Fractal models for the fragmentation of rocks and soils: a review

Fragmentation, the process of breaking apart into fragments, is caused by the propagation of multiple fractures at different length scales. Such fractures can be induced by dynamic crack growth during compressive/tensile loading or by stress waves during impact loading. Fragmentation of rocks occurs in resoonse to tectonic activity, percussive drilling, grinding and blasting. Soil fragmentation is the result of tillage and planting operations. Fractal theory, which deals with the scaling of hierarchical and irregur systems, offers new opportunities for modeling the fragmentation process. This paper reviews the literature on fractal models for the fragmentation of heterogeneous brittle earth materials. Fractal models are available for the fragmentation of: (1) classical aggregate; (2) aggregates with fractal pore space; and (3) aggregates with fractal surfaces. In each case, the aggregates are composed of building blocks of finite size. Structural failure is hierarchical in nature and takes place by multiple fracturing of the aggregated building blocks. The resulting number-size distribution of fragments depends on the probability of failure, P(1/bⁱ) at each level in the hierarchy. Models for both scale-invariant and scale-dependent are reviewed. In the case of scale-invariant P(1/bⁱ)< 1, theory predict: D_f = 3 + log [P(1/bⁱ)]/log[b] for classical aggregates; D_f=D_m+log[P(1/bⁱ)]/log[b] for aggregates with fractal pore space; and D_f=D_s for aggregates with fractal surfaces. where b is a scaling factor and D_f, D_m and D_s are the fragmentation, mass and surface fractal dimensions, respectively. The physical significance of these parameters is discussed, methods of estimating them are reviewed, and topics needing further research are identified.     

Fractal analysis of mingled/mixed magmas: an example from the Upper Pollara eruption (Salina Island, southern Tyrrhenian Sea, Italy)

Upper Pollara eruption products (13 ka, Salina Island, Italy) include both homogeneous and heterogeneous pumices resulting from mixing/mingling processes between an HK andesite and a high-SiO₂ rhyolite. Representative samples of heterogeneous pumices are collected and analyzed in order to check the correspondence between glass composition and morphological features of the mingling/mixing structures. Image analysis techniques are applied and eight grey color ranges (classes) are extracted from high-resolution scans of pumice. Class 1 (lighter colors) and class 8 (darker colors) show end-member glass compositions, i.e. HK andesite and high-SiO₂ rhyolite, respectively. These two classes show spot- to cluster-like morphological structures. Intermediate classes show an HK dacitic to rhyolitic composition and a banding- to fold-like morphology. Fractal analysis by box-counting of the boundary pattern of eight grey classified images is performed over a length scale of 0.028–1.8 cm. Fractal dimension D is between 1.01 and 1.84. Coupled fractal analysis and geochemical data reveal that D increases as the degree of magma interaction (homogenization) increases. This feature well fits the results from numerical models on the convective mixing of fluids driven by thermal convection. We conclude that the increase of D observed in the Upper Pollara samples reflects the transition from fractal mixing to homogenization. End-member magmas (HK andesite and high-SiO₂ rhyolite) represent isolated mixing regions, while homogenized magmas represent active mixing regions. In the analyzed pumices, isolated and active mixing regions coexist at scales between 10⁻⁴ and 10⁻² m. Morphological and compositional features of the Upper Pollara pumices result from turbulence.     

The fractal dimension of pores in sedimentary rocks and its influence on permeability

Perimeter-area power-law relationship of pores in five sedimentary rocks are estimated from scanning electron micrographs of thin sections. These relationships for the pores of four sandstones were found to lie between 1.43 and 1.49, while that of an Indiana limestone was found to be 1.67. We show how the perimeter-area power-law relationship of pores, along with a pore-size distribution, can be used to estimate the hydraulic permeability. A discussion is given of how the fractal dimension of the pore perimeter derived by Mandelbrot for islands whose boundaries are fractal: P = ε^DA^D/2, where ε is some constant that depends on the length of the measuring grid size and D is the fractal dimension of the pore perimeter, influences permeability.     

