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1.
Natural rock joint roughness quantification through fractal techniques   总被引：8，自引：0，他引：8  
Accurate quantification of roughness is important in modeling hydro-mechanical behavior of rock joints. A highly refined variogram technique was used to investigate possible existence of anisotropy in natural rock joint roughness. Investigated natural rock joints showed randomly varying roughness anisotropy with the direction. A scale dependant fractal parameter, K v, seems to play a prominent role than the fractal dimension, D r1d, with respect to quantification of roughness of natural rock joints. Because the roughness varies randomly, it is impossible to predict the roughness variation of rock joint surfaces from measurements made in only two perpendicular directions on a particular sample. The parameter D r1d × K v seems to capture the overall roughness characteristics of natural rock joints well. The one-dimensional modified divider technique was extended to two dimensions to quantify the two-dimensional roughness of rock joints. The developed technique was validated by applying to a generated fractional Brownian surface with fractal dimension equal to 2.5. It was found that the calculated fractal parameters quantify the rock joint roughness well. A new technique is introduced to study the effect of scale on two-dimensional roughness variability and anisotropy. The roughness anisotropy and variability reduced with increasing scale.  相似文献   

2.
The observed fractal nature of both fault length distributions and earthquake magnitude-frequency distributions suggests that there may be a relationship between the structure of active fault systems and the resulting seismicity. In previous theoretical work, a positive correlation between the exponent D from the fracture length distribution, and the seismic or acoustic emission (AE) b-value has been inferred from a simple dislocation model of the seismic source. Here, we present the first experimental evidence for a correlation between D and b from a series of tensile fracture mechanics tests on crystalline rock, carried out in different environmental conditions, both air-dry and water-saturated, and at ambient temperature and pressure. The microseismic acoustic emissions were monitored during subcritical crack growth under controlled conditions of constant stress intensity, KI, and quantitative analyses of the resulting fracture patterns were carried out on the same specimens. It is found that AE b-values, ranging from 1.0 to 2.3, correlate negatively with the normalized stress intensity KI/KIC, where KIC is the fracture toughness of the specimen. The microcrack length distribution exponent D, ranges from 1.0 to 1.7. Fluid presence has a first-order influence on both the AE and structure produced in these experiments. For experiments at low stress intensity or high fluid content, the activation of the stress corrosion mechanism for KI < KIC leads to a greater relative proportion both of small cracks and of low amplitude acoustic emissions, reflected in higher values of D and b. The exponent D is found to correlate positively with the AE b-value.  相似文献   

3.
Summary Thirteen natural rock profiles (Barton and Choubey, 1977) are analyzed for their fractal properties. Most of the profiles were found to approximate fractal curves but some also showed features of specific wavelengths and amplitudes superimposed on fractal characteristics. The profiles showed fractal dimensions from 1.1 to 1.5 covering a range of selfsimilar and self-affine curves. The analysis results suggest a negative correlation between fractal dimension,D, and amplitude,A. Joint roughness coefficients (JRC) show a positive correlation with amplitude,A, and a negative correlation with fractal dimension,D. A numerical model of fracture closure is used to investigate the effects of different profile characteristics (D, A and sample size) on the nature of dilation and contact area, using the natural profiles and synthetic fractional Brownian motion profiles. Smooth profiles (low JRC, highD, lowA) display many small contact regions whereas rough fractures (high JRC, lowD, highA) display few large contact areas. The agreement with published experimental data supports the suggested correlations between JRC and the fractal parameters,A andD. It is suggested that observed scale effects in JRC and joint dilation can be explained by small differential strain discontinuities across fractures, which originate at the time of fracture formation.  相似文献   

