Developments in a non-destructive method of determining rock strength

Material strength is an important variable for any study of the relationships between rock mass geomechanical characteristics and landform development. Standard field and laboratory tests for measuring strength present a variety of problems to the geomorphologist. Recent studies (Allison, 1988) have described a laboratory based non-destructive method for indirectly determining material strength, by measuring Dynamic Young's Modulus. Data presented here suggest that the same apparatus can be used as a field technique. Tests have been conducted on the Devonian limestone of the Napier Range, Western Australia. Laboratory results obtained using the non-destructive ultrasonic apparatus have a high correlation with triaxial Hoek Cell tests. Results from on-site tests have much greater accuracy than data collected using the Schmidt hammer, which is currently the most widely used geomorphological field technique for determining rock strength.     

Developments in a non-destructive method of determining rock strength: A reply

In a previous publication (Allison, 1989), a non-destructive method for indirectly determining rock strength by measuring Dynamic Young's Modulus was described. Data were presented to assess the Grindosonic apparatus in relation to standard laboratory techniques. A further Short Communication (Allison, 1990) evaluated the non-destructive test as a field technique, in part achieved by comparing the Grindosonic results with data collected using the Schmidt hammer. The Schmidt hammer is a widely used field technique in geomorphology for determining rock strength (see for example Day and Goudie, 1977; Day, 1981). Allison (1989, 1990) also suggested that the elastic properties of materials are becoming increasingly important in geomorphological studies. The opportunity to provide additional information and comments here is appreciated.     

Rock resistance to erosion: Some further considerations

Rock resistance to erosion is an often described factor in geomorphic studies, and is generally considered to strongly influence the shape of erosional landforms. However, the property of the rock mass that enables it to resist erosion is rarely considered, and its measurement is rarely justified and assessed adequately. Allison (1988, 1990) examined the intact strength properties of several types of carbonate rocks and considered that dynamic Young's modulus is a good indicator of rock material strength for geomorphic purposes, and cast doubts on the reliability of Schmidt hammer tests for this purpose. Alternative approaches to rock characterization from the view point of evaluating rock intact strength are considered.     

Amplitude variation with incident angle and azimuth inversion for Young's impedance,Poisson's ratio and fracture weaknesses in shale gas reservoirs

By analogy with P- and S-wave impedances, the product of Young's modulus and density can be termed as Young's impedance, which indicates the rock lithology and brittleness of unconventional hydrocarbon reservoirs. Poisson's ratio is also an effective indicator of rock brittleness and fluid property of unconventional reservoirs, and fracture weaknesses indicate the fracture properties (fracturing intensity and fracture fillings) in fracture-induced unconventional reservoirs. We aim to simultaneously estimate the Young's impedance, Poisson's ratio and fracture weaknesses from wide-azimuth surface seismic data in a fracture-induced shale gas reservoir, and use the horizontal transversely isotropic model to characterize the fractures. First, the linearized PP-wave reflection coefficient in terms of Young's impedance, Poisson's ratio, density and fracture weaknesses is derived for the case of a weak-contrast interface separating two weakly horizontal transversely isotropic media. In addition, an orthorhombic anisotropic case is also discussed in this paper. Then a Bayesian amplitude variation with incident angle and azimuth scheme with a model constraint is used to stably estimate Young's impedance, Poisson's ratio and fracture weaknesses with only PP-wave azimuthal seismic data. The proposed approach is finally demonstrated on both synthetic and real data sets with reasonable results.     

