wind conditions during the eruption. The plume corner is estimated to have been ca. 11–12 km from the vent. After an opening phase with gradually increasing intensity, a high discharge rate was maintained throughout the eruption, without fountain collapse as is evidenced by a lack of pyroclastic density current deposits.     

Numerical investigation of an oceanic resonant regime induced by hurricane winds

The oceanic mixed layer (OML) response to an idealized hurricane with different propagation speeds is investigated using a two-layer reduced gravity ocean model. First, the model performances are examined with respect to available observations relative to Hurricane Frances (2004). Then, 11 idealized simulations are performed with a Holland (Mon Weather Rev 108(8):1212–1218, 1980) symmetric wind profile as surface forcing with storm propagation speeds ranging from 2 to 12 m s⁻¹. By varying this parameter, the phasing between atmospheric and oceanic scales is modified. Consequently, it leads to different momentum exchanges between the hurricane and the OML and to various oceanic responses. The present study determines how OML momentum and heat budgets depend on this parameter. The kinetic energy flux due to surface wind stress is found to strongly depend on the propagation speed and on the cross-track distance from the hurricane center. A resonant regime between surface winds and near-inertial currents is clearly identified. This regime maximizes locally the energy flux into the OML. For fast-moving hurricanes (>6 m s⁻¹), the ratio of kinetic energy converted into turbulence depends only on the wind stress energy input. For slow-moving hurricanes (<6 m s⁻¹), the upwelling induced by current divergence enhances this conversion by shallowing the OML depth. Regarding the thermodynamic response, two regimes are identified with respect to the propagation speed. For slow-moving hurricanes, the upwelling combined with a sharp temperature gradient at the OML base formed in the leading part of the storm maximizes the oceanic heat loss. For fast propagation speeds, the resonance mechanism sets up the cold wake on the right side of the hurricane track. These results suggest that the propagation speed is a parameter as important as the surface wind speed to accurately describe the oceanic response to a moving hurricane.     

Emplacement conditions of igneous dikes in Ethiopian Traps

The emplacement conditions for 39 igneous dikes cutting basalts in northwestern Ethiopia are evaluated by analyzing their displacement–length scaling relations. Maximum opening displacements and lengths of the dikes demonstrate displacement–length scaling of the form D_max = 0.088L^0.48, consistent with other populations of dikes and veins and different than the power-law scaling relation typically found for faults. The dikes propagated through the thin Trap basalt sequence under conditions of constant fracture toughness, with values corrected for three-dimensional dike geometry of ~ 77–273 MPa m^1/2. The large values of fracture toughness are likely associated with (1) the toughening effects of near-tip damage, (2) mixed-mode dike propagation, as shown by magma flow fabric analysis through anisotropy of magnetic susceptibility (AMS) and image analysis of thin sections, and (3) elevated temperature within the blocky and ductile basaltic host rock, evidence of which has been found in the field.