4.
Epoxy casts were created of five naturally occurring fractures in dolostone and aperture distribution was measured using a light attenuation method. The optically determined aperture matrices showed a skew towards smaller apertures, with the larger models demonstrating a lognormal distribution and the smaller models a normal distribution. Surface variograms of each display a significant degree of anisotropy. The models had spatial correlation ranges between 1.8 and 5 cm. The optical mean aperture, mean hydraulic aperture and mass-balance aperture were all determined. In addition, the coefficient of variation (C v) and anisotropy ratio (AR) for each model was determined to compare their predictions with the actual tracer behavior in each of the models. In all cases, the hydraulically determined mean aperture was the same order of magnitude as the optically determined mean aperture. The mass-balance-derived mean aperture differed significantly from the optical mean aperture based on the degree of channeling in the model. However, neither the C v nor the AR correlated well to the actual behavior of the tracers, suggesting they are insufficient to predict void connectivity. Overall the epoxy replicas performed moderately well and can be well characterized for use in studies where visualization is of primary importance.  相似文献   

5.
《Engineering Geology》2002,63(1-2):141-155
Fractal theory is used in the present study to develop a more reliable method for rock mass characterization. Field studies have been carried out in opencast mines of dolomite, limestone, fluorite; sandstone and shale in coalmines. Fractal dimension of blasted fragments (Dfrag) and in situ rock blocks (Din situ) is calculated using size distribution curves according to Schumann's model. Based on the co-relation between Uniaxial Compressive Strength (UCS) and Dfrag, it is observed that change in fractal dimension is nominal beyond the UCS value of 20. From the co-relation between Bieniawaski's Rock Mass Rating (RMR) and Din situ, it is found that there is a sharp increase in fractal dimension for RMR greater than 40. Co-relation between RMR and Dfrag/Din situ shows that as RMR increases, Dfrag/Din situ ratio decreases. Rock mass classification based on fractal geometry is suggested.  相似文献   

6.
In order to investigate the effect of stress history on in-situ test results in granular sediments, a series of CPTs and DMTs are performed on Busan sand prepared in the calibration chamber. KD is found to be the most sensitive to the stress history among CPT and DMT measurements. ED and qc are observed to be similarly affected by the stress history and, therefore, the ED–qc relation appears to be almost independent of the stress history. The KD–DR relation established without considering the stress history is likely to overestimate the relative density of OC sand. It is shown that the existence of the pre-stress of the granular sediment can be indirectly recognized by an estimation of the relative density larger than 100% when using the KD–σv′–DR relation suggested for NC sand. Although qc/σv′–KD/K0 and ED/σv′–KD/K0 relations are heavily influenced by the stress history, qc/σm′–KD/K0 and ED/σm′–KD/K0 relations are observed to be independent of the stress history. Based on these relations, charts to evaluate the K0 value from qc and/or DMT indices are developed for both NC and OC sands. The design chart based on ED/σm′–KD/K0 and ED/σv′–KD/K0 relations is expected to be practically useful as the usage of this chart requires only DMT indices. The developed design charts are applicable to Busan sand but different sets of equations and charts may be developed for other sands.  相似文献   

7.
This paper describes a new procedure for assessing the ratio between in situ stresses in rock masses by means of K (K = σH / σv, being σH and σv principal stress) and tectonics for purposes of engineering geology and rock mechanics. The method combines the use of the logic decision tree and the empirical relationship between the Tectonic Stress Index, TSI, and a series of K in situ values obtained from an extensive database. The decision tree considers geological and geophysical factors affecting stress magnitudes both on the regional and local scale. The TSI index is defined by geological and geomechanical parameters. The method proposed provides an assessment of the magnitude of horizontal stresses of tectonic origin. Results for several regions of Europe are presented and the possible applications of the procedure are discussed.  相似文献   

8.
Measurement of streambed hydraulic conductivity and its anisotropy   总被引：17，自引：0，他引：17  
 A method is described for the measurement of streambed hydraulic conductivity. Unlike permeameter methods, this method applies straight and l-shaped standpipes directly to streambeds for measurements of in-situ hydraulic conductivity in the vertical (K v ) and horizontal (K h ) directions, as well as in other oblique directions (K s ). This method has advantages in determination of K v values over grain-size analysis, permeameter tests, or slug test methods. Also unique to this method is that it provides K s values of a streambed. The measured results can be used to construct a hydraulic conductivity ellipse and to evaluate the anisotropy of streambed sediments. Field examples from the Republican River, Nebraska, demonstrated the usefulness of this method in the determination of streambed hydraulic conductivity and anisotropy along or across a river channel. Results indicate that the K h is about three to four times larger than K v , whereas K s values are larger than K v but smaller than K h . Received: 6 March 2000 · Accepted: 18 April 2000  相似文献   