A warning system for rainfall-induced shallow failures

It is widely recognised that soil slips and debris flows are triggered by short intense storms. Owing its geologic, geomorphologic and climatic settings, the Piedmont Region (NW Italy) is highly prone to the occurrence of this kind of landslides. In the last two centuries, in fact, a total of 105 severe meteoric events which triggered shallow failures occurred and, of these, 18 events took place from 1990 to 2002. A fair number of rainfall thresholds have been proposed in the literature, defined both on empirical or on physical bases. Empirical thresholds are defined collecting rainfall data for landslide meteoric events and for events without landslides, while physical thresholds are based on numerical models that consider the relation between rainfall, pore pressure and slope stability. The main objective of this paper is the identification of the empirical triggering thresholds for the Piedmont Region. Four meteoric events were selected and analysed (November 4–5, 1994; July 7–8, 1996; April 27–30, 2000; October 13–16, 2000) because they supply a wide range of variation for both rainfall parameters (duration, intensity, cumulative rainfalls) and the number of induced landslides. In the intensity–duration plot, the critical limit is described by the equation: I=19D^−0.50 (where I=rainfall intensity expressed in mm/h and D=rainfall duration expressed in hours). Such a limit is traced to envelop 90% of the points on the graph. In the NI–D diagram the triggering thresholds are given by the equations NI=0.76D^−0.33 and NI=4.62D^−0.79 (where NI=normalised intensity with respect to the annual precipitation, MAP, expressed in %, [(mm/h)/PMA]×100). In the article the different meaning of these thresholds is discussed. Finally, the diagram NI–NCR is proposed; the triggering threshold is given by the expression: NI=−0.09ln[NCR]+0.54 (where NCR is the normalised cumulative critical rainfall, [mm/PMA]×100). The application of the triggering thresholds as a fundamental element in a warning system dedicated to the safeguarding of population in landslide-prone areas is discussed. In detail an operating procedure which is presently being verified and tested in the studied area is described.     

Scaling of fault displacements from the Badajoz-Córdoba shear zone, SW spain

Faulting occurs over a large range of scale, parts of which are sampled by various techniques (e.g., microscopy, outcrop measurement, mapping, seismic reflection and other forms of remote sensing). Use of a single technique to measure displacement or strain will not sample faults at all scales and hence will give a biased estimate. In order to assess this bias, a knowledge of the distribution over all scales is needed.

Many samples of fault displacement appear to follow a power-law distribution, with departures which can be attributed to sampling effects. The number of faults with a displacement u is given by N(u) = Cu^−D. The power-law distribution of displacement is consistent with similar distributions of other fault parameters and earthquake magnitudes. When sampling along a line (e.g., a bedding trace on a map or section), a self-similar fault population would have D = 1, whereas self-affine geometries yield D≠ 1. Displacement and extension are dominated by small faults when D > 1 and by large faults when D < 1. When sampling over areas or volumes these critical values are 2 and 3, respectively.

A set of strike-slip faults from the Badajoz-Córdoba Shear Zone, Spain, were sampled at two different scales using 1:50000 maps and outcrop measurements. Displacement ranges over 6 orders of magnitude. These and other fault populations typically have D ranging from 0.6 to 1.5.

The power-law relationship may be integrated to yield estimates of the displacement (or extension) for faults which lie beyond the resolution of the sampling system. For example, a knowledge of D allows the extension measured on a map or seismic section to be “corrected” for faults whose displacement is below the resolution of the survey. Based on an overall estimate of D = 0.9 for the Badajoz-Córdoba data, only some 40% of the extension would be recorded by map-scale faults. A corrected extension of 41% along the shear zone is estimated; which if typical for the entire 300 km zone represents some 87 km of along-strike extension. Thus, work suggests that significant displacement occurs on faults which are too small to be interpreted from conventional seismic profiles and geological maps.     

