Rock-quality designation (RQD) plays a significant role in rock mass analysis and is an important parameter in geotechnical and geological engineering...

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March 2013 Vol.56 No.3: 739–748 doi: 10.1007/s11431-013-5132-6

Investigation of RQD variation with scanline length and optimal threshold based on three-dimensional fracture network modeling ZHANG Wen1, CHEN JianPing1*, WANG Qing1, MA DongHe2, NIU CenCen1 & ZHANG Wu3 2

1 College of Construction Engineering, Jilin University, Changchun 130026, China; China Water Northeastern Investigation, Design & Research Co., Ltd., Changchun 130026, China; 3 College of Automotive Engineering, Jilin University, Changchun 130026, China

Received October 29, 2012; accepted December 25, 2012; published online January 22, 2013

Rock-quality designation (RQD) plays a significant role in rock mass analysis and is an important parameter in geotechnical and geological engineering. However, the RQD variation with scanline length has not yet been comprehensively considered in RQD. In this study, three-dimensional fracture network modeling was used to simulate actual rock mass, and numerous scanlines were set in the fracture network for investigation on RQD variation. Models and equations (i.e., models A-A, N-N, and A-A-S, as well as the Priest-Hudson and Sen-Kazi equations) were summarized for the study. A corrected equation was proposed to eliminate the errors from using the Priest-Hudson and Sen-Kazi equations. In addition, inhomogeneous and anisotropic features were investigated, and the optimal thresholds for RQD calculation were determined, which varied with the study orientation and rock mass feature. When the inhomogeneity was studied in the x direction, the optimal threshold was found to be 4 m. When anisotropy was studied, the optimal threshold was found to be 3 m. rock mass, inhomogeneity, anisotropy, fracture Citation:

Zhang W, Chen J P, Wang Q, et al. Investigation of RQD variation with scanline length and optimal threshold based on three-dimensional fracture network modeling. Sci China Tech Sci, 2013, 56: 739748, doi: 10.1007/s11431-013-5132-6

1 Introduction Since RQD (rock-quality designation) was introduced by Deere [1], it has been widely used in the surveying and designing of water conservancies, mines, and ports, as well as in underground engineering, among others [2–4]. Engineers generally calculate RQD based directly on the lengths of the core pieces within the drill run while ignoring the RQD variation. RQD varies with the length of the drill run and can only remain stable when the length of the drill run is larger than a fixed length. Only the invariable RQD can be used to represent the quality of rock masses. In addition, *Corresponding author (email: [email protected]) © Science China Press and Springer-Verlag Berlin Heidelberg 2013

RQD has low sensitivity. For drill runs that have large differences in fracture frequency, which is defined as the number of fractures per meter along a scanline, RQD values differ at a smaller scale and cannot fully reflect the inhomogeneity and anisotropy of rock masses. To mitigate this problem, the optimal threshold of RQD was introduced. A number of scholars have recently undertaken in-depth study on the variation with scanline length and the optimal threshold for RQD. Priest and Hudson [5–7] have studied RQD and proposed a relationship between the fracture frequency and RQD. They highlighted that RQD values were characterized by the variation with the scanline length. Sen and Kaiz [8, 9] also studied RQD and improved the relationship between the RQD value and fracture frequency. Choi and Park [10] studied two-dimensional (2D) fractures tech.scichina.com