9.
Summary A new concept of feature size range of a roughness profile is introduced in the paper. It is shown that this feature size range plays an important role in estimating the fractal dimension,D, accurately using the divider method. Discussions are given to indicate the difficulty of using both the divider and the box methods in estimatingD accurately for self-affine profiles. The line scaling method's capability in quantifying roughness of natural rock joint profiles, which may be self-affine, is explored. Fractional Brownian profiles (self-affine profiles) with and without global trends were generated using known values ofD, input standard deviation, , and global trend angles. For different values of the input parameter of the line scaling method (step sizea 0),D and another associated fractal parameterC were calculated for the aforementioned profiles. Suitable ranges fora 0 were estimated to obtain computedD within ±10% of theD used for the generation. Minimum and maximum feature sizes of the profiles were defined and calculated. The feature size range was found to increase with increasingD and , in addition to being dependent on the total horizontal length of the profile and the total number of data points in the profile. The suitable range fora 0 was found to depend on bothD and , and then, in turn, on the feature size range, indicating the importance of calculating feature size range for roughness profiles to obtain accurate estimates for the fractal parameters. Procedures are given to estimate the suitablea 0 range for a given natural rock joint profile to use with the line scaling method in estimating fractal parameters within ±10% error. Results indicate the importance of removal of global trends of roughness profiles to obtain accurate estimates for the fractal parameters. The parametersC andD are recommended to use with the line scaling method in quantifying stationary roughness. In addition, one or more parameters should be used to quantify the non-stationary part of roughness, if it exists. The estimatedC was found to depend on bothD and and seems to have potential to capture the scale effect of roughness profiles.  相似文献   

10.
The response of deformable fractures to changes in fluid pressure controls phenomena ranging from the flow of fluids near wells to the propagation of hydraulic fractures. We developed an analysis designed to simulate fluid flows in the vicinity of asperity‐supported fractures at rest, or fully open fractures that might be propagating. Transitions between at‐rest and propagating fractures can also be simulated. This is accomplished by defining contact aperture as the aperture when asperities on a closing fracture first make contact. Locations on a fracture where the aperture is less than the contact aperture are loaded by both fluid pressure and effective stress, whereas locations where the aperture exceeds the contact aperture are loaded only by fluid pressure. Fluid pressure and effective stress on the fracture are determined as functions of time by solving equations of continuity in the fracture and matrix, and by matching the global displacements of the fracture walls to the local deformation of asperities. The resulting analysis is implemented in a numerical code that can simulate well tests or hydraulic fracturing operations. Aperture changes during hydraulic well tests can be measured in the field, and the results predicted using this analysis are similar to field observations. The hydraulic fracturing process can be simulated from the inflation of a pre‐existing crack, to the propagation of a fracture, and the closure of the fracture to rest on asperities or proppant. Two‐dimensional, multi‐phase fluid flow in the matrix is included to provide details that are obscured by simplifications of the leakoff process (Carter‐type assumptions) used in many hydraulic fracture models. Execution times are relatively short, so it is practical to implement this code with parameter estimation algorithms to facilitate interpretation of field data. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