循环应力比和振动频率对盐渍土微观结构影响分析

以青海省察尔汗地区盐渍土为研究对象, 借助扫描电子显微镜（SEM）设备和颗粒孔隙及裂隙图像识别与分析系统（PCAS）, 应用图像分割原理和分形理论, 对交通循环荷载作用下的盐渍土微观结构进行研究, 探讨不同循环应力比和不同振动频率下孔隙分布特征及其微观机制。结果表明： 循环应力比R由0.375增加到0.75, 临界破坏动应变由2.32%增高到3.17%, 动载循环次数相应减少; 振动频率f由0.5 Hz增加到2.0 Hz, 临界破坏动应变由2.82%减小到2.48%, 动载循环次数相应增多; 盐渍土孔隙参数随循环应力比的增大, 孔隙尺度分维值D_v 增长了0.12, 概率熵H_m 减小了0.017, 孔隙的形态分形维数D减小了0.27, 平均形状系数F增加了0.14, 变化规律较明显; 随振动频率的增大, D_v 增长了0.014, H_m 减小了0.002, D变化了0.06, F变化了0.003, 变化规律不明显; 在动荷载作用下, 试样的孔隙空间排列与宏观上的褶皱鼓状变形具有一致性。通过未加载试样与加载后试样的微观结构参数变化对比, 从循环应力比和振动频率对盐渍土微观孔隙特征的影响到宏观变形的相互作用机制进行了系统分析。     

Effect of Fe on garnet–melt trace element partitioning: experiments in FCMAS and quantification of crystal-chemical controls in natural systems

Garnet–melt trace element partitioning experiments were performed in the system FeO–CaO–MgO–Al₂O₃–SiO₂ (FCMAS) at 3 GPa and 1540°C, aimed specifically at studying the effect of garnet Fe²⁺ content on partition coefficients (D^Grt/Melt). D^Grt/Melt, measured by SIMS, for trivalent elements entering the garnet X-site show a small but significant dependence on garnet almandine content. This dependence is rationalised using the lattice strain model of Blundy and Wood [Blundy, J.D., Wood, B.J., 1994. Prediction of crystal–melt partition coefficients from elastic moduli. Nature 372, 452–454], which describes partitioning of an element i with radius r_i and valency Z in terms of three parameters: the effective radius of the site r₀(Z), the strain-free partition coefficient D₀(Z) for a cation with radius r₀(Z), and the apparent compressibility of the garnet X-site given by its Young's modulus E_X(Z). Combination of these results with data in Fe-free systems [Van Westrenen, W., Blundy, J.D., Wood, B.J., 1999. Crystal-chemical controls on trace element partitioning between garnet and anhydrous silicate melt. Am. Mineral. 84, 838–847] and crystal structure data for spessartine, andradite, and uvarovite, leads to the following equations for r₀(3+) and E_X(3+) as a function of garnet composition (X) and pressure (P):

r₀(3+) [Å]=0.930X_Py+0.993X_Gr+0.916X_Alm+0.946X_Spes+1.05(X_And+X_Uv)−0.005(P [GPa]−3.0)(±0.005 Å)

E_X(3+) [GPa]=3.5×10¹²(1.38+r₀(3+) [Å])^−26.7(±30 GPa)

Accuracy of these equations is shown by application to the existing garnet–melt partitioning database, covering a wide range of P and T conditions (1.8 GPa<P<5.0 GPa; 975°C<T<1640°C). D^Grt/Melt for all 3+ elements entering the X-site (REE, Sc and Y) are predicted to within 10–40% at given P, T, and X, when D^Grt/Melt for just one of these elements is known. In the absence of such knowledge, relative element fractionation (e.g. D_Sm^Grt/Melt/D_Nd^Grt/Melt) can be predicted. As an example, we predict that during partial melting of garnet peridotite, group A eclogite, and garnet pyroxenite, r₀(3+) for garnets ranges from 0.939±0.005 to 0.953±0.009 Å. These values are consistently smaller than the ionic radius of the heaviest REE, Lu. The above equations quantify the crystal-chemical controls on garnet–melt partitioning for the REE, Y and Sc. As such, they represent a major advance en route to predicting D^Grt/Melt for these elements as a function of P, T and X.     

Strontium diffusion in sanidine and albite, and general comments on strontium diffusion in alkali feldspars

Strontium chemical diffusion has been measured in albite and sanidine under dry, 1 atm, and QFM buffered conditions. Strontium oxide-aluminosilicate powdered sources were used to introduce the diffusant and Rutherford Backscattering Spectroscopy (RBS) used to measure diffusion profiles. For the 1 atm experiments, the following Arrhenius relations were obtained:

Sanidine (Or₆₁), temperature range 725–1075°C, diffusion normal to (001): D=8.4 exp(−450±13 kJ mol⁻¹/RT) m²s⁻¹. Albite (Or₁), temperature range 675–1025°C, diffusion normal to (001): D=2.9 × exp(−224±11 kJ mol⁻¹/RT) m²s⁻¹.