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in Korea and calculated RQD values with different study sizes. Their results showed that RQD values increase when the scanline lengths are small and remain stable at a critical length. Harrison [11] showed that the fracture frequency varied with the orientation of the scanline. He presented equations for determining the optimal thresholds of different distribution types. Researchers have established the relationships between RQD and other rock mass parameters such as the hydraulic conductivity, deformation modulus, volumetric joint count, and the aforementioned fracture frequency. Zhang and Einstein [12] and Jiang et al. [13] deduced the relationship between RQD and the deformation modulus. In addition, Jiang et al. [13] elucidated the relationship between RQD and hydraulic conductivity. Milne et al. [14] suggested that the volumetric joint count was influenced by RQD, with a negative correlation between these two parameters. Sarma and Ravikumar [15] determined the Q-factor using a spectral ratio technique for strata evaluation and established the relationship between the Q-factor and RQD. Rock masses are inhomogeneous. RQD values vary with the study regions. To reflect the characteristics or to decrease the effect on the whole rock mass design, a substantial amount of data on drill runs must be comprehensively studied. In practice, however, this requirement usually cannot be satisfied because of economic issues. In addition, drill runs generally need to be perpendicular to the ground. Therefore, drill runs cannot reflect the RQD variation at different directions. In this paper, there-dimensional (3D) fracture network simulation is used to study the inhomogeneity and anisotropy of a rock mass. Unlike in-situ drilling, the 3D fracture network can set a large amount of scanlines through computer simulation. The RQD values of different locations and directions within the fracture network can be calculated [16–18]. The threshold is the only parameter that affects the RQD value for samples of rock fragments. This threshold can be changed to determine a wider range of RQD values. The optimal threshold can generate the widest range of RQD values for a given rock mass. This threshold was determined in this paper to best reflect the inhomogeneity and anisotropy of the said rock mass.

2 Database 2.1

Study area

The rock mass in the dam site of the Baihetan hydropower station, located in southwest China, was studied for RQD

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calculations. A double-curvature arch type dam was designed. The dam crest elevation is 825 m, with a water surface elevation of 590 m. The storage water level is 820 m, and the maximum generation capacity of the station is 59.55 billion kwh. The dam site is characterized by a mountain-canyon geomorphology, and the valley has an asymmetric “V” shape. Cliffs surround the area and reach elevations of 900 to 1100 m on the left bank and 1000 to 1400 m on the right bank. Mesas and gentle slopes are widely distributed at the top. Basalt from the Permian period (P2) comprises the rock mass in the dam site. The dam will be built on the basalt area. Therefore, the features of basalt are important factors for the engineering stability of the dam. At a horizontal depth of 40 to 80 m, the free-face layer of the rock mass of the dam site is moderately weathered, with developments of columnar jointing and unloading fractures. The inner layer of the rock mass is either unweathered or only slightly weathered. The stochastic fractures developed with few columnar joints and unloading fractures. Given that the inner rock mass is important in dam analysis, the 3D fracture network simulation focuses on the stochastic fractures. To study the basalt in the dam site, a large amount of exploration adits were set. Adit PD933, which has an elevation of 830 m, was used to study the RQD. The exploration adit strikes north-east/south-west, with a size of 110 m× 2 m × 2 m. The fractures from the right lateral surface in the adit that have trace lengths longer than 0.5 m were collected. The sampling window method was used to gather the fractures. A total of 111 fractures were gathered (Figure 1). 2.2 Determination of the 3D fracture network A 3D fracture network simulation was used in this paper to study the RQD. The 3D fracture network simulation includes the following steps. 1) Delineation of dominant fracture sets. The fracture sets were determined by the method proposed by Chen et al. [18] (Figure 2). The Kulatilake and Wu correction [19] was then performed. Table 1 shows the occurrences of the three fracture sets. The Fisher parameter was used to determine the aggregation degree (preferred orientation) of each fracture set [7]. 2) Determination of trace length, diameter, and density. The sampling window was of finite size. The trace lengths should be corrected using the method introduced by Kulatilake and Wu [20]. The corrected trace lengths, which followed a Gamma distribution, are summarized in Table 1.

Figure 1 2D traces of the collected fractures.

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Figure 2

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Equal-area projection diagram for fracture sets.

