ROCK TUNNELLING QUALITY INDEX, Q-SYSTEM
Introduction
Rock Tunnelling Quality Index, Q was developed by Barton, N., R Lien and
J Lunde, 1974 [5] at Norwegian Geotechnical Institute (NGI) in period from 1971 to 1974 When Q-system was presented in 1974, it had been significantly advanced in support philosophy and excavating technology in tunnelling The considerable number of sorts of rock bolts was displayed and there are various ways in applying support based on the development of fiber reinforced shotcrete The using sprayed shotcrete in tunnelling was approved even in high quality rock mass by safety in excavating during recent years The cast concrete was used as exchanging methods for reinforced ribs in shotcrete
In 1993, Grimstad and Barton summarized 1,050 examples from Norwegian underground excavation to update the support chart By 2002, an additional update was made, incorporating over 900 new cases from tunnels in Norway, Switzerland, and India This update focused on the thickness, spacing, and reinforcement of reinforced ribs of shotcrete (RRS), with elements dependent on load and rock mass quality (Grimstad E K., 2002).
The Q-system was applied in two principal aims as [19]:
1 The stability of tunnel was considered in relationship with classification of rock mass The Q-system was used either the part of surface investigations and geological mapping, or the part of ground condition during excavations In last case, Q-value depended on rock cover of underground excavating
2 The Q-classification and support chart in Q-system will determine the choosing rock support for tunnels The guidelines related rock support was based on the great number of support example database before It included the recommends for immediate, temporary, permanent supports.
Determine the Q value for rock masses during Tunnelling
The Tunnelling Quality Index (Q), developed by the Norwegian Geotechnical Institute, is used to assess rock mass characteristics and necessary support in tunnelling projects The Q value ranges from a minimum of 0.001, indicating exceptionally poor rock quality, to a maximum of 1000, representing exceptionally good rock quality.
RQD is the Rock Quality Designation;
Jn is the joint set number;
Jr is the joint roughness number;
Ja is the joint alteration number;
Jw is the joint water reduction factor;
SRF is the stress reduction factor
The first quotient (RQD/Jn) reflects the rock mass structure, with extreme values ranging from 100/0.5 to 10/20, representing a significant difference of 400 times When measured in centimeters, the extreme values of 200 cm and 0.5 cm serve as rough yet realistic estimates, suggesting that the largest rock blocks are likely several times larger, while the smallest fragments are typically less than half of this size.
The second quotient (Jr/Ja) assesses the roughness and frictional characteristics of discontinuous or filling materials, evaluating the degrees of roughness in direct contact It is anticipated that significant pick strength and dilation will occur during shearing This quotient is a crucial factor influencing the stability of tunnels.
The choice of filling material significantly influences joint strength; specifically, a thin clay layer between contact-joint walls can greatly reduce this strength Additionally, the lack of interaction at these contact-joint walls creates unfavorable conditions that jeopardize tunnel stability and safety.
The third quotient (Jw/SRF) encompasses three key factors: SRF accounts for the loosening load during tunnel excavation through shear zones and clay-bearing rock, rock stress in competent rock, and squeezing loads in plastic incompetent rocks, all of which relate to the total stress in the rock mass The element Jw, estimated by water pressure, negatively impacts the shear strength of discontinuities by reducing the effect of normal stress Water present in discontinuities can soften and wash away filling materials such as clay or minerals, often combining with other factors to create unfavorable conditions for tunnel stability Consequently, the quotient (Jw/SRF) presents inherent complexities.
The equation of Q value impresses the three effect groups It can be seen as a function of:
2 Inter-block shear strength (Jr/Ja);
To enhance the accuracy of equations in the Q-system, it is essential to incorporate additional factors, such as the orientation of joints (dip and strike), which are currently omitted from the Q equation Including joint orientations significantly influences the selection of tunnel direction, allowing for the avoidance of major joints that are unfavorably oriented Therefore, addressing this limitation in the Q-system is crucial for improving the precision of geological assessments.