The alkali feldspars in this and earlier work display a broad range of activation energies for Sr diffusion, which may be a consequence of the thermodynamic non-ideality of the alkali feldspar system and/or the mixed alkali effect.     

Scale-invariance of soil moisture variability and its implications for the frequency-size distribution of landslides

Power spectral analyses of soil moisture variability are carried out from scales of 100 m to 10 km on the microwave remotely-sensed data from the Washita experimental watershed during 1992. The power spectrum S(k) has an approximate power-law dependence on wave number k with the exponent −1.8. This behavior is consistent with the behavior of a stochastic differential equation for soil moisture at a point, and it has important consequences for the frequency-size distribution of landslides. We present the cumulative frequency-size distributions of landslides induced by precipitation in Japan and Bolivia as well as landslides triggered by the 1994 Northridge, California earthquake. Large landslides in these regions, despite being triggered by different mechanisms, have a cumulative frequency-size distribution with a power-law dependence on area with an exponent ranging from −1.5 to −2. We use a soil moisture field with the above statistics in conjunction with a slope stability analysis to model the frequency-size distribution of landslides. In our model, landslides occur when a threshold shear stress dependent on cohesion, pore pressure, internal friction and slope angle is exceeded. This implies a threshold dependence on soil moisture and slope angle since cohesion, pore pressure and internal friction are primarily dependent on soil moisture. The cumulative frequency-size distribution of domains of shear stress greater than a threshold value with soil moisture modeled as above and topography modeled as a Brownian walk is a power-law function of area with an exponent of −1.8 for large landslide areas. This distribution is similar to that observed for landslides. The effect of strong ground motion from earthquakes lowers the shear stress necessary for failure, but does not change the frequency-size distribution of failed areas. This is consistent with observations. This work suggests that remote sensing of soil moisture can be of great importance in monitoring landslide hazards and proposes a specific quantitative model for landslide hazard assessment.     

三峡库区重庆段滑坡活动时间分布的物理分形研究

在许多研究滑坡活动分布的分形特征中,未能考虑无标度区的范围,并将滑坡分布作为数学点来描述而未考虑滑坡规模对分形结果的影响。这种研究结果主要反映了数量众多的规模较小滑坡活动的特点,掩盖了规模较大的滑坡分布特征。本文研究了重庆三峡库区1594个规模大于1×10^4m^3的滑坡活动时间分布资料,分析了滑坡活动时间的均匀分布、Poisson分布和分形分布结果。提出运用物理分形的方法,将滑坡活动按不同规模等级划分为4个子集,分析了各个子集的分维D,无标度区的范围和自然周期。表明运用物理分形的方法能描述不同规模等级滑坡活动时间分布的分形特征。     

Petrogenesis of the Maowu pyroxenite–eclogite body from the UHP metamorphic terrane of Dabieshan: chemical and isotopic constraints

The Maowu eclogite–pyroxenite body is a small (250×50 m) layered intrusion that occurs in the ultra-high-pressure (UHP) metamorphic terrane of Dabieshan, China. Like the adjacent Bixiling complex, the Maowu intrusion was initially emplaced at a crustal level, then subducted along with the country gneisses to mantle depths and underwent UHP metamorphism during the collision of the North and South China Blocks in the Triassic. This paper presents the results of a geochemical and isotopic investigation on the metamorphosed Maowu body. The Maowu intrusion has undergone open system chemical and isotopic behavior three times. Early crustal contamination during magmatic differentiation is manifested by high initial ⁸⁷Sr/⁸⁶Sr ratios (0.707–0.708) and inhomogeneous negative _Nd(T) values of −3 to −10 at 500 Ma (probable protolith age). Post-magmatic and pre-UHP metamorphic metasomatism is indicated by sinusoidal REE patterns of garnet orthopyroxenites, lack of whole-rock (WR) Sm–Nd isochronal relationship, low δ¹⁸O values and an extreme enrichment of Th and REE in a clinopyroxenite. Finally, K and Rb depletion during UHP metamorphism is deduced from the high initial ⁸⁷Sr/⁸⁶Sr ratios unsupported by in situ Rb/Sr ratios. Laser ICP-MS spot analyses on mineral grains show that (1) Grt and Cpx attained chemical equilibrium during UHP metamorphism, (2) Cpx/Grt partition coefficients for REE correlate with Ca, and (3) LREE abundances in whole rocks are not balanced by that of the principal phases (Grt and Cpx), implying that the presence of LREE-rich accessory phases, such as monazite and apatite, is required to account for the REE budget.