Prestack amplitude versus angle inversion for Young's modulus and Poisson's ratio based on the exact Zoeppritz equations

Elastic parameters such as Young's modulus, Poisson's ratio, and density are very important characteristic parameters that are required to properly characterise shale gas reservoir rock brittleness, evaluate gas characteristics of reservoirs, and directly interpret lithology and oil‐bearing properties. Therefore, it is significant to obtain accurate information of these elastic parameters. Conventionally, they are indirectly calculated by the rock physics method or estimated by approximate formula inversion. The cumulative errors caused by the indirect calculation and low calculation accuracy of the approximate Zoeppritz equations make accurate estimation of Young's modulus, Poisson's ratio, and density difficult in the conventional method. In this paper, based on the assumption of isotropy, we perform several substitutions to convert the Zoeppritz equations from the classical form to a new form containing the chosen elastic constants of Young's modulus, Poisson's ratio, and density. The inversion objective function is then constructed by utilising Bayesian theory. Meanwhile, the Cauchy distribution is introduced as a priori information. We then combine the idea of generalised linear inversion with an iterative reweighed least squares algorithm in order to solve the problem. Finally, we obtain the iterative updating formula of the three elastic parameters and achieve the direct inversion of these elastic parameters based on the exact Zoeppritz equations. Both synthetic and field data examples show that the new method is not only able to obtain the two elastic parameters of Young's modulus and Poisson's ratio stably and reasonably from prestack seismic data but also able to provide an accurate estimation of density information, which demonstrates the feasibility and effectiveness of the proposed method. The proposed method offers an efficient seismic method to identify a “sweet spot” within a shale gas reservoir.     

SPECIFICATION OF TWO MODULI OF A VISCOELASTIC MATERIAL *

In order to adequately understand the complicated, anelastic processes governing wave propagation in soils or highly weathered rock it seems desirable first to have available a convenient laboratory material for such propagation studies the frequency dependent rheological parameters of which are known beforehand. A property measurement program has been conducted to determine the complex Young's modulus and the complex shear modulus of a commercially available viscoelastic material over a broad spectral region.     

Transient response of a thick beam of bimodular material

Certain materials have different elastic behaviour when they are loaded in tension as compared to compression. As an engineering approximation, they are usually modelled as a bimodular material, i.e. a bilinear material having different Young's moduli in tension and in compression. All of the previous analyses of bimodular beams known to the present investigators have been concerned with either static loading or harmonic vibration. Thus, the present work is believed to be the first to consider transient response of such beams. The transfer-matrix method is used to discretize spatially, while the timewise discretization is accomplished by use of the Newmark beta method.     

AN ULTRASONIC PROFILING INVESTIGATION ON SOME FRESH AND WEATHERED GRANITES OF HYDERABAD,INDIA*

The ultrasonic profiling method of measuring the compressional and shear wave velocities in cylindrical rock samples is extended to measurements in some weathered and fresh granite blocks collected from the Hyderabad (India) region. This possibility of the method provides a means of investigating the elastic properties of the less compact rocks, of which the near-surface formations are particularly important. In this article the important parts of the ultrasonic profiling instrument developed are described and the relevant aspects of the seismic wave fields and identification of the individual waves in the wavetrain responses to longitudinal excitation are considered. Compressional, shear and surface (Rayleigh) wave velocities in some fresh and weathered granites are detailed. The compressional velocities range from 4.8 km/s to 5.5 km/s in fresh granites and lie between 1.1 km/s and 2.5 km/s in weathered granites. Young's modulus and Poisson's ratios computed from the measured velocities are also presented. An empirical relation of the form log E= 4.27 + 2.11 log V_p between Young's modulus E and compressional velocities V_p in the fresh granites studied is deduced. The versatility of the approach is thus demonstrated.     

Dynamic properties of microfine cement grouted sands

Torsional resonant column and bender element tests were conducted on microfine and ordinary cement grouted sands and the effects of confining pressure, shear strain, grout water-to-cement (W/C) ratio, cement type and gradation on the dynamic properties were evaluated. The shear and initial Young's moduli of the grouted sands increased with increasing confining pressure and decreasing shear strain, while damping ratio had the opposite behavior. The grout W/C ratio had the strongest effect on the values of the dynamic properties of the grouted sands, followed by cement grain size and cement pozzolan content. Depending on grout W/C ratio and confining pressure, the shear and initial Young's moduli values and the damping ratio values of the clean sands were improved by a factor of 4–25 and 2–6, respectively. The effect of testing conditions or material parameters on the Poisson ratio values of the grouted sands was negligible.     

