Fractures density

Although formation fracturing is generally undesirable with chemical grouts, it is often deliberately practiced with cement grouts, much more so in Europe than in the U.S. If cement-filled fractures density the soil with a material stronger than the untreated formation, the practice has obvious benefits. 

The analysis developed here is based in the assumption that chain scission occurs at random. A fracture density is defined as... 

T-M Granite Fracture density r] = fit) (f), linear increase Kou Shaoquan, 1987... 

Abstract A methodology for quantifying the contributions of hydro-mechanical processes to fractured rock hydraulic property distributions has been developed and tested. Simulations have been carried out on discrete fracture networks to study the sensitivity of hydraulic properties to mechanical properties, stress changes with depth, mechanical boundary conditions, initial mechanical apertures and fracture network geometry. The results indicate that the most important (and uncertain) parameters for modelling HM processes in fractured rock are fracture density and rock/fracture mechanical properties. Aperture variation with depth below ground surface is found to be of second order importance. 

Figure 3. DFN with different fracture densities and a power-law length distribution (lOmxIOm).

An extensive examination of the fracture network and mechanical data has been undertaken to determine models of the fracture characteristics of the three formations, the uncertainties in the parameterisation of the models, and the sensitivity of the upscaled flow properties to the underlying parameter variations. The methodology used to calculate effective hydraulic conductivity values and their sensitivity to the small-scale model is described in Blum el al. (2003). The study undertaken to obtain the effective hydraulic conductivity under different stress conditions and presented in Blum et al. (2003) revealed that the important parameters in modelling HM processes in the fractured rock mass are the fracture density, the mechanical (M) properties and the M property variations through the rock mass. 

While alternative fracture densities were studied for the effective hydraulic conductivity... 

Figure 1. An example of a DFN for Formation 2 with a medium fracture density of 13.2 m/m. The block size is 10 m xW m.

For the hydraulic base case, constant hydraulic apertures and fracture densities were considered. Homogeneous hydraulic conductivity tensors and porosities were applied to each formation. The case with a constant hydraulic aperture of 10 im and medium fracture density for all formations is illustrated in Figure 5, where the streamlines and the particle travel times are shown. The time of travel between each marker is 1000 days. Owing to the low effective porosity values and the relatively high fracture density, particle travel times through the host rock are fast. The mean particle travel time from the repository to the seabed is only 123 years, when a constant hydraulic aperture of 10 pm is used. 

The results for the particle travel times for various constant hydraulic apertures and fracture densities from the repository to the seabed are presented graphically in Figure 4. For the low fracture density case, the hydraulic conductivity estimated for a block size of 25 m x 25 m has been used even though this size does not correspond to the REV, which is estimated to be greater than 100 m x 100 m. This block size does allow, however, a calculation of the mechanical closure of the fracture apertures for the HM case and therefore a comparison of the results between the two cases for low-density conditions. The results of the continuum model based on constant hydraulic apertures display very rapid mean particle travel times from the repository to the seabed. For example, for the low and high fracture density networks adopting a constant hydraulic aperture of 10 pm, particle travel times from the repository to the seabed are 580 years and 106 years respectively. A doubling of the aperture increases the conductivity by a factor of... 

One outcome of this study demonstrates the impact of different fracture densities on the large-scale analysis. The comparison between the... 

The main conclusions drawn from the small-and large-scale analyses of the studied rock mass are that for this data set, the uncertainty in the mechanical properties and their spatial variations are the most important factors in performance assessment of deep waste disposal, followed by the uncertainty of the fracture density and the spatial distribution of the fracture density. 

Elastic constants, obtained from core or wireline data, are presented in Table 1. For the sake of brevity, only parameters specific to Formation 1 are presented in this paper (Table 2). Parameters for Formations 2 and 3 are not significantly different from those of Formation 1. In the table, the lineal fracture densities (PIO or pFr, number of fractures/ m), dip angles, and dip azimuth angles were obtained from core logs. The shear stiffness constant (gsh, dimensionless) and the initial joint normal stiffness (K , Pa/m) were obtained... 

Notes (1) Assumed caleulated at 500 below ordnance datum (2) Fractured density reduced by a factor of 3 (3) Calculated at ground surface. 

Fracture density by which the number of generated fracture is determined is defined by P2i- Pi is assumed to be given by the 2-D fracture density (Nirex, 1997b)... 

To investigate the effect of fracture geometry on the scale effect of the permeability, some parametric study is carried out. Table 1 shows the parameters examined for this aim. Case 1 is the reference case in which the original measured data at Sella-field are used. Case2 is the case to examine the effect of uncertainty on the fracture density, in which the density is defined by Eq. (6). Thus the number of fracture in this case is about 4 times that in Case 1. Case 3 is related to the uncertainty on the... 

For the effect of the fracture density, it is found that the difference is not seen between Figures 3 and 4. This is probably because the density larger than 4.8 m gives the enough connectivity of the flow paths. 

It can be concluded from the above discussion that the uncertainty of the fracture length is more important than that of fracture density. 

Two methods are developed for calculating gridblock-scale stress-permeability relationships. Although the first method is developed by assuming identical properties for individual hactures and spatially variable fracture densities, it can be mathematically shown that the model is also valid for individual fractures with different aperture parameters (e.g., b, and bmu) as long as Rb is the same for individual fractures. 

Fracture density (number of fracture per unit volume of rock - P31) is assumed to follow a Poisson law ... 

Table 2 Extermination of fracture density from RESOBLOK fracture network simulations.

Cause I. The CFF in True-1 was found to be such that is about 8 m /m . The mean of the transmissivity of all fractures was about 5 times smaller than that of Feature A. However the fracture density is such that about 30 fractures would carry the collected flowrate in addition to Feature A. This would give a considerably larger FWS for the collected flow rate. 

In Figure 1, we compare the complementary cumulative distribution functions (C(2DF) and cumulative distribution function (CDF) for P obtained directly from simulations using (2) or (4), with the approximate value of P using the linear expression P = kt. For the 100m scale, k is estimated using fracture density and flow porosity as k = 2Sj jn, whereas... 

Trace length (m) normal distribution Fracture density (/mh uniform distribution... 

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