Sm–Nd isotope analyses of minerals yielded three internal isochrons with ages of 221±5 Ma and (T)=−5.4 for an eclogite, 231±16 Ma and (T)=−6.2 for a garnet websterite, and 236±19 Ma and (T)=−6.9 for a garnet clinopyroxenite. The Cpx/Grt chemical equilibrium and the consistent mineral isochron ages indicate that the metasomatic processes mentioned above must have occurred prior to the UHP metamorphism. These Sm–Nd ages agree with published zircon and monazite U–Pb ages and constrain the time of UHP metamorphism to 220–236 Ma. The Maowu and Bixiling layered intrusions are similar in their in situ tectonic relationship with their country gneisses, but the two bodies are distinguished by their magma-chamber processes. The Bixiling magmas were contaminated by the lower crust, whereas the Maowu magmas were contaminated by the upper crustal rocks during their emplacement and differentiation. The two complexes represent two distinct suites of magmatic rocks, which have resided in the continental crust for about 300–400 Ma before their ultimate subduction to mantle depths, UHP metamorphism and return to the crustal level.     

汶川地震诱发大型滑坡分布规律研究

2008年5.12汶川地震由于其超常的地震动力,触发了数百处大型滑坡灾害。本文以遥感解译所获取的汶川地震区112处面积大于50000m2大型滑坡的基本信息为基础,结合代表性大型滑坡实例的现场调绘,对汶川地震诱发大型滑坡的发育分布规律进行了较系统的研究。结果表明,汶川地震大型滑坡分布除表现出与汶川地震诱发区域性地质灾害类似的分布规律之外,因主要源于发震断层瞬间大幅度错动的直接地震动力引发的大型滑坡,其发育分布及滑动、运动方式还表现出自身的特点,具体可归结为以下几种效应:(1)距离效应:约80%的大型滑坡集中分布于发震断裂地表破裂带两侧5km的范围内,距离越远,滑坡分布数量越少;(2)锁固段效应:汶川地震诱发的大型滑坡主要集中分布在与发震断裂的交叉、错列、转换部位及NE段末端等5个集中区段。其中,红白-茶坪段是大型滑坡最为集中发育段,不仅滑坡数量多,而且规模大,汶川地震诱发的最大两处滑坡均分布于此段。其次为断裂NE段末端的南坝-东河口段,该段大型滑坡密集发育,东河口滑坡和窝前滑坡等大型滑坡均出露于此段;(3)上下盘效应:绝大多数(70%)大型滑坡都位于活动断裂的上盘,存在明显的"上下盘效应;"(4)方向效应:在与发震断裂带近于垂直的沟谷斜坡中,在地震波传播的背坡面一侧的滑坡发育密度明显大于迎坡面一侧,存在"背坡面效应"。同时,大型滑坡的滑动及运动方向还与各区段断层的错动方向有一定的相关性。在断层活动以右旋走滑为主的青川境内,有相当数量的滑坡表现出向NE方向滑动和运动的特点。     