11.
To investigate inhomogeneous and porous structures in nature, the concept of fractal dimension was established. This paper briefly introduces the definition and measurement methods of fractal dimension. Three different methods including mercury injection capillary pressure (MICP), nuclear magnetic resonance (NMR), and nitrogen adsorption (BET) were applied to determine the fractal dimensions of the pore space of eight carbonate rock samples taken from West Tushka area, Egypt. In the case of fractal behavior, the capillary pressure P c and cumulative fraction V c resulting from MICP are linearly related with a slope of D-3 in a double logarithmic plot with D being the value of fractal dimension. For NMR, the cumulative intensity fraction V c and relaxation time T 2 show a linear relation with a slope of 3-D in a double logarithmic plot. Fractal dimension can also be determined by the specific surface area S por derived from nitrogen adsorption measurements and the effective hydraulic radius. The fractal dimension D shows a linear relation with the logarithm of S por . The fractal dimension is also used in models of permeability prediction. To consider a more comprehensive data set, another 34 carbonate samples taken from the same study area were integrated in the discussion on BET method and permeability prediction. Most of the 42 rock samples show a good agreement between measured permeability and predicted permeability if the mean surface fractal dimension for each facies is used.  相似文献   

12.
Non-ferromagnetic minerals constitute what is called the rock matrix, whose susceptibility (K1) is directly accessible using only high magnetic fields. Measurements on minerals and a wide range of rock types show that K1 is mainly due to paramagnetism and hardly exceeds 10−3 SI, with an anisotropy degree (P) less than 1.35. Different methods to estimate the role of the matrix component in low-field susceptibility (K) and its anisotropy include petrological and chemical analysis, evolution of P vs K, low temperature studies and comparison of K with remanent magnetizations.  相似文献   

13.
Summary Many rock mass classification systems exist to assist the engineer in assessing the rock support requirements for underground design. On-going research in this area is directed at attempting to utilize the fractal dimension and the acoustic emission response of the tuffs at the Nevada Yucca Mountain to further aid in rock mass classification. Acoustic emission response is shown to be correlated with the porosity of the sample. Engineering behaviour of the rock varies dramatically with porosity; events and peak amplitude offer a means to distinguish between fracture porosity and pore porosity and consequently the engineering behaviour of the rock. Fractal dimension is used to characterize the roughness of fracture surfaces. Two fractal dimension calculation methods, one based on the semi-variogram for the surface and the other based on the use of dividers, are applied for this purpose. The divider method is shown to resolve deviation from a straight line; the semi-variogram method is shown to identify statistical similarity to various types of noise.Nomenclature D fractal dimension - AE acoustic emission - b b-value determined from log(frequency) against log(amplitude) plots - (h) semi-variogram function - h lag distance for semi-variogram function - H an exponent term related to fractal dimension asD=2 –H  相似文献   

14.
Friction Factor of Water Flow Through Rough Rock Fractures   总被引：2，自引：1，他引：1  
Fluid flow through rock joints occurs in many rock engineering applications. As the fluid flows through rough-walled rock fractures, pressure head loss occurs due to friction drag of the wall and local aperture changes. In this study, the friction factor was experimentally investigated by performing flow tests through sandstone fractures with joint roughness coefficient ranging from 5.5 to 15.4 under changing normal stress from 0.5 to 3.5 MPa. According to the experimental results, the friction factor was formulated as a function of two-independent variables—Reynolds number and relative roughness. Relative roughness is defined as the ratio of maximum asperity height to equivalent hydraulic aperture. The experimental results show that the proposed predictor of the friction factor fits the data with a coefficient of determination R 2 > 0.93. Sensitivity analyses indicate that in general, the proposed friction factor increases with the relative roughness of confined fractures. The large difference of friction factor induced by relative roughness occurs when the Reynolds number is lower than unity, especially for Re < 0.2. For Reynolds numbers greater than unity, the difference of friction factor induced by relative roughness is smaller. Inclusion of joint roughness in calculating the friction resistance to fluid flow in rough rock joints and the influence of normal stress to the joints is a major step towards more accurate predictions for fluid flow in underground joint networks. This study provides a significant improvement in fundamental understanding of fluid flow in the jointed strata.  相似文献   

15.
The aim of this short note is to test whether the morphological skeletal network (MSN) of water bodies that resembles a river network follows Horton's laws. A fractal relationship of MSN of a water body is also shown. This investigation shows that the MSN of the Nizamsagar reservoir follows Horton's laws. Furthermore, this reservoir has a fractal dimension (D m) of 1.92 which was computed by using two morphometric quantities and the fractal dimension of the main skeletal length (d). This value tallies exactly with the fractal dimension (D f) of the whole MSN computed through box-counting method.  相似文献   