The diameter of each fracture set was affirmed using the method of Kulatilake and Wu [21]. The diameter of each fracture set also followed a Gamma distribution (Table 1). The fracture frequency can be derived according to the method by Karzulovic and Goodman [22]. Consequently, the fracture density can be determined [23] (Table 1). 3) Monte-Carlo simulation. As required by the project simulation, the size of the 3D fracture network was 110 m×50 m×50 m. The aim of this step is to create a complete model using the Poisson process. The occurrence, diameter, and density were simulated five times based on the Monte-Carlo simulation. Eventually, 125 3D fracture network models were generated. Table 1

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4) Model checking. The generated 3D fracture network models can be cut along a plane, the occurrence of which is the same as that of the surveyed surface. The fractures in the cut plane were then compared with the field fractures to determine an optimal numerical model. The compared data include the average dip, average dip angle, surveyed average trace length, corrected average trace length, and number of the fractures. In the current study, the Kolmogorov-Smirnov (KS) test was used to check the similarity degree among the aforementioned data of the model and those in situ. The model accepted by the KS test was adopted to represent the field rock mass. The comparison between the 125 generated models and the field data is not shown in this paper. Only the comparison showing the final selected model is summarized in Table 2. Based on the above steps, an optimal model was chosen to provide the basic data for studying the RQD. Only the fractures with x, y, and z coordinates of the fracture centers located between 20 and 40 m were visualized based on the OpenGL program, as shown in Figure 3.

3 Variation of RQD with scanline length Engineers tend to use the drilling data in RQD calculations in practical engineering, regardless of the length of the drill run. However, not all drill runs can determine the real RQD value of the rock mass. This paper conducts research on the RQD variation based on the 3D network simulation and aims to provide a basis for determining reasonable drill run lengths. The RQD used in this paper is the generalized one, that is, the threshold can be any positive value.

Modeling parameters of the field data Trace length Average dip angle (°) Mean (m) Std. (m) Distribution

Fracture diameter

Spacing

Density (m3)

K

1

0.162

19

6.4

0.9

0.157

32.6

9.8

1.2

0.009

40.4

Fracture set

Average dip (°)

1

235

87

1.3

0.4

Gamma

1.4

0.4

Gamma

6.2

2

310

86

1.4

0.5

Gamma

1.9

0.2

Gamma

3

128

26

3.1

1.1

Gamma

4.5

1.4

Gamma

Table 2

Distribution

Mean (m) Std. (m)

The comparison between the final selected model and the field data

Adit

Fracture set 1

933

Mean (m) Std. (m)

2 3

Surveyed

Fracture number

Average dip angle (°)

Average dip (°)

Surveyed average trace length (m)

Corrected average trace length (m)

26

87

235

1.3

2.07

Predicted

26

85

237

0.96

1.95

Surveyed

35

86

310

1.42

2.66

Predicted

35

86

310

1.1

2.48

Surveyed

15

26

128

3.11

7.89

Predicted

15

24

130.2

3.46

7.81

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Figure 3

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Visualization of the 3D fractures.

3.1 Calculation model of RQD As shown in Figure 4, the end of the drill run or scanline does not necessarily intersect with the fracture. Therefore, Priest [7] proposed two RQD calculation models, namely, models A (the augmented model) and T (the terminated model). The two models assume that the fracture is the starting point of the scanline. However, in practical engineering, the starting point of the scanline does not necessarily coincide with the fracture. Therefore, Choi and Park [10] proposed models A-A and A-A-S. Considering the aforementioned models, this paper classifies the RQD calculation model into three types, namely, models A-A, T-T, and A-A-S. The calculation methods of each model are as follows. 1) Model A-A. This model is often used in the calculation of RQD. The RQD derived from this model is the percentage of the intact lengths greater than a given threshold t to the total length of a drill run, namely

RQDA-A

lt l 100 t lt

l1 l2 , l l1 , l l2 , l

l1 t , l2 t , l1 t , l2 t , l1 t , l2 t ,

Calculation model of RQD.

lt . l l1 l2

(2)

3) Model A-A-S. The layout of the scanline is relatively random. When the scanline translates, the first and the last core pieces are likely to add up to a certain impact on RQD. The lengths of the two pieces are added and then compared with threshold value t. If the cumulative length is greater than t, it will be considered in the RQD calculation. Otherwise, the cumulative length will be ignored. Model A-A-S has a more correct statistical meaning compared with the other two models. Model A-A-S can be expressed as

RQDA-A-S

lt l1 l2 , l 100 lt , l

l1 l2 t ,

(3)

l1 l2 t .