稀有金属矿物溶解度对花岗伟晶岩成矿作用的制约

花岗伟晶岩型矿床是稀有金属矿床重要的类型之一。在花岗伟晶岩中,稀有金属元素Li、Be、Nb和Ta主要以独立矿物的形式存在,前人对稀有金属独立矿物在硅酸盐熔体中的溶解度及其影响因素展开了系统研究。本文综合分析了已有的实验数据,其结果表明,影响稀有金属独立矿物溶解度最为重要的2个参数是温度(T)和铝饱和指数(ASI)。因此本文建立了稀有金属独立矿物,尤其是铌锰矿和钽锰矿溶解度,与温度(T)和铝饱和指数(ASI)之间的定量关系: lg [w(Li)/10^-6]=-0.37×[1 000/(T/K)]+4.56,R²=0.44 lg [w(BeO)/10^-6]=-4.21×[1 000/(T/K)]+6.86,R²=0.91 lg [K_sp(Nb)/(mg²·kg^-2)]=-(2.86±0.14)×ASI_(Mn+Li)-(4.95±0.31)×[1 000/(T/K)]+(4.20+0.28),R²=0.86 lg [K_sp(Ta)/(mg²·kg^-2)]=-(2.46±0.11)×ASI_(Mn+Li)-(4.86±0.30)×[1 000/(T/K)]+(4.00+0.30),R²=0.80 式中,温度T为热力学温度,ASI_(Mn+Li)(ASI=Al₂O₃/(CaO+Na₂O+K₂O+Li₂O+MnO),摩尔分数比)和T的适用范围分别为0.6~1.2和1 073~1 373 K的范围内。上述公式为估算硅酸盐熔体中稀有金属含量提供了便利,为量化花岗伟晶岩成矿模型提供了基础。 稀有金属独立矿物溶解度随温度降低和铝饱和指数的增加而急剧降低,因此,在岩浆演化过程中,由岩浆侵位、分离结晶以及流体作用等因素引起的岩浆温度降低和铝饱和指数的增加,是导致稀有金属独立矿物结晶的主要机制。     

A seismic landslide susceptibility rating of geologic units based on analysis of characteristics of landslides triggered by the 17 January, 1994 Northridge, California earthquake

One of the most significant effects of the 17 January, 1994 Northridge, California earthquake (M=6.7) was the triggering of thousands of landslides over a broad area. Some of these landslides damaged and destroyed homes and other structures, blocked roads, disrupted pipelines, and caused other serious damage. Analysis of the distribution and characteristics of these landslides is important in understanding what areas may be susceptible to landsliding in future earthquakes. We analyzed the frequency, distribution, and geometries of triggered landslides in the Santa Susana 7.5′ quadrangle, an area of intense seismic landslide activity near the earthquake epicenter. Landslides occurred primarily in young (Late Miocene through Pleistocene) uncemented or very weakly cemented sediment that has been repeatedly folded, faulted, and uplifted in the past 1.5 million years. The most common types of landslide triggered by the earthquake were highly disrupted, shallow falls and slides of rock and debris. Far less numerous were deeper, more coherent slumps and block slides, primarily occurring in more cohesive or competent materials. The landslides in the Santa Susana quadrangle were divided into two samples: single landslides (1502) and landslide complexes (60), which involved multiple coalescing failures of surficial material. We described landslide morphologies by computing simple morphometric parameters (area, length, width, aspect ratio, slope angle). To quantify and rank the relative susceptibility of each geologic unit to seismic landsliding, we calculated two indices: (1) the susceptibility index, which is the ratio (given as a percentage) of the area covered by landslide sources within a geologic unit to the total outcrop area of that unit; and (2) the frequency index [given in landslides per square kilometer (ls/km²)], which is the total number of landslides within each geologic unit divided by the outcrop area of that unit. Susceptibility categories include very high (>2.5% landslide area or >30 ls/km²), high (1.0–2.5% landslide area or 10–30 ls/km²), moderate (0.5–1.0% landslide area or 3–10 ls/km²), and low (<0.5% landslide area and <3 ls/km²).     

Groundwater radon anomalies associated with earthquakes

Earthquake-related changes in groundwater radon have been detected at a sensitive observation site located right on a major active fault in Northeast Japan. A time-series analysis based on Bayesian statistics was successfully applied to remove background variations from the observed radon data, enabling us to examine the earthquake-related changes in detail.

We set a simple criterion of amplitude and duration for an anomaly observed in our radon data; we define an anomaly as a radon change that kept its level beyond 2σ (a standard deviation over the whole observation period) during a period longer than one day. We have observed 20 radon anomalies that satisfied this criterion from January 1984 to December 1988. Most of these anomalies have turned out to be related to large earthquakes that occurred in East Japan and its surrounding area; we have identified 12 post-seismic and 2-pre-seismic radon anomalies out of a total of 30 earthquakes with magnitude M 6.0 and hypocentral distance D 1000 km.

