During construction of 3D geological models, it is difficult to determine the uniform between geological model and true model. As a comprehensive index, rock quality designation (RQD) is reliable to assess the rationality of geological models. Unfortunately, The RQD of rockmass is determined completely by the deterministic threshold value and directions of the scan lines presently. To avoid this drawback, the modified method of the RQD value based on the threshold value and 3D space is proposed in this paper. Simultaneously, the analogue-simulation method based on rupture mechanism and classification of discontinuities is proposed. The elliptical discontinuity is considered for general discontinuity, and the special discontinuities, such as bedding, fault, and interlayer are dealt with individually. The accuracy of the 3D model is verified by the modified RQD. The 3D model of the rockmass is analogue simulated through repetitively obtaining data from the interval confidence of geometrical parameters of discontinuities, which are determined by a mass of data derived from field investigation. Besides, the dam base of the Xiangjiaba hydropower station is taken as an example, and the 3D model of the dam base is analog-simulated; its stability is evaluated by DDA method. The safety coefficient of the dam base is obtained by utilizing the overload method.
At present, 3D geological simulation methods have been developed from model construction to practical computation [
Rock quality designation (RQD) has been widely used to classify the discontinuity of rock masses and assess the intactness of rock masses. In previous studies, the applications of RQD have been mainly based on a deterministic threshold value and a single scanline direction. Priest and Hudson [
The discontinuous deformation analysis (DDA) method has been widely used to assess the stability of rock mass engineering. The method has been developed for 2D problems by Shi and Goodman [
At present, a wide variety of rock quality assessment methods have taken rock structure into account; however, it is necessary to determine how to adapt the rock structure model into the adaptive mechanical model for providing the basic data for model experiments and rock masses intactness assessment. The 3D structure model of rock masses is typically acquired by using discontinuities and spacing, block size, and other rock intactness indexes. There are three issues involved in the acquaintance of rock structure: (i) how to gain the reasonable values for the geometrical characteristics of the discontinuities. It remains open to discuss how to describe the whole rock masses through the representative data from field measurements, when simulating the space geometry of discontinuities, and the effects of the geometrical characteristics of the rock are partially caused by tectonic movement and so forth. The second issue is (ii) how to reasonably understand the rock masses formed by discontinuities. Rock masses are the combination of discontinuities and structural body. Under the condition that the geometrical characteristics of the rock masses have been confirmed, it is worth considering how to simulate the rock masses using these characteristics and how to compare the simulated rock masses with the virtual ones. Furthermore, there are several different beliefs concerning how to define the index reflecting the intactness of rock masses. (iii) How to build the connection between the numerical computational and the geological models constructed using the 3D network simulation method is the third one. Currently, most numerical computational methods which take rock as a continuous medium are not effective in distinguishing the characteristics of rock masses. Even if the discontinuous analysis method is adopted in some cases, the general means will not compensate for the deficiencies in the numerical calculation of engineering; thus it is necessary to establish the relationships between the 3D geological models and discontinuous deformation analysis methods.
Despite the fact that the technique of discontinuous network simulation (DNS) has been greatly improved in recent years, this method is not particularly accurate, due to its hypothesis. It assumes that the spatial shape of the discontinuities is circular, while this is not necessarily true. In addition, the technique of the DNS ignores the effects of the large-scale discontinuities, taking only the grade IV and V discontinuities into account. It is easy to understand that the application and decision of the 3D simulation technique are restricted, and, as matter of a fact, the grade IV and V discontinuities are the ones which play controlling roles in the local stabilization of rock masses. In this paper, the large-scale discontinuities are firstly considered during the construction of the 3D geological model. The production of the grade IV and V discontinuities is based on the 3D model, including the large scale discontinuities such as fault and weak interlayers. Through a large amount of the field observations and research regarding the shape of the discontinuities, it is believed that the discontinuities should not be categorized into a single circular shape, due to the fact that the production of the discontinuities is affected mainly by the tectonic movement. As known, the stress ellipsoid is applied to structure geology for explaining rock failure and deformation of rock masses based on the definition of mathematics and the physical meaning. Therefore, the shape of discontinuities directly affected by tectonic stress should not be circular in shape, but elliptical, generally due to the unequality of the values of the maximum and minimum principal stresses. Based on this view, the elliptical shape would be adopted to corresponding discontinuities affected by tectonic stress, and the steps of the DNS are as follows: (i) take samples of the discontinuities through field measurements; (ii) create probabilistic models of geometrical parameters of the discontinuities such as orientation, spacing, and trace length; (iii) make use of the Monte-Carlo random simulation technique to obtain random data from the confidence interval of geometrical parameters of discontinuities; (iv) construct the large-scale discontinuities in the 3D model, such as the fault, bedding, and interlayer; (v) construct the grade IV and V discontinuities in the 3D model; and (vi) create a complete network map of the DNS and form its boundaries. The boundaries formed by the discontinuities are shown in Figure
Map of the DNS for the Xiangjiaba hydropower station dam base.