Priest and Hudson [5] and Sen and Kazi [8] proposed RQD equations related to the change in the drill run (scanline) length. In this paper, eqs. (4) and (5) are referred to as the Priest-Hudson and Sen-Kazi equations, respectively.

RQD 100 1 t e t 1 s L e L ,

(1)

where l1 and l2 are the lengths of the core piece at the start and end of the scanline, respectively; and lt is the total length of the inner core pieces that are greater than the given threshold t. 2) Model T-T. Model T-T ignores the core pieces at the start and end of the scanline and can be expressed as

Figure 4

RQDT-T 100

(4)

RQD 100 1 t e t 1 s L e L 1 e L s Le L , (5)

where is the fracture frequency, t is the threshold, and L is the study drill run length. As previously mentioned, model A-A considers the core pieces at the start and end of the scanline, model N-N ignores the core pieces, whereas model A-A-S considers the core pieces as a whole. Eqs. (1) to (3) can be used to determine the RQD values. The following relationships of the RQD values can be determined by mathematical manipulation. When the core pieces at the start and end of the scanline are all larger than or equal to the threshold, the RQD of model A-A-S is equal to that of model A-A, which is greater than that of model N-N. When the core pieces are all smaller than the threshold, the RQD of model N-N is greater than

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that of model A-A-S, which is greater than or equal to that of model A-A. When only one core piece is larger than or equal to the threshold, the RQD of model A-A-S is greater than those of models A-A and N-N. The relationships between the RQD values of models A-A and N-N depend on the core piece lengths at the start and end of the scanline. In actual project cases, model A-A is always used for RQD determination. Other models are used for scientific research only. Eqs. (4) and (5) determine the RQD values based on the easily obtainable fracture frequency, which is widely used and more cost-effective [7, 10]. 3.2

RQD variation

The calculated RQD values based on the 3D fracture network can represent the measured RQD values because the fractures in the 3D network can represent those in the field rock mass. To validate this conclusion, the measured RQD values of the actual rock mass were compared with the calculated RQD values along the z direction. A total of 10 drill runs with lengths of greater than 50 m were set in the field to study the quality of the rock mass. Thresholds of 1 and 2 m were selected to determine the respective calculated and measured RQD values. The measured RQD values along the 10 drill runs for the 1 and 2 m thresholds were located at (82%, 94%) and (58%, 70%), whereas the calculated RQD values were at (79%, 95%) and (60%, 75%), respectively (Table 3). The measured and calculated RQD values were not equal because the network was generated based on the stochastic theory, which implies that only the statistical features of the network can represent the field features. However, the RQD values were located in approximately the same range, and the average RQD values are approximately the same. Therefore, the calculated RQD values based on the 3D fracture network can be used to represent the measured RQD values in the actual rock mass. Rock mass has significant inhomogeneity, that is, RQD value varies at different regions in the rock mass and in the 3D fracture network model. Therefore, a large number of scanlines are required to determine the variable RQD values and obtain a characteristic RQD. The RQD variation can be investigated based on the scanlines. The setting of the scanlines can be referred to Zhang et al. [24] (Figure 5). The setting of scanlines includes setting both the scanline groups and the single scanlines. Given the scanline setting in the x Table 3