16.
Migration properties characterized by physico-chemical factors such as distribution coefficient (Kd) and diffusion coefficient (De) are of great concern in performance assessment of high-level radioactive waste disposal in a deep geologic environment. These coefficients are normally obtained with different sample geometries using conventional methods, i.e., crushed samples by the batch sorption method for Kd determination and block samples by the through-diffusion method for De. A size dependence on both Kd and De has been reported and an additional correction due to size difference is required to maintain consistency of the data set. A fast method was developed, hereafter referred to as the micro-channel method, to determine both the sorption coefficient (Rd) and De using non-crushed rock sample by adopting the micro-reactor technique. In this method, a radionuclide solution is injected into a micro-channel (20 mm length, 4 mm width, 160 μm depth), which is in contact with a plate-shaped rock sample. A part of the injected radionuclide can diffuse into the rock matrix and/or adsorb on the rock surface and this results in an inlet-outlet concentration difference. A breakthrough curve is easily obtained with a short observation period because the injection amount is extremely small and is comparable to that escaping by diffusion into the matrix. The breakthrough curve is analyzed by a two-dimensional diffusion-advection equation to evaluate Rd and De.In the present study, tritiated water (specific activity, 1.2 × 104 Bq/mL; pH, 6) was injected into the micro-channel, and the breakthrough curve of 3H obtained. A series of experiments was carried out by changing the flow rate of the tritiated water (2.6 × 10−5–7.7 × 10−4 m/s). Rock samples were biotite granite from the Makabe area, Japan. The diffusion coefficient evaluated by least squares fitting to the numerical solutions (De = 1.5 × 10−11 m2/s) agreed well with that obtained by the through-diffusion method (1.3 × 10−11 m2/s). The breakthrough curve of Cs ([Cs] = 1.0 × 10−7 mol/L, pH 6) labeled with 134Cs (specific activity adjusted to 4.9 × 101 Bq/mL) was also obtained. A nearly constant Rd value (5.5 × 10−2 m3/kg) was found when the flow rate was less than 2.5 × 10−4 m/s. This implied that the sorption equilibrium is reached and Kd is obtained by the present method. This value was almost identical to Kd obtained by the batch sorption method (5.0 × 10−2 m3/kg), but the testing period was very different; 1 day and 7 days, respectively. It is concluded that application of the micro-channel method provided advantages when compared with the conventional methods.  相似文献   

17.
The low-grade Palaeoproterozoic stratabound banded iron ores of the Krivoy Rog basin (Ukraine) underwent strong tectonometamorphic deformation into superimposed folds of several orders, with amplitudes from centimetres to hundreds of metres. The across-strike sections of bed surfaces defining the low-grade ore bodies resemble self-similar fractal curves; hence, a fractal geometrical model was developed in order to quantify the complexity and sinuosity of bed contours. Two different methods of measurement (polygonal approximation and two-dimensional grid cell counting) were used for 5–8 different scales. Factual similarity dimension D and other model parameters have been estimated by means of linear regression and compared for both measurement methods. From the fractal model a sinuosity coefficient of contours of the folded bed surfaces K s and a coefficient of degree of exploration of iron ore bodies K e were constructed. It is pointed out that parameters of the model can be used for determination of the optimal exploration length scales.  相似文献   

18.
Gu  Xiaoqiang  Li  Youhong  Hu  Jing  Shi  Zhenhao  Liang  Fayun  Huang  Maosong 《Acta Geotechnica》2022,17(8):3229-3243