Discontinuities
Structural bodies
Rock masses are discontinuous, inhomogeneous, and anisotropic in terms of their discontinuous geometry; thus it is a difficult task to simulate the whole characteristics of rock masses. At present, ROD, a method used to evaluate the intactness and quality of rock masses, is the main means of simulating the discontinued properties of rock. The intactness coefficient of rock masses deals with the anisotropic property from the whole rock mass. However, RQD makes an objective appraisal of the intactness of the rock mass using the scanlines, such as borehole, tunnel, and field outcrop. The advantages and disadvantages of the method are described as follows. It is not proper to use the RQD method to merely evaluate the quality of rock mass through a borehole which narrowly shows the condition of rock masses, because the rock mass has the property of anisotropy. In addition, the RQD method proposed by DEER in 1964 gave the deterministic value of 10 cm, which is defective at measuring the intactness of rock masses, and increases the amount of calculation if it is used to evaluate the stability of the rock mass, due to the production of a mass of structural elements separated by discontinuities. For example, the actual direction of a scanline in the project is often vertical in the borehole and horizontal in the tunnel, and the RQD value of single direction scanline cannot reflect the intact degree of the rock masses quality if considering the anisotropy of the rock masses. In addition, a threshold value of 10 cm is nevertheless an arbitrarily selected value. Therefore, if the variable threshold can have a dramatic effect on the computed RQD, it is appropriate that the assessment of the RQD can be further investigated in order to determine a method for selecting the threshold value, rather than always relying on the customary value. In order to avoid these dimensional effects, another threshold value should be adopted according to the specific engineering project. The rock masses are constituted by blocks of different sizes and shapes, which are formed by the separation of the discontinuities. When analyzing the stability of the rock masses in the project using the DDA method, every structural element will be formed by a closed loop constituted by several traces, and the traces which do not constitute a closed loop will be deleted or trimmed. Therefore, the RQD values are not reasonable due to the different quantity traces in the measure scanlines intersecting with the redundant traces, and thus both should be taken into account during the analysis of RQD. The dam base model formed by structural elements should be reliable from the perspectives of theory and field investigation.
Two main approaches for RQD evaluation are proposed as follows.
Four RQD balls formed in four different threshold values are shown in Figure
3D RQD of the Xiangjiaba hydropower station dam base rock masses.
In order to verify the reasonability of 3D geological model of DNS, the actual measured RQD is compared with the simulated one. The steps of the measurement method are as follows. Calibration of the borehole: according to the simulated rock masses, the RQD of the rock masses in the actual position of the drill hole is evaluated, and the results with those of the actual measurements are compared. The error between the actual measured values and the simulated values of the geometrical parameters must not be avoided. RQD is used to calibrate the simulated model by adjusting the geometrical parameters of the discontinuities, because RQD is a comprehensive index, which contains the geometrical characteristics of discontinuities, such as orientation, spacing, and trace length, to reflect the intactness of rock masses. Therefore, it is necessary to verify the RQD by adjusting the geometrical characteristic of the discontinuities until the results satisfy the demands. Calibration of the block characteristic of the rock masses: contrast the size and magnitude of the block formed from the 3D model with those of the actual field investigation. The span of the block may be satisfied by adjusting the geometrical parameters of the discontinuities.
It is believed to be very difficult to simultaneously satisfy the two aforementioned aspects. In general, the first one aspect is fulfilled, and then the other assessment aspect is calibrated accordingly.