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direction as an example, xoy is the parallel surface of the scanline group, which is composed of several single scanlines. The spacing between scanline groups and between individual scanlines is 2.5 m. A fracture network of 100 m× 40 m×40 m can hold 16 scanline groups. This network is smaller than the original network to eliminate the edge effects. Each group contains 16 single scanlines. A total of 256 scanlines were set in the x direction. Scanlines with increasing lengths can be set to study the RQD variation. The scanline length is designated as l*. The RQD calculation in the x direction is used as an example. The length of the single scanline is 100 m. This single scanline can be divided into 100/l* parts with length of l*. The part that is smaller than l* can be ignored. For 256 single scanlines, the number of the scanlines with the length l* can be determined as 25600 n int * , l

(6)

where int (x) can transform x into the largest integer that is no greater than x. The average RQD value of n scanlines is taken as the RQD value with a drill run length of l*. By changing l*, the RQD values for models A-A, N-N, and A-A-S can be determined. The fracture frequency λ can also be obtained. The RQD value can then derived using eqs. (4) and (5). As shown in Figure 6, an obvious variation exists in the RQD values. The RQD value increases constantly as the scanline length increases. When the length reaches a critical value, the RQD value stabilizes or only changes slightly. Therefore, RQD values in different drill run lengths should be calculated when these runs are set in the field. Only a sufficiently long drill run with a stable RQD value can be used to obtain the characteristic RQD. The RQD variations of different models with scanline length vary. Models A-A and T-T change significantly, whereas model A-A-S exhibits the least changes. Under the same threshold, model N-N has the largest critical scanline length. Model A-A-S has the shortest critical scanline length, and model A-A has a critical scanline length that falls between the first two (Table 4). When the scanline is sufficiently long, the RQD values of models A-A, N-N, and A-A-S converge to the same value (Table 4). This finding can be attributed to the fact that when the scanline is relatively longer, the starting and ending core pieces are significantly

The calculated and measured RQD values

Passing points of the scanlines (m, m, m)

(20, 10, 50)

(40, 10, 50)

(70, 10, 50)

(100, 10, 50)

(20, 20, 50)

(40, 20, 50)

(60, 30, 50)

(60, 40, 50)

(90, 30, 50)

(90, 40, 50)

Average value

Calculated Threshold 1 m RQD (%) Threshold 2 m

82

85

90

91

83

94

87

88

82

90

87.2

63

58

61

70

64

69

59

62

68

65

63.9

Measured Threshold 1 m RQD (%) Threshold 2 m

79

90

93

95

78

84

89

82

94

82

86.6

65

62

63

75

60

62

72

69

63

71

66.2

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Figure 5

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As shown in Figure 6, when the scanline is relatively short, the RQD values calculated using the Priest-Hudson and Sen-Kazi equations are inconsistent. An RQD variation with the scanline length exists. The critical scanline length is smaller than those of models A-A and N-N. However, the length is greater than that of model A-A-S (Table 4). When the scanline is relatively long, the RQD values calculated using the Priest-Hudson and Sen-Kazi equations converge to the same value (Table 4). As previously mentioned, the RQD variation with scanline length must be considered in practical projects. When the actual scenario cannot satisfy the layout of a relatively long drill run, model A-A-S must be adopted for the RQD calculation to ensure that the error resulting from variation with scanline length can be countered as much as possible. When the threshold value is 1 m, the stable RQD values calculated by Priest-Hudson equation, Sen-Kazi equation,

Setting of scanlines in the rock mass.

Figure 6

Table 4

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RQD variations with scanline length.