Dynamics of deformation and water flow in heterogeneous porous media and its impact on soil properties

The interaction of geomechanics and flow within a soil body induces deformation and pore pressure change. Deformation may change hydrogeological and elastic properties, which alters the mechanical behaviour and results in non‐linearity. To investigate this interaction effect in a heterogeneous porous medium, a stochastic poroelastic model is proposed. Monte Carlo simulations are performed to determine the mean and uncertainty of the parameter changes, displacement, and change in pore water pressure. Hydraulic conductivity is treated as the only random variable in the coupled geomechanics‐flow system due to its large variation compared to other mechanical and hydrogeological properties in natural environments. The three considered non‐linear models for the interaction between parameters and deformation are those that consider (1) porosity and hydraulic conductivity; (2) porosity and Young's modulus; and (3) a combined effect that includes porosity, hydraulic conductivity, and Young's modulus. Boundary effects on the coupled system are also explored. The relationships between changes of porosity, hydraulic conductivity, and Young's modulus are analytically shown to be non‐linear. Among the considered parameters, the deformation effect induces the largest reduction in hydraulic conductivity. The deformation‐induced change in hydraulic conductivity shows the most significant effect on the mean and variance of the change in pore water pressure and displacement, while changes in Young's modulus have the least effect. When the deformation effect is considered, the superposition relationship does not exist in the mean displacement and mean change in pore water pressure for the three scenarios considered; it exists for the case without deformation effects. Deformation also causes a reduction in the effective hydraulic conductivity for the whole domain. The scenario that considers both loading and discharge boundaries has larger changes in hydrogeological and geo‐mechanical parameters than those in scenarios that consider loading and discharge boundaries separately. The results indicate that the interaction between deformation and changes in parameters has a profound effect on the poroelastic system. The effect of deformation should thus be considered in modelling and practice. Copyright © 2009 John Wiley & Sons, Ltd.     

The excavation disturbed zone (EDZ) at Kiirunavaara mine,Sweden—by seismic measurements

The presence of an excavation disturbed zone (EDZ) around an excavation boundary can significantly affect the overall performance of the excavation and the general safety of men and equipment. Hence, it has been an important subject of research in various rock excavation projects. The EDZ is generally defined as the rock zone beyond the excavation boundary where the physical, mechanical and hydraulic properties of the rock have been significantly affected due to the excavation and redistribution of stresses. For LKAB's Kiirunavaara underground iron ore mine in Sweden, the understanding of the EDZ is essential for optimal design of rock support. With this main objective an EDZ investigation was conducted at the mine using seismic measurement techniques. Cross-hole seismics and spectral analyses of surfaces waves (SASW) were the main techniques used. Borehole Image Processing Systems (BIPS) complemented the seismic measurements. The results show that an EDZ with a thickness of 0.5–1. 0 m existed behind the boundaries of the mining drifts being investigated. The magnitude of the Young's modulus of this zone was 50% to 90% of that of the undisturbed rock.     

Laboratory measurements of seismic attenuation and Young's modulus dispersion in a partially and fully water‐saturated porous sample made of sintered borosilicate glass

We measured the extensional‐mode attenuation and Young's modulus in a porous sample made of sintered borosilicate glass at microseismic to seismic frequencies (0.05–50 Hz) using the forced oscillation method. Partial saturation was achieved by water imbibition, varying the water saturation from an initial dry state up to ～99%, and by gas exsolution from an initially fully water‐saturated state down to ～99%. During forced oscillations of the sample effective stresses up to 10 MPa were applied. We observe frequency‐dependent attenuation, with a peak at 1–5 Hz, for ～99% water saturation achieved both by imbibition and by gas exsolution. The magnitude of this attenuation peak is consistently reduced with increasing fluid pressure and is largely insensitive to changes in effective stress. Similar observations have recently been attributed to wave‐induced gas exsolution–dissolution. At full water saturation, the left‐hand side of an attenuation curve, with a peak beyond the highest measured frequency, is observed at 3 MPa effective stress, while at 10 MPa effective stress the measured attenuation is negligible. This observation is consistent with wave‐induced fluid flow associated with mesoscopic compressibility contrasts in the sample's frame. These variations in compressibility could be due to fractures and/or compaction bands that formed between separate sets of forced‐oscillation experiments in response to the applied stresses. The agreement of the measured frequency‐dependent attenuation and Young's modulus with the Kramers–Kronig relations and additional data analyses indicate the good quality of the measurements. Our observations point to the complex interplay between structural and fluid heterogeneities on the measured seismic attenuation and they illustrate how these heterogeneities can facilitate the dominance of one attenuation mechanism over another.     