The typical pattern of the post-seismic anomalies is a radon decrease which started just after an earthquake, lasting for periods ranging from a few days to more than one week. The amplitude of the post-seismic anomalies depends on both magnitude and hypocentral distance, and can, in general, be expressed by a simple magnitude-distance relationships.

A possible pre-seismic anomaly was observed about one week before the largest earthquake that occurred in this region during the observation period (March 6, 1984; M = 7.9, D = 1000 km). Another possible pre-seismic anomaly was observed about three days before two nearby large earthquakes that occurred at almost the same place in a time interval of 53 min (February 6, 1987; M = 6.4 and M = 6.7, D = 130 km).     

Box fractal dimension as a measure of statistical homogeneity of jointed rock masses

A written computer programme to estimate the box fractal dimension (D_B) is verified by estimating D_B of the triadic Koch curve for which the theoretical D is known. The influence of a number of input parameters of the box-counting method on the accuracy of estimated D_B is evaluated using the same Koch curve. The employed size range of the applied box networks was found to be the parameter which has the strongest influence on the accuracy of estimated D_B. This indicated the importance of finding the range of self-similarity or self-affinity for the object considered to select the proper range for the box sizes and, in turn, to obtain accurate estimates of D_B. By calculating D_B for different block sizes sampled from three generated two-dimensional joint patterns, it is shown that D_B can capture the combined effect of joint-size distribution and joint density on the statistical homogeneity of rock masses. The spatial variation of D_B along a 350 m stretch of a tunnel in the shiplock area of the Three Gorges dam site is computed using the joint data mapped on the walls and the roof of the tunnel. This spatial variation of D_B is used, along with the visual geological evaluation of the joint trace maps of the tunnel, in making decisions about statistical homogeneity of the rock mass around the tunnel. The results obtained on statistically homogeneous regions were found to be quite similar to the results obtained from a previous statistical homogeneity investigation which incorporated the effect of number of joint sets and their orientation distributions, but not the spatial variation of D_B. It is recommended that the spatial variation of D_B is used, along with the results of other methods such as contingency table analysis and equal area plots, which incorporate the effect of joint orientation distribution, in addition to the geology of the site, in determining the statistically homogeneous regions of jointed rock masses.     

青藏高原大型深层蠕滑型滑坡变形机制研究进展与展望

大型深层蠕滑型滑坡在青藏高原怒江、澜沧江、金沙江、岷江等地形地貌和地质构造复杂区极为发育,具有规模大、滑带深、渐进变形破坏显著等特点,按照滑坡空间结构主要有后缘洼地蠕滑型、顺层基岩蠕滑型和厚层松散堆积物蠕滑型等3种类型,往往表现为长期蠕滑-间歇性复活-整体滑动.通过梳理大型深层蠕滑型滑坡稳定性影响因素、滑带土工程地质力学性质、地下水渗流场特征与降雨诱发滑坡滞后性以及渐进变形破坏机制和动态稳定性等4个方面的研究进展,提出了3个关键科学问题与4个主要研究方向.建议加强深层滑带土在渗流场-应力场等多场耦合作用下的工程地质力学特性研究、加强剖析滑坡岩土体的非均质渗透特性及地下水分布特征分析,研究不同雨强和历时条件下降雨有效入渗机理,研究大型深层蠕滑型滑坡的降水入渗响应过程和降水诱发滑坡变形的滞后性,提出基于渐进变形破坏的滑坡动态稳定性评价方法,为地质灾害早期判识和综合防范提供理论依据.     

The effect of Ca-Tschermaks component on trace element partitioning between clinopyroxene and silicate melt