Different critical scanline lengths and stable RQD values for the models and equations

Models and equations

Threshold 1 m

Threshold 2 m

Threshold 3 m

Threshold 4 m

Critical scanline Stable RQD length (m) (%)

Critical scanline Stable RQD (%) length (m)

Critical scanline Stable RQD length (m) (%)

Critical scanline Stable RQD (%) length (m)

Model A-A

8

88.5

10

64

13

44

14

27

Model N-N

12

88.5

14

64

18

44

20

27

Model A-A-S

6

88.5

7

64

7

44

6

27

Priest-Hudson equation

10

88.5

11

68

9

48

9

32

Senz-Kazi equation

6

88.5

9

68

9

48

9

32

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and other models converge to the same value. However, as the threshold value increases, the relative errors among the calculation equations and models increase continuously (Figure 6). Thus, the accuracy of the equations changes with the selected threshold value. The errors must be considered when the Priest-Hudson and Sen-Kazi equations are used to calculate RQD, and certain safety factors must be considered in the engineering design. In this study, the Priest-Hudson and Sen-Kazi equations were corrected using fracture frequency and threshold t to obtain a stable RQD value equal to that derived from the models. The errors between the equations and the models are shown in Figure 7, and eq. (7) can be derived as follows: x x* t 0.024 0.023, * x

(7)

where x is the stable RQD value calculated by the PriestHudson or the Sen-Kazi equation, and x* is the stable RQD value calculated by models A-A, T-T, or A-A-S. The equation can be transformed into x*

0.024t 0.977

x.

(8)

If the Priest-Hudson equation is considered, the equation can be transformed into RQD 100

0.024t 0.977

1 t exp t .

(9)

The RQD value can be derived using eq. (9) with the fracture frequency λ and threshold t.

4 Optimal threshold investigation The 3D fracture network can be used to represent the actual rock mass in a project case. This 3D fracture network was generated based on statistical mathematics. Therefore, the location of an individual fracture in the network is not con-

Figure 7 The errors between the RQD values calculated based on the equations and those calculated based on the models.

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sistent with that of the actual fracture. However, the statistical properties of large numbers of parameter values can be considered consistent with that of the actual rock mass. Inhomogeneity and anisotropy are determined based on large numbers of RQD values along the scanlines and can be considered consistent with those of the actual rock mass. 4.1

Inhomogeneity

The rock mass or the 3D fracture network is inhomogeneous. Different regions have different mechanics and deformation properties [25, 26]. In this section, the optimal threshold, which can fully expand the RQD range to reflect the inhomogeneous feature, was explored based on the 3D fracture network. To study the inhomogeneity of the rock mass, drill runs must be set in different locations, and the variable RQD values must be investigated. However, economic issues make the achievement of the above measures difficult. The 3D fracture network simulation may help in achieving the goal. Scanlines, which represent drill runs, can be set in different locations. The 3D fracture network is generated based on statistical theory and cannot entirely represent the actual locations of the fractures in the field rock mass. However, the statistical characteristics of the fractures can reflect those of the real rock mass. Generalized RQD was used in this section. The values 1, 2, 3, and 4 m were used as the thresholds to study the RQD variations. Based on the calculation method described in Section 3, the RQD values of 256 scanlines were calculated, and the results are shown in Figure 8. The RQD values clearly changed with the threshold. A larger threshold resulted in a smaller overall RQD value. The RQD values were located within [77%, 96.8%], [38.2%, 84.4%], [7.8% and 74.8%], and [0%, 67.8%] for thresholds 1, 2, 3, and 4 m, respectively. The RQD values at different locations vary significantly, thus reflecting the inhomogeneity of the rock mass. The results are very important for guiding the field project analysis. When the number of the drill runs is small, the obtained RQD values could not be used to describe the

Figure 8

RQD values for thresholds 1–4 m.

