Upscaling of elastic properties for large scale geomechanical simulations

Large scale geomechanical simulations are being increasingly used to model the compaction of stress dependent reservoirs, predict the long term integrity of under‐ground radioactive waste disposals, and analyse the viability of hot‐dry rock geothermal sites. These large scale simulations require the definition of homogenous mechanical properties for each geomechanical cell whereas the rock properties are expected to vary at a smaller scale. Therefore, this paper proposes a new methodology that makes possible to define the equivalent mechanical properties of the geomechanical cells using the fine scale information given in the geological model. This methodology is implemented on a synthetic reservoir case and two upscaling procedures providing the effective elastic properties of the Hooke's law are tested. The first upscaling procedure is an analytical method for perfectly stratified rock mass, whereas the second procedure computes lower and upper bounds of the equivalent properties with no assumption on the small scale heterogeneity distribution. Both procedures are applied to one geomechanical cell extracted from the reservoir structure. The results show that the analytical and numerical upscaling procedures provide accurate estimations of the effective parameters. Furthermore, a large scale simulation using the homogenized properties of each geomechanical cell calculated with the analytical method demonstrates that the overall behaviour of the reservoir structure is well reproduced for two different loading cases. Copyright © 2004 John Wiley & Sons, Ltd.     

Fluid infiltration during contact metamorphism of interbedded marble and calc-silicate hornfels, Twin Lakes area, central Sierra Nevada, California

Abstract In the Twin Lakes area, central Sierra Nevada, California, most contact metamorphosed marbles contain calcite + dolomite + forsterite ± diopside ± phlogopite ± tremolite, and most calc-silicate hornfelses contain calcite + diopside + wollastonite + quartz ± anorthite ± K-feldspar ± grossular ± titanite. Mineral-fluid equilibria involving calcite + dolomite + tremolite + diopside + forsterite in two marble samples and wollastonite + anorthite + quartz + grossular in three hornfels samples record P± 3 kbar and T± 630° C. Various isobaric univariant assemblages record CO₂-H₂O fluid compositions of χCO₂= 0.61–0.74 in the marbles and χCO₂= 0.11 in the hornfelses. Assuming a siliceous dolomitic limestone protolith consisting of dolomite + quartz ° Calcite ± K-feldspar ± muscovite ± rutile, all plausible prograde reaction pathways were deduced for marble and hornfels on isobaric T-XCO₂ diagrams in the model system K₂O-CaO-MgO-Al₂O₃-SiO₂-H₂O-CO₂. Progress of the prograde reactions was estimated from measured modes and mass-balance calculations. Time-integrated fluxes of reactive fluid which infiltrated samples were computed for a temperature gradient of 150 °C/km along the fluid flow path, calculated fluid compositions, and estimated reaction progress using the mass-continuity equation. Marbles and hornfelses record values in the range 0.1–3.6 × 10⁴ cm³/cm² and 4.8–12.9 × 10⁴ cm³/cm², respectively. For an estimated duration of metamorphism of 10⁵ years, average in situ metamorphic rock permeabilities, calculated from Darcy's Law, are 0.1–8 × 10^?6 D in the marbles and 10–27 × 10^?6 D in the hornfelses. Reactive metamorphic fluids flowed up-temperature, and were preferentially channellized in hornfelses relative to the marbles. These results appear to give a general characterization of hydrothermal activity during contact metamorphism of small pendants and screens (dimensions ± 1 km or less) associated with emplacement of the Sierra Nevada batholith.     

Contribution of storms to groundwater recharge in the semi‐arid region of Karnataka,India

This paper describes the application of environmental isotopes and injected tracer techniques in estimating the contribution of storms as well as annual precipitation to groundwater recharge and its circulation, in the semi‐arid region of Bagepalli, Kolar district, Karnataka. Environmental isotopes ²H, ¹⁸O and ³H were used to study the effect of storms on the hydrological system, and an isotope balance was used to compute the contribution of a storm component to the groundwater. Some of the groundwater samples collected during the post‐storm periods were highly depleted in stable isotope content with higher deuterium excess relative to groundwater from the pre‐storm periods. Significant variation in deuterium excess in groundwater from the same area, collected in two different periods, indicates the different origin of air masses. The estimated recharge component of a storm event of 600 mm to the groundwater was found to be in the range of 117–165 mm. There was no significant variation in environmental tritium content of post‐storm and pre‐storm groundwater, indicating the fast circulation of groundwater in the system. After completion of the environmental isotope work, an injected radiotracer ³H technique was applied to estimate the direct recharge of total precipitation to the groundwater. The estimated recharge to the groundwater is 33 mm of the 550 mm annual precipitation during 1992. Copyright © 2003 John Wiley & Sons, Ltd.     