“应力窗口”的数学模拟

本文采用二维平面应变问题的有限单元法,对唐山地震前华北冀中断块坳陷地区的“应力窗口”进行了数值模拟。初步讨论了模拟区的应力集中部位与介质杨氏模量、压应力值、主压应力取向、边界约束条件变化的关系,根据模拟区地震活动与唐山大震前“应力窗口”的时空分布特征,粗略地模拟了邢台余震区“应力窗口”显示、消失的过程。     

An indirect method of determining magnitudes of erosion using the c/p' ratio

An approximate method is described for determining the maximum consolidating pressure in a hard, heavily overconsolidated fissured clay. From this, the overburden thickness producing the observed degree of consolidation has been calculated. The normal method of calculating preconsolidation pressure using an oedometer was not possible. The ratio c/p' is used in conjunction with the undrained shear strength. Values of c/p' are determined using empirical relationships with Atterberg Limit values. The results allow an overburden thickness to be calculated by assuming a value for unit weight.     

Strength matters: Resisting erosion across upland landscapes

Soil-covered upland landscapes comprise a critical part of the habitable world and our understanding of their evolution as a function of different climatic, tectonic, and geologic regimes is important across a wide range of disciplines. Soil production and transport play essential roles in controlling the spatial variation of soil depth and therefore hillslope hydrological processes, distribution of vegetation, and soil biological activity. Field-based confirmation of the hypothesized relationship between soil thickness and soil production is relatively recent, however, and here we quantify a direct, material strength-based influence on variable soil production across landscapes. We report clear empirical linkages between the shear strength of the parent material (its erodibility) and the overlying soil thickness. Specifically, we use a cone penetrometer and a shear vane to determine saprolite resistance to shear. We find that saprolite shear strength increases systematically with overlying soil thickness across three very different field sites where we previously quantified soil production rates. At these sites, soil production rates, determined from in situ produced beryllium-10 (¹⁰Be) and aluminum-26 (²⁶Al), decrease with overlying soil thickness and we therefore infer that the efficiency of soil production must decrease with increasing parent material shear strength. We use our field-based data to help explain the linkages between biogenic processes, chemical weathering, hillslope hydrology, and the evolution of the Earth's surface. © 2019 John Wiley & Sons, Ltd.     

Soil-structure interaction for tower structures

The soil-structure system is modelled as a uniform vertical beam, which terminates in a base or foundation mass; this mass is attached to the surface of an elastic half-space. Using known force-displacement relations for the coupled vibrations of a rigid disc on an elastic half-space, the natural frequencies and response to a transverse harmonic force, applied at the tip of the beam, are determined through a continuum approach. Effectively the problem reduces to a beam with frequency-dependent boundary conditions. A parametric study shows that changes in the three ratios, Young's modulus for the beam to that for the half-space, the radius of the base mass to the length of the beam, L, and the second moment of area of the beam cross-section/L⁴, cause large variations in the maximum response, which due to interaction can be considerably smaller or larger than that for a comparable fixed-base cantilever beam. This dynamic behaviour can be explained by considering the variation of natural frequencies, mode shapes and modal damping factors with these ratios. A brief study of the response of the structure to a free-field harmonic acceleration, applied at the soil-structure interface, suggests that interaction depends upon material and geometric properties of the system, rather than on the nature of the excitation.     