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overall rock mass because these limited drill runs cannot reflect the spatial variation of the rock mass quality. Given the economic factors, the use of a 3D fracture network to determine the inhomogeneity of a rock mass is a feasible method. As the thresholds change, the ranges of RQD vary. For example, when the threshold is 4 m, the RQD range is 68%, which is significantly larger than the range when the threshold is 1 m (Figure 8). Maximizing the RQD variation range is an effective way of obtaining an optimal threshold that best reflects the inhomogeneity of the rock mass. The 256 scanlines were used to calculate the RQD values. Besides 1–4 m, thresholds 5–10 m were also investigated. The difference between the maximum and the minimum RQD values were used to reflect the inhomogeneity degree of the rock mass. If the RQD range is the largest for a given threshold, the threshold is the optimal one which can best reflect the inhomogeneity degree of the rock mass. The maximum and minimum RQD values with different thresholds are shown in Figure 9. As the threshold increases, the RQD difference value increases continuously to a certain critical value, beyond which the RQD values begin to decrease. When the threshold was 4 m, the RQD difference value reached its maximum. The optimal thresholds were often determined to best reflect the features of rock masses. Inhomogeneity is an important property of rock masses. Therefore, the threshold, which assures the wildest range of RQD values for an actual rock mass, can be considered the optimal value. The 3D fracture network is a statistical homogeneity; thus, RQD values are uniformly distributed. The maximum and minimum differences in the RQD values consequently ensure the widest range of RQD values. The aforementioned optimal threshold of the study rock mass is 4 m. In this section, the RQD values in the x direction are used to study the inhomogeneity of the rock mass. When the threshold is 4 m, the RQD variation range is the largest, which can best reflect the inhomogeneity in the x direction. Notably, the inhomogeneity characteristic of the RQD and the calculated optimal threshold differ for different direc-

Figure 9 The maximum and minimum RQD values for different thresholds in different locations.

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tions. Therefore, to study the optimal threshold for RQD, the research direction of the project must be set before the optimal threshold is derived. In this section, 1 m is chosen as the threshold change interval to study the RQD difference values. When the precise threshold needs to be considered, the threshold change interval can be decreased to increase the number of the study thresholds and to derive the optimal threshold accurately according to the aforementioned method. However, the calculation is not discussed in detail here. 4.2

Anisotropy

The rock mass has another important feature: anisotropy. An optimal threshold can be determined to best reflect the change of the RQD with different study directions [11]. Priest [7] proposed that the fracture frequency can be determined using N

s i cosi ,

(10)

i 1

where s is the fracture frequency along a scanline, i is the fracture frequency normal to set i, N is the number of fracture sets, and i is the acute angle between the scanline and the normal to set i. The fracture frequencies in different directions can be calculated using eq. (10). The study direction is defined by its dip and dip angle. The dip is the angle between the projection line of the study direction in the horizontal plane and the x direction, ranging from 0° to 180°. The dip angle is the angle between the study direction and the z direction, ranging from 0° to 90°. In this study, 1° is adopted as the change interval of the dip and dip angle to study the fracture frequencies at different directions. In total, 16471 (181×91) fracture frequencies were obtained. The dip and the dip angle are illustrated at 10° and 5° as the change interval in Figure 10. Different study directions clearly yield different fracture frequencies. This finding has also been reported by a large

Figure 10

Fracture frequencies in different directions.