A new stereo‐analytical method for determination of removal blocks in discontinuous rock masses

The paper provides a new stereo‐analytical method, which is a combination of the stereographic method and analytical methods, to separate finite removable blocks from the infinite and tapered blocks in discontinuous rock masses. The methodology has applicability to both convex and concave blocks. Application of the methodology is illustrated through examples. Addition of this method to the existing block theory procedures available in the literature improves the capability of block theory in solving practical problems in rock engineering. Copyright © 2003 John Wiley & Sons, Ltd.     

Hysteresis‐based analysis of overland metal transport

Introducing a concept of equivalent mass depth of flow, this study describes the phenomenon of non‐point source pollutant (metal) transport for pavement (or overland) flow in analogy with wave propagation in wide open channels. Hysteretic and normal mass rating curves are developed for runoff rate and mass of 12 dissolved and particulate‐bound metal elements (pollutants) using the rainfall‐runoff and water quality data of the 15 × 20 m² instrumented pavement in Cincinnati, USA. Normal mass rating curves developed for easy computation of pollutant load are found to be of a form similar to Manning's, which is valid for open channel flows. Based on the hysteresis analysis, wave types for dissolution and mixing of particulate‐bound metals are identified. The analysis finds that the second‐order partial‐differential equation normally used for metal transport does not have the efficacy to describe fully the strong non‐linear phenomena such as is described for various metal elements by dynamic waves. In addition, the proportionality concept of the popular SCS‐CN concept is extended for determining the potential maximum metal mass M_p of all the 12 elements transported by a rain storm and related to the antecedent dry period (ADP). For the primary metal zinc element, M_p is found to increase with the ADP and vice versa. Copyright © 2003 John Wiley & Sons, Ltd.     

四川某矿山边坡失稳机理及稳定性评价

四川某矿山开采边坡迄今已有30余年,随采区规模的逐渐扩大,在矿区南坡构成一典型的顺层开挖边坡,因矿层中夹有不同数量的软弱夹层,在边坡前缘破坏坡角、并加上降雨及爆破振动影响,时常发生颁层滑坡,不仅给矿山人民生命财产带来严重危害,而且也严重制约矿山的正常发展。通过对典型开挖边坡所在部位的工程地质条件凋查,在确定影响边坡稳定的主要控制因素和边界条件的基础上。考虑四种工况条件下的稳定性分析和评价,为矿山下一步施工提出了较为合理的开挖方案。     

Vertical structures of PM10 and PM 2.5 and their dynamical character in low atmosphere in Beijing urban areas