Influence of Bedding and Mineral Composition on Mechanical Properties and Its Implication for Hydraulic Fracturing of Shale Oil Reservoirs

The premise of hydraulic fracturing is to have an accurate and detailed understanding of the rock mechanical properties and fracture propagation law of shale reservoirs. In this paper, a comprehensive evaluation of the mechanical properties of the shale oil reservoir in the south of Songliao Basin is carried out. Based on the experiments and the in-situ stress analysis, the fracture propagation law of three types of shale reservoirs is obtained, and the suggestions for fracturing are put forward. The results have shown that the fracture propagation of pure shale and low mature reservoir is easy to open along the bedding plane under compression loading, which is greatly influenced by the bedding. Sand-bearing shale is slightly better, the fractures of which are not easy to open along the bedding plane. The mechanical experimental results show that all the samples have the characteristics of low compressive strength, low Young''s modulus and strong anisotropy, indicating that the shale oil reservoir is certain plastic, which is related to its high clay mineral content and controlled by the bedding development. Compared with pure shale and low mature shale, the sand-bearing shale has less clay content and less developed bedding, which maybe the main reason for its slightly better brittleness. Overall, the expansion of hydraulic fracture is controlled by in-situ stress and bedding. Because of the development of bedding, it is easy to form horizontal fractures. Thus it is not suitable for horizontal well fracturing. Because of the high content of clay minerals, the applicability of conventional slick hydraulic fracturing fluid is poor. It is suggested to use vertical well or directional well to carry out volume fracturing. In this way, the effect of bedding can be effectively used to open and connect the bedding and form a larger fracture network.     

PHYSICAL PROPERTIES OF SYNTHETIC SANDSTONE ROCKS1

A novel process is used to coat glass spheres with a polymerizing thermo-setting resin, only microns thick. Synthetic rocks of known grain size distribution and pore space characteristics are then made by heating the resin-coated glass spheres under compression in a special mould. The dynamic Young's moduli of these rocks are found to be affected by the percentage of resin content (cement) and the synthetic diagenesis rather than the grain size and permeability.     

Stiffened steel box columns. Part 2: Ductility evaluation

The purpose of this study is to evaluate the ultimate strength and ductility capacity of stiffened steel box columns failed by local and overall interaction instability under a constant compressive axial force and cyclic lateral loading. In a companion paper, a finite element formulation accounting for both geometrical and material non‐linearity was developed to obtain cyclic hysteretic behaviour of such columns. In this paper, the effect of loading patterns on the cyclic inelastic behaviour is first studied; then, a parametric study is carried out to investigate the effects of flange plate width–thickness ratio parameter, column slenderness ratio parameter, stiffener's equivalent slenderness ratio parameter, magnitude of axial load, and material type of stiffeners on the strength and ductility of the columns. Last but not least, empirical formulae of both the ultimate strength and ductility capacities are proposed for stiffened steel box columns, and the limit values of various parameters for the required ductility demand are also discussed. Copyright © 2000 John Wiley & Sons, Ltd.     

平面应变条件下基于弹性理论的土压力计算及适用性研究

针对工程中大量存在的平面应变问题,依据平面应变条件和广义胡克定律,基于SMP、Lade-Duncan、AC-SMP和广义Mises强度准则,推导出考虑中主应力及泊松比影响的无黏性土主、被动土压力计算公式,并将其扩展至黏性土,讨论基于各强度准则土压力计算公式的适用范围。结果表明：考虑中主应力对土强度的贡献后,基于各强度准则所计算的主动土压力均小于朗肯主动土压力,被动土压力均大于朗肯被动土压力;主动土压力P_a随着泊松比的增大而减小,被动土压力P_P随着泊松比的增大而增大,且泊松比越大,与实测数据更为接近;基于同一强度准则下得到的主、被动土压力适用的内摩擦角范围随着泊松比的增大而增大;基于各强度准则的土压力计算公式均能较好的描述挡土结构上土压力的大小,其中广义Mises强度准则计算结果与实际工程更为吻合,研究成果可为挡土结构上土压力的计算提供一定理论参考。