Recently, the basic theory of DDA begins to reach maturity in correlative research and has made significant development in engineering application. The key contents of DDA are discussed below. Blocks in DDA are connective and form a block system by the contact constraint between two blocks. Within representing the number of blocks in the block system, the following equations are listed together in
Every block possesses six degrees of freedom. Each element [
DDA is based on the principle of the minimum potential energy; the total potential energy
All the terms in (
All the terms of (
Many components of the total stiffness matrix are provided by the single block and block systems, including the elastic, initial stress, point load, volume force, inertia force, initial displacement, bolt connection, normal contact force, tangent contact force, and friction force submatrices. The role played by each part of the total stiffness matrix in every situation may be clarified, provided that the appropriate potential energy expression is performed for each situation, and (
The Xiangjiaba hydropower station is the final planned stepped hydropower station along the Jinsha River (Figure
Location of dam base zone.
Layout of dam base zone.
In the dam site zone, the joint and fissure developments differ from each other due to their different tectonic locations. If the zone is divided based on tectonic location, the stratum steep-dip is located within the core of the fold. The right side of the bed and the right bank are both on the SW limbs of the fold, and the left side of the bed and the left bank are both on the NE limbs. The joint and fissure develop greatly, with the strikes of the superiority jointing groups being 40~70° and 320~340°, the former of which are fissures with medium- to high-dip angles, and the latter are joints with low-dip angles. The density of the joint and fissure is 10–20 per m. The joints on the left bank develop better than those on the right bank; there are two superiority jointing groups on the left bank, which have strikes of 280~300° and 60~80° and the density is 2–5 per m; and there are two superiority joint groups in the right with strikes of 60~80° and 280~300° and the density is 1–3 per m. The geometrical characteristics and corresponding probability distribution models of the main discontinuities are listed in Table
Statistical results of geometrical parameters of discontinuities.
No. | Orientation | Statistical indexes | Model | Mean | Standard variation | Samples | |
---|---|---|---|---|---|---|---|
Dip/° | Dip angle/° | ||||||
(1) | 45.54~115.54 | 8.46~58.46 | Spacing/m | Log-normal | 0.60 | 0.79 | 360 |
Dip/° | Normal | 85.24 | 13.32 | 374 | |||
Dip angle/° | Uniform | 36.77 | 11.44 | 374 | |||
Trace length/m | Log-normal | 23.80 | 19.76 | 374 | |||
(2) | 170.0~190.0 | 64.61~89.61 | Spacing/m | Log-normal | 11.10 | 32.64 | 23 |
Dip/° | Normal | 181.46 | 6.33 | 28 | |||
Dip angle/° | Normal | 81.21 | 7.17 | 28 | |||
Trace length/m | Uniform | 2.01 | 0.34 | 28 | |||
(3) | 326.57~360.00 | 41.47~76.47 | Spacing/m | Log-normal | 5.29 | 24.44 | 49 |
Dip/° | Uniform | 345.84 | 8.84 | 58 | |||
Dip angle/° | Uniform | 60.22 | 8.56 | 58 | |||
Trace length/m | Log-normal | 2.07 | 1.49 | 58 | |||
(4) | 262.01~327.01 | 24.81~69.81 | Spacing/m | Log-normal | 3.50 | 12.64 | 54 |
Dip/° | Uniform | 292.48 | 16.96 | 63 | |||
Dip angle/° | Uniform | 43.47 | 6.07 | 63 | |||
Trace length/m | Log-normal | 0.95 | 0.54 | 63 | |||
(5) | 44.74~74.74 | 58.30~88.30 | Spacing/m | Log-normal | 2.20 | 7.66 | 22 |
Dip/° | Normal | 60.44 | 7.95 | 27 | |||
Dip angle/° | Log-normal | 69.33 | 9.83 | 27 | |||
Trace length/m | Log-normal | 3.64 | 2.12 | 27 |
The material parameters used for calculation in the DDA method are shown in Table
Physical-mechanical parameters of rock masses in the dam base.
