Fractures lengths

Hatton, C.G., Main, l.G. and Meredith, P.G. 1994. Non-universal scaling of fracture length and opening displacement (letter). Nature, 367 160-162. 

Stage 1 concerns the DFN generation, which was performed with the code FracFrac. The uncertainties in the statistical parameterisation of the fracture length and density data are examined and show the importance of careful fitting of the power-law length distribution to the data. 

Figure 2. Power-law distribution of fracture length (based on Nirex 1997b).

Finally, the sensitivity of fracture aperture to block size and fracture length was analysed. Fracture networks with domain sizes of 5 m x 5 m and 10 mx 10 m revealed differences in median hydraulic apertures of less than 0.5 pm. Even with a block size of 15mxl5m and effectively infinitely long fractures, the change in median hydraulic aperture remained less than I pm. It can be concluded that the size of the REV determined for flow only is also suitable for mechanical calculations, and that, for the assumed spatial distribution and orientation of fracturing, fracture length has only a minor impact on the hydraulic aperture distribution. 

A key uncertainty for modelling fracture patterns arises from the inference of the parameters of the power-law fracture length distribution. Several models have been fitted to the BVG data, each yielding different hydraulic results. The main geo-... 

In this process, the maximum length of 250 m and the minimum length of 0.5 m are assumed. Thus, the probability density function, PDF, of fracture length is written by... 

To examine the uncertainty related to the fracture length, the case that the mean length is 2.13m and the exponent of Z. is 1.2 is examined. Moreover, the case having the lognormal distribution of the fracture length with the mean length and variance from 4,000 realizations of Equation (4) is also examined. The latter case is to examine the uncertainty for the interpretation of the observation result. 

However, the other consideration can be made by obtaining the total fracture length through the mean fracture length and total number of fracture. 

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

Case B is the case in which mean fracture length is doubled, which case is corresponding to Case 3 in the above section. It is expected from this case that the uncertainty related to the fracture length data is examined. 

Fracture length is assumed to follow a power law distribution of the form N=CL° where N is the number of fractures which are equal to or greater than a given trace length L, D is the fractal dimension and C is a constant. 

The simulations have been done considering initial value of P31 equal to the value of Pn (for a Fracture Length Threshold of 0.5 m) given in Table 1. Average values of P22, computed from several RESOBLOK simulations, were compared to P22 measurements (5m/m for a fracture length threshold of 0.5 m) to evaluate the realism of the simulations. The results are gathered in Table 2. 

We have assumed that the hydraulic apertures were constant and equal to 6,5 10 m. The equivalent permeability tensor is given below at 2 m scale for the fracture network of formation 1 and considering a fracture length threshold of 0.5 m ... 

In this work we have assumed no relation between the joint stiffness and the stress or with the fracture length. This assumption could be revisited later on. We have also considered an isotropic state of stress. Others stress conditions could be applied and would probably involve other kinds of evolution of the equivalent permeability tensor. 

Tijki has also been determined at 2 m scale considering the real length of the joint. Differences with the previous simulation remain below 10 %. This could lead us to think that this factor is not very important for the equivalent mechanical behaviour. This result is consistent with the fact that no significant fracture length threshold effect has been shown on Tijn. 

Note that if L = 100 m, Da, = 1.5 x 10 , then Da, scales directly with L. This value of Dai in the slow reaction part of Figure 8.1, indicating that the solution does not reach equilibrium within a 10 or even 100 m fracture length because of the very slow precipitation rate of quartz. 

Baghbanan, A. Jing, L. 2008. Stress effects on permeability in a fractured rock mass with correlated fracture length and aperture. International Journal of Rock Mechanics and Mining Sciences 45(08) 1320-1334. 

Extent of damage Brittle or ductile fracture Length and number of cracks Degree of deformation Depth of corrosive attack or wear... 

Measure fluid travel distance to extend fracture length. 

Equation 2-47 still contains the unknown constant Ft. To determine Ft, we return to Equation 2-44 and evaluate it for distances that are large compared with the fracture length. Thus, the exact expression for pressure... 

Now assume that the fracture length greatly exceeds its thickness, that is, 8 1. This is the thin airfoil limit in elassieal aerodynamics, or the thin fracture limit for fracture modeling. Then, the results of Example 2-2 apply to leading order. Our main task is to develop a mathematical formalism that captures this leading order description when 8 vanishes but provides systematic, straightforward corrections when it is nonvanishing but small. 

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