The vertical structures and their dynamical character of PM2.5 and PM10 over Beijing urban areas are revealed using the 1 min mean continuous mass concentration data of PM2.5 and PM10 at 8, 100, and 320 m heights of the meteorological observation tower of 325 m at Institute of Atmospheric Physics, Chinese Academy of Sciences (IAP CAS tower hereafter) on 10―26 August, 2003, as well as the daily mean mass concentration data of PM2.5 and PM10 and the continuous data of CO and NO2 at 8, 100 (low layer), 200 (middle layer), and 320 m (high layer) heights, in combination with the same period meteorological field observation data of the meteorological tower. The vertical distributions of aerosols observed on IAP CAS tower in Beijing can be roughly divided into two patterns: gradually and rapidly decreasing patterns, I.e. The vertical distribution of aerosols in calm weather or on pollution day belongs to the gradually decreasing pattern, while one on clean day or weak cold air day belongs to the rapidly decreasing pattern. The vertical distributive characters of aerosols were closely related with the dynamical/thermal structure and turbulence character of the atmosphere boundary layer. On the clean day, the low layer PM2.5 and PM10 concentrations were close to those at 8 m height, while the concentrations rapidly decreased at the high layer, and their values were only one half of those at 8 m, especially, the concentration of PM2.5 dropped even more. On the clean day, there existed stronger turbulence below 150 m, aerosols were well mixed, but blocked by the more stronger inversion layer aloft, and meanwhile, at various heights, especially in the high layer, the horizontal wind speed was larger, resulting in the rapid decrease of aerosol concentration, I.e. Resulting in the obvious vertical difference of aerosol concentrations between the low and high layers. On the pollution day, the concentrations of PM2.5 and PM10 at the low, middle, and high layers dropped successively by, on average, about 10% for each layer in comparison with those at 8 m height. On pollution days, in company with the low wind speed, there existed two shallow inversion layers in the boundary layer, but aerosols might be, to some extent, mixed below the inversion layer, therefore, on the pollution day the concentrations of PM2.5 and PM10 dropped with height slowly; and the observational results also show that the concentrations at 320 m height were obviously high under SW and SE winds, but at other heights, the concentrations were not correlated with wind directions. The computational results of footprint analysis suggest that this was due to the fact that the 320 m height was impacted by the pollutants transfer of southerly flow from the southern peripheral heavier polluted areas, such as Baoding, and Shijiazhuang of Hebei Province, Tianjin, and Shandong Province, etc., while the low layer was only affected by Beijing's local pollution source. The computational results of power spectra and periods preliminarily reveal that under the condition of calm weather, the periods of PM10 concentration at various heights of the tower were on the order of minutes, while in cases of larger wind speed, the concentrations of PM2.5 and PM10 at 320 m height not only had the short periods of minute-order, but also the longer periods of hour order. Consistent with the conclusion previously drawn by Ding et al., that air pollutants at different heights and at different sites in Beijing had the character of "in-phase" variation, was also observed for the diurnal variation and mean diurnal variation of PM2.5 and PM10 at various heights of the tower in this experiment, again confirming the "in-phase" temporal/spatial distributive character of air pollutants in the urban canopy of Beijing. The gentle double-peak character of the mean diurnal variation of PM2.5 and PM10 was closely related with the evident/similar diurnal variation of turbulent momentum fluxes, sensible heat fluxes, and turbulent kinetic energy at various heights in the urban canopy. Besides, under the condition of calm weather, the concentration of PM2.5 and PM10 declined with height slowly, it was 90% of 8 m concentration at the low layer, a little lesser than 90% at the middle layer, and 80% at the high layer, respectively. Under the condition of weak cold air weather, the concentration remarkably dropped with height, it was 70% of 8 m concentration at the low layer, and 20%―30% at the middle and high layers, especially the concentration of PM2.5 was even lower.     

FluBiDi – a model to estimate flood based on runoff: validation using extreme and natural basin conditions

FluBiDi is a two-dimensional model created to simulate real events that can take days and months, as well as short events (minutes or hours) and inclusive laboratory tests. To verify the robustness of FluBiDi, it was tested using a previous study with both designed and real digital elevation models. The results highlight good agreement between the models (i.e. Mike Flood, SOBEK, ISIS 2D, and others) tested and FluBiDi (around 90% for a specific instant and 95% for the complete time simulation). In the simulated hydrographs, the discharge peak value, time to peak, and water level results were accurate, reproducing them with an error of less than 5%. The velocity differences observed in a couple of tests in FluBiDi were associated with very short periods of time (seconds). However, FluBiDi is highly accurate for simulating floods under real topographical conditions with differences of around 2 cm when water depth is around 150 cm. The average water depth and velocities are precise, and the model describes with high accuracy the pattern and extent of floods. FluBiDi has the capability to be adjusted to different types of events and only requires limited input data.     

厦蓉高速公路某隧道洞口段开挖对仰坡变形影响的数值分析

针对一座浅埋偏压隧道,采用FLAC3D对该隧道进口段进洞开挖进行动态施工三维数值模拟。基于围岩应力分布特征,仰坡坡面轴向和横向位移的变化特征,分析了偏压浅埋隧道洞口段开挖引起的仰坡变形规律。计算结果揭示：仰坡后缘下沉,前缘向洞心外有移动趋势;隧道开挖引起隧洞洞身附近岩体出现较大应力集中和变形现象,洞口段洞身以上仰坡坡面主要以竖向沉降为主,洞身两侧向洞内挤压。在此基础上提出了保证仰坡稳定和安全进洞的一些建议。