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number of scholars [6, 8, 26]. The calculation results show that the maximum fracture frequency is 0.85 m1, and the minimum fracture frequency is 0.32 m1. The results indicate that the RQD values obtained using drill runs are not representative because they only describe the rock mass quality in the z direction. The RQD values in different directions are very important to comprehensively describe the quality of the overall rock mass. By considering the economic factors, 3D fracture network modeling is a rational method to investigate the varying RQD values because it can obtain RQD values in different directions. A negative correlation exists between the fracture frequency and the RQD value. That is, the maximum fracture frequency corresponds to the minimum RQD value and the minimum fracture frequency corresponds to the maximum RQD value. Therefore, based on the fracture frequencies in different directions, the maximum and minimum RQD values can be obtained using eq. (9). The difference between the maximum and the minimum RQD values can reflect the anisotropic degree of the rock mass. If the RQD range is the largest for a given threshold, the threshold is the optimal one which can best reflect the anisotropy of the rock mass. The maximum and minimum RQD values for different thresholds are shown in Figure 11. As the threshold increases, the RQD difference value increases and then starts to decrease at a certain point. This finding suggests that the anisotropic degree changes with the threshold. When the threshold is 3 m, the difference between the maximum and minimum RQD values reaches as high as 36.3%. As previously mentioned in Section 4.1, the 3 m threshold assures the widest RQD range. Therefore, 3 m is the optimal threshold that can fully reflect the anisotropic features of the rock mass. The optimal thresholds considering the anisotropy and inhomogeneity differ from each other. From the perspective of inhomogeneity, the optimal threshold changes with the study direction. However, from the perspective of anisotropy, only one optimal threshold exists. The optimal threshold varies for rock masses with different properties. Therefore, the study direction and the properties must be determined before the optimal threshold can be obtained. In this paper, RQD and its characteristics were determined based on 3D fracture network simulation. When the 3D fracture network for the field rock mass is generated, the RQD variation with scanline length and the optimal threshold can be investigated. The 3D fracture network is only applicable to structural fractures. However, RQD depends on all forms of discontinuities, including stratification planes, fault planes, and unloading joints. For a minority of discontinuities, the fault and stratification planes can be added into the fracture network manually, and the RQD can then be calculated. Concentrated unloading zones are always excavated. Therefore, the determination of RQD values in the unloading zones is usually not conducted in actual project cases. As mentioned above, the calculations proposed in this

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Figure 11 The maximum and minimum RQD values for different thresholds in different directions.

paper are applicable to fractured rock masses with only structure fractures and minorities of the extremely long discontinuities.

5

Conclusion

The RQD variation with scanline length and the optimal threshold are important concepts in the study of RQD. However, economic considerations hinder the use of actual drilling in studying the concepts. Therefore, a 3D fracture network simulation was used in this work. The calculation models and equations for RQD were summarized as models A-A, T-T, A-A-S, as well as the Priest-Hudson and Sen-Kazi equations. Using the 3D fracture network, the RQD values of the models and equations at different scanline lengths were studied. The RQD value was proven to exhibit a noticeable variation with scanline length. When the RQD is used to evaluate a rock mass, the variation must be considered. This value can be used as the parameter to evaluate the rock mass when the RQD reaches a constant value. The RQD variations with scanline lengths differ for different models and equations, of which model A-A-S possesses the shortest critical scanline length (6 to 7 m). Therefore, model A-A-S can be chosen for RQD calculation and can reduce the errors generated by the RQD variation. The precisions of the Priest-Hudson and Sen-Kazi equations vary with the threshold. When the fracture frequency is used to estimate the RQD, the threshold must be selected carefully. In this paper, a modified equation was proposed to counter the error of the RQD value calculated using the Priest-Hudson and Sen-Kazi equations. However, the feasibility of applying the modified equation requires further study. Evident inhomogeneity and anisotropy exist in the rock mass. RQD values calculated using the optimal threshold can fully reflect these special properties of the rock mass. The RQD distribution in the x direction can be taken as an example. When the threshold is 4 m, the RQD values locate

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between 0% and 67.8%. This result best illustrates RQD inhomogeneity. When the threshold is 3 m, the difference between the maximum and minimum RQD values at different directions is 36.3%. This result best illustrates the anisotropy of the rock mass. The optimal thresholds differ when anisotropy and inhomogeneity are considered. From the perspective of inhomogeneity, the optimal threshold changes with the study direction. However, from the perspective of anisotropy, only one optimal threshold exists. The optimal threshold varies for different rock mass properties. Therefore, the study direction and the to-be reflected properties must be analyzed before the optimal threshold can be determined. This work was supported by the National Natural Science Foundations of China (Grant Nos. 40872170, 40902077 and 41072196), the Doctoral Program Foundation of Higher Education of China (Grant No. 20090061110054), 2010 non-profit scientific special research funds of Ministry of Water Resources (Grant No. 201001008), Jilin University's 985 project (Grant No. 450070021107), and the Graduate Innovation Fund of Jilin University (Grant No. 20121073). 1 2

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