Natural clays usually show anisotropic stiffness due to their deposition process and anisotropic in situ stress state. The stiffness anisotropy depends on both of the stress anisotropy and fabric anisotropy, while the latter can be quantified by the stiffness anisotropy at isotropic stress states. This paper measures the K0 value (i.e., stress anisotropy) and elastic shear stiffness anisotropy of natural Shanghai clay in a triaxial apparatus with horizontal and vertical bender elements. The results show that the K0 value of Shanghai clay lies in the range of 0.40–0.66, and an empirical equation is proposed to estimate the K0 value based on the plasticity index and initial void ratio. The fabric anisotropy of natural Shanghai clay lies in the range of 1.2–1.4 with a stronger fabric in the horizontal plane. Moreover, the experimental data of the stiffness anisotropy and fabric anisotropy of different clays in the literature are reviewed and analyzed. It reveals that the stiffness anisotropy generally increases, while the fabric anisotropy remains nearly the same during K0 consolidation. For normally consolidated clay, the fabric anisotropy generally lies in the range of 1.1–1.7. For overconsolidated clays, the fabric anisotropy generally increases as the overconsolidation ratio increases. Empirical equations are proposed to approximately estimate the fabric anisotropy of clays based on its stress normalized elastic shear stiffness.

  相似文献   

19.
In order to explore possible quantitative relations between crystal field stabilization energy, CFSE, and partitioning behaviour of the 3d 6-configured Fe2+ ion, a suite of 29 paragenetic rock-forming minerals from 12 high-grade metamorphic rock samples of the Ukrainian shield, including the parageneses garnet/orthopyroxene/clinopyroxene (2x), orthopyroxene/clinopyroxene, garnet/clinopyroxene, garnet/orthopyroxene/biotite, garnet/biotite, garnet/cordierite, garnet/cordierite/biotite, garnet/orthopyroxene/clinopyroxene/Ca-amphibole, Ca-amphibole/biotite (retrograde), was studied by electron microprobe analysis to obtain the respective K D Fe2+ (Ph1/Ph2) values and by polarized single crystal electronic absorption spectroscopy to evaluate the respective CFSEFe2+ values. Other than in the case of Cr3+, a clear quantitative relation between K D (Ph1/Ph2) and the ΔCFSE(Ph1/Ph2) was only observed when geometrical factors, mainly the volume of crystallographic sites and ionic radii of ions competing in the partitioning process, are similar in the respective two paragenetic phases to within 15–20%. In such cases, the ΔCFSEFe2+ contribution to K D (Ph1/Ph2) amounts to 0.1 to 0.2 log K D per 100 cm−1ΔCFSE. The conclusion is that ΔCFSEFe2+ plays only a secondary role after geometrical factors, in the partitioning behaviour of Fe2+. The reason for this is seen in the facts that, compared to the 3d  3-configured Cr3+ ion, CFSE of the 3d 6-configured Fe2+ amounts only to 20–25%, and that the former ion enters only octahedral sites with similar geometrical properties in the paragenetic mineral phases. Received: 17 November 1998 / Accepted: 28 June 1999  相似文献   

20.
The combined influence of dip angle and adsorption heterogeneity on solute transport mechanisms in heterogeneous media can be understood by performing simulations of steady-state flow and transient transport in a heterogeneous aquifer with dipping anisotropy. Reactive and non-reactive contaminant transport in various types of heterogeneous aquifer is studied by simulations. The hydraulic conductivity (K) of the heterogeneous aquifer is generated by HYDRO_GEN with a Gaussian correlation spectrum. By considering the heterogeneity of the adsorption distribution coefficient (K d), a perfect negative correlation between lnK and lnK d is obtained by using the spherical grains model. The generated K and K d are used as input to groundwater flow and transport models to investigate the effects of dipping sedimentary heterogeneity on contaminant plume evolution. Simulation results showed that the magnitude of the dip angle strongly controls the plume evolution in the studied anisotropic and heterogeneous aquifer. The retarded average pore-water velocity (v/R) of the adsorption model significantly controls the horizontal spreading of the plume. The bottom plume is intensively retarded in the zones between the dipping lenses of lower hydraulic conductivity and the no-flow bottom boundary. The implications of these findings are very important for the management of contaminated heterogeneous aquifers.  相似文献   

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