Materials | Density/kN/m3 | Modulus/GPa | Poisson’s ratio |
|
|
---|---|---|---|---|---|
Concrete | 24.0 | 17.60 | 0.167 | ||
Bed rock (II) | 26.0 | 15.00 | 0.220 | 1.20 | 1.40 |
Bed rock (III1) | 26.0 | 7.00 | 0.250 | 0.99 | 1.00 |
Bed rock (III2) | 26.0 | 5.50 | 0.280 | 0.86 | 0.80 |
Bed rock (III2~IV) | 26.0 | 4.00 | 0.290 | 0.77 | 0.65 |
Soft layers |
20.0 | 0.75 | 0.400 | 0.35 | 0.10 |
Figure
Computation model of dam base of Xiangjiaba hydropower station.
In Figure
It may be concluded from Figure
Table
Intactness assessment of rock masses of Xiangjiaba hydropower station dam base.
Rock quality grade | Degree of weathering | Intactness of rock masses | Location of distribution | ||
---|---|---|---|---|---|
Velocity of acoustic wave/m/s | RQD in the tunnel/% | RQD in the borehole/% | |||
I | Unweathered | >5000 | >90 | >85 | Depth of dam base |
II | Unweathered to weak weathering | 4000–5000 | 75–90 | 60–85 | Zones 1, 2, 4 |
III | Moderate weathering (lower) to weak weathering | 3500–4000 | 62.5–75 | 45–60 | Zones 1, 4, 5, 6 |
Moderate weathering (upper) | 3000–3500 | 50–62.5 | 30–45 | Zone 6 | |
Weak weathering to unweathered | Zone 3 | ||||
IV | Weak weathering to unweathered | 2000–3000 | 25–50 | 5–30 | Zones 3, 5 |
Influence band of fault and concentrated joint band | |||||
V |
|
<2000 |
|
|
Shattered fault zone and weak interlayer |
Notes: The zone of the dam base is divided by six sub-zones, which are arranged in order from the right bank to left bank of the Jinsha River.
RQD map of the dam base controlled by the rock mass discontinuities.
Location and scale of RQD method application
Results of RQD method at different locations
Figure
Actual and model distribution of the rock block size.
As seen in Figure
Displacement and velocity with time of different measure points in the dam base.
Measure points in the dam base
X-displacement with time of measure points
Y-displacement with time of measure point
X-velocity with time of measure points
Y-velocity with time of measure points
Similar trends with different measure points are seen in both Figures
As seen in Figure
It is convenient to examine the actual damage of the rock masses through the DDA program. The results are calculated via 1000 calculation steps in DDA and are shown in Figure
Fracture of rock masses in the dam base.
According to the overload method used in the DDA program, the rock mass failure of the dam base is classified as tensile fracture damage. The large circles in Figure
Relationship between overload and displacement of the measure points.
Horizontal displacement with overload times
Vertical displacement with overload times
RQD is one of the most important indexes for assessing the intactness of rock masses which depend on the geometrical characteristics of their discontinuities. In this paper it is shown that the use of the optimal RQD threshold value greatly extends the range of RQD values. A series of methods is used to assess rock quality, construct a 3D model, and evaluate the stability of the dam base. The conclusions of the study are as follows. Based on the mechanism of the geological mechanics, the elliptical discontinuities are used to simulate the rock structure, and this method is applied to the dam base of Xiangjiaba hydropower station. This study shows that the effects of the rock structure are caused by the special discontinuities during the simulation, and this method is very valid for application to the simulation of the rock structure. Based on the anisotropic characteristic of the rock masses, the modified RQD method with the threshold value and 3D space is applied to confirm the rationality of the 3D simulation and evaluate the rock mass quality of the dam base. Based on the 3D structure of the dam base, the ground profile applied in the discontinuous deformation analysis is obtained by cutting the model and the rock mass quality and the strain characteristic of the dam base are analyzed. The overload method is used to consider the failures occurring near the contact surface of the dam base and the rock masses, and the stability coefficient of the dam is determined through calculation.
This study is financially supported by the Natural Science Foundation of China (Grants nos. 41002089 & 41102162) and Jiangsu Overseas Research & Training Program for University Prominent Young and Middle-aged Teachers and Presidents. The authors would also like to acknowledge the editors and reviewers of this paper for their very helpful comments and valuable remarks.