We have studied the influence of Ca-Tschermaks (Calcium Tschermaks or CaTs) content of clinopyroxene on the partitioning of trace elements between this phase and silicate melt at fixed temperature and pressure. Ion probe analyses of experiments carried out in the system Na₂O–CaO–MgO–Al₂O₃–SiO₂, at 0.1 MPa and 1218°C, produced crystal-melt partition coefficients (D) of 36 trace elements (Li, Cl, Sc, Ti, V, Cr, Fe, Co, Ge, Sr, Y, Zr, Nb, Mo, Ru, Rh, In, Sn, Sb, Ba, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Ta and W), for clinopyroxene compositions between 10 and 32 mol% CaTs. Partition coefficients for 2+ to 5+ cations show, for each charge, a near parabolic dependence of log D on ionic radius of the substituting cation, for partitioning into both the M1 and M2 sites of clinopyroxene. Fitting the results to the elastic strain model of Blundy and Wood [Blundy, J.D., Wood, B.J., 1994. Prediction of crystal-melt partition coefficients from elastic moduli. Nature 372, 452–454] we obtain results for the strain-free partition coefficients of theoretical cations (D₀), with site radius r₀, and for the site's Young's Modulus (E).

In agreement with earlier data our results show that increasing ^ivAl concentration in cpx is matched by increasing D, E_M1, E_M2 and D₀ for tri-, tetra- and pentavalent cations. The degree of fractionation between chemically similar elements (i.e. Ta/Nb, Zr/Hf) also increases. In contrast, D values for mono-, di- and hexavalent cations decrease with increasing ^ivAl in the cpx. The large suite of trace elements used has allowed us to study the effects of cation charge on D₀, r₀ and E. We have found that D₀ and r₀ decrease with increasing cation charge, e.g. r₀=0.66 Å for 4+ cations and 0.59 Å for 5+ cations substituting into M1. Values of E_M1 and E_M2 increase with cation charge as well as with increasing ^ivAl content. The increase in E_M2 is linear and close to the trend set by Hazen and Finger [Hazen, R.M., Finger, L.W., 1979. Bulk modulus-volume relationship for cation–anion polyhedra. J. Geophys. Res. 84 (10) 6723–6728] for oxides. E_M1 values are much higher and do not fit the trend predicted by the Hazen and Finger relationship.     

A palaeomagnetic study of some basaltoids and ores from the Pontic Ranges, Northern Turkey: Palaeogeographic implications

The palaeomagnetism of basic rocks and sulphide ores has been studied in the Küre area, Pontic Ranges, Turkey. Progressive alternating-field demagnetization revealed a characteristic remanent magnetization in all investigated rock types except a dacite. The following virtual geomagnetic poles were obtained:

Basalt and quartz diabase (oldest): D = 59°, I = +66°, ₉₅ = 4.8, pole 49°N, 93°E. Diabase: D = 210°, I = −15°, ₉₅ = 15.0, pole 47°N, 167°E. Massive sulphide ores: D = 107°, I = +63°, ₉₅ = 8.7, pole 18°N, 80°E. Peridotite: D = 131°, I = +54°, ₉₅ = 10.9, pole 2°S, 72°E. Amphibolitized diabase (youngest): D = 293°, I = +59°, ₉₅ = 12.6, pole 40°S, 145°E.

The longidutinal difference in pole positions between the oldest and the youngest rocks is interpreted as being due to a post-Permian counterclockwise rotation of the studied region in relation to the African continent. In addition, there are indications of local rotational movements within the Küre area.     

Estimation of dynamic friction and movement history of large landslides

We performed seismic waveform inversions and numerical landslide simulations of deep-seated landslides in Japan to understand the dynamic evolution of friction of the landslides. By comparing the forces obtained from a numerical simulation to those resolved from seismic waveform inversion, the coefficient of friction during sliding was well-constrained between 0.3 and 0.4 for landslides with volumes of 2–8 ×10⁶ m³. We obtained similar coefficients of friction for landslides with similar scale and geology, and they are consistent with the empirical relationship between the volume and dynamic coefficient of friction obtained from the past studies. This hybrid method of the numerical simulation and seismic waveform inversion shows the possibility of reproducing or predicting the movement of a large-scale landslide. Our numerical simulation allows us to estimate the velocity distribution for each time step. The maximum velocity at the center of mass is 12–36 m/s and is proportional to the square root of the elevation change at the center of mass of the landslide body, which suggests that they can be estimated from the initial DEMs. About 20% of the total potential energy is transferred to the kinetic energy in our volume range. The combination of the seismic waveform inversion and the numerical simulation helps to obtain the well-constrained dynamic coefficients of friction and velocity distribution during sliding, which will be used in numerical models to estimate the hazard of potential landslides.