A new estimation method and an anisotropy index for the deformation modulus of jointed rock masses

The deformation modulus of a rock mass is an important parameter to describe its mechanical behavior.In this study,an analytical method is developed to determine the deformation modulus of jointed rock masses,which considers the mechanical properties of intact rocks and joints based on the superposition principle.Due to incorporating the variations in the orientations and sizes of joint sets,the proposed method is applicable to the rock mass with persistent and parallel joints as well as that with nonpersistent and nonparallel joints.In addition,an anisotropy index AIdmfor the deformation modulus is defined to quantitatively describe the anisotropy of rock masses.The range of AIdmis from 0 to 1,and the more anisotropic the rock mass is,the larger the value of AIdmwill be.To evaluate the proposed method,20 groups of numerical experiments are conducted with the universal distinct element code(UDEC).For each experimental group,the deformation modulus in 24 directions are obtained by UDEC(numerical value)and the proposed method(predicted value),and then the mean error rates are calculated.Note that the mean error rate is the mean value of the error rates of the deformation modulus in 24 directions,where for each direction,the error rate is equal to the ratio of numerical value minus predicted value to the numerical value.The results show that(i)for different experimental groups,the mean error rates vary between 5.06%and 22.03%;(ii)the error rates for the discrete fracture networks(DFNs)with two sets of joints are at the same level as those with one set of joints;and(iii)therefore,the proposed method for estimating the deformation modulus of jointed rock masses is valid.

A novel approach to structural anisotropy classification for jointed rock masses using theoretical rock quality designation formulation adjusted to joint spacing

Rock quality designation(RQD)has been considered as a one-dimensional jointing degree property since it should be determined by measuring the core lengths obtained from drilling.Anisotropy index of jointing degree(AI_(jd))was formulated by Zheng et al.(2018)by considering maximum and minimum values of RQD for a jointed rock medium in three-dimensional space.In accordance with spacing terminology by ISRM(1981),defining the jointing degree for the rock masses composed of extremely closely spaced joints as well as for the rock masses including widely to extremely widely spaced joints is practically impossible because of the use of 10 cm as a threshold value in the conventional form of RQD.To overcome this limitation,theoretical RQD(TRQD_(t))introduced by Priest and Hudson(1976)can be taken into consideration only when the statistical distribution of discontinuity spacing has a negative exponential distribution.Anisotropy index of the jointing degree was improved using TRQD_(t) which was adjusted to wider joint spacing by considering Priest(1993)’s recommendation on the use of variable threshold value(t)in TRQD_(t) formulation.After applications of the improved anisotropy index of a jointing degree(AI'_(jd))to hypothetical jointed rock mass cases,the effect of persistency of joints on structural anisotropy of rock mass was introduced to the improved AI'_(jd) formulation by considering the ratings of persistency of joints as proposed by Bieniawski(1989)’s rock mass rating(RMR)classification.Two real cases were assessed in the stratified marl and the columnar basalt using the weighted anisotropy index of jointing degree(W_AI'_(jd)).A structural anisotropy classification was developed using the RQD classification proposed by Deere(1963).The proposed methodology is capable of defining the structural anisotropy of a rock mass including joint pattern from extremely closely to extremely widely spaced joints.

Spatial distribution of ion polytropic index joint-modulated by temperature anisotropy and MHD disturbances in the southern high latitude magnetosheath

Using the Cluster data from 2001 to 2010, we studied spatial distribution of effective ion polytropic index in the southern high latitude magnetosheath, and joint-modulation of ion polytropic index by temperature anisotropy and MHD disturbances. The magnetosheath ions generally experience various polytropic processes with different polytropic index. The median polytropic indexes of magnetosheath ions in the GSE X-Y plane decrease toward the bow shock. Near the magnetopause, the median polytropic indexes are basically between isothermal and adiabatic except in the duskside flank close to the terminator. The analysis of correlation coefficient of perturbed ion number density with parallel magnetic field CC_δnδB_‖ and ion temperature anisotropy parameter A_T, indicates that the dominant MHD disturbance near magnetopause is slow mode with larger ion temperature anisotropy, and there are various modes of MHD disturbances with insignificant ion temperature anisotropy near the bow shock.The polytropic index modulated by slow mode disturbances is generally larger than that modulated by fast mode disturbances, and the larger ion temperature anisotropy, the larger polytropic index. The median polytropic indexes modulated jointly by slow mode disturbances and the strong ion temperature anisotropy can be larger than 1.0, while those modulated by fast mode disturbances and weak temperature anisotropy can be even possibly close to zero. Moreover, because of pronounced dusk-favored asymmetry of ion temperature anisotropy, the median polytropic index in the dawnside flank of the magnetosheath near the terminator is smaller than that in the duskside flank of the magnetosheath. The good correspondence between the distributions of median polytropic indexes and ion temperature anisotropy and MHD disturbances indicates that the ion temperature anisotropy and MHD disturbances determine the distribution of the polytropic index in the magnetosheath.