The Rock Quality Designation Index (RQD), introduced by Deere et al in 1967, is a key metric for assessing rock mass quality through drill core logs RQD measures the percentage of intact core pieces that exceed 100 mm (4 inches) in length relative to the total length of the cores.
Figure 1.1 Procedure for measurement and calculation of RQD [9]
Total length of core run× 100% (1.2)
RQD value varies from 0 to 100 percent, but if the Q value between 0 and 10 percent will be taken as 10 percent
Table 1.1 Rock mass quality group and RQD value respectively
RQD (Rock Quality Designation) RQD
Note: i ) Where RQD is reported or measured as ≤ 10 (including 0) the value 10 is used to evaluate the Q-value ii) RQD-intervals of 5, i.e 100, 95, 90, etc., are sufficiently accurate
During excavation, three-dimensional views of rock mass can often be obtained, making it essential to determine the Rock Quality Designation (RQD) in these views According to Palmström (2005), an equation has been provided to calculate RQD for specific cases.
RQD = 110 − 2.5J v (for J v between 4 and 44) (1.3) Where Jv is the number of joint per cubic
Table 1.2 presents the number of joints per cubic meter for each RQD class derived from Equation (3) To accurately calculate the Q-value, multiple RQD readings should be taken from surfaces of varying orientations, ideally at right angles to one another The fluctuations in RQD values can be effectively represented through histograms.
Table 1.2 An example of histogram presentation of Q-parameters from a tunnel section
Q - VALUES (RQD / Jn) (Jr / Ja) (Jw / SRF) Q
The dimensions and shapes of blocks within a rock mass are influenced by joint geometry, with joints often running parallel within a joint set, and block size being determined by joint spacing Additionally, random joints may exist without any systematic arrangement The impact of joint spacing is notably affected by the width and height of tunnels; when multiple joints from a joint set are present in a tunnel, they can influence its stability It is important to note that the Jn value does not represent the number of joint sets, but is estimated using Table 1.3.
A Massive, no or few joints 0.5-1.0
C One joint set plus random joints 3
E Two joint sets plus random joints 6
G Three joint sets plus random joints 12
H Four or more joint sets, random heavily jointed “sugar cube”, etc
Note: i) For tunnel intersections, use 3 x Jn; ii) For portals, use 2 x Jn
The Jn value in Table 1.3 was estimated by counting the number of joint sets and accounting for random joints During excavation, joint sets are typically easy to identify; however, if they are not readily visible, the dip and strike of the joints can be analyzed using a stereo net to determine their orientation This analysis is represented on a stereo diagram, highlighting the concentration of joint pole orientations.
The identification of joint sets is influenced by both joint spacing and the tunnel's span and height When joints are widely spaced, exceeding the span or height, the resulting blocks may become excessively large, causing the joints to appear random in nature.
Joint friction is affected by the properties of joint walls and the materials used to fill the joints Joint walls can vary in texture, being undulating, planar, rough, or smooth The joint roughness number illustrates these characteristics, as shown in Figure 1.3 and Table 1.4 The description of the joint is based on roughness assessed on two scales.
1) The conditions of rough, smooth and slickenside according to small structure in centimeters or millimeters It is easy to determine by estimating by the finger along the joint wall and touching on the small roughness face
2) Large scale roughness is determined in the decimeter to meter It can be scaled by 1 meter long ruler on the joint surface to measure the roughness amplitude The conditions of stepped, undulating and planer are used for large scale roughness The large scale roughness have to be taken care in relationship to the block size and falling direction
Figure 1.3 Joint wall surface with various Jr value
Joint Roughness Number J r a) Rock-wall contact b) Rock-wall contact before 10 cm of shear movement
Note: i) Description refers to small scale features and intermediate scale features, in that order c) No rock-wall contact when sheared
H Zone containing clay minerals thick enough to prevent rock- wall contact when sheared
DIGITALIZING Q-SYSTEM BY EXCEL SHEETS
Tunnel and Rock support parameters for tunnel in Excel sheets
This thesis presents the digitalization of the Q-system from paper to an Excel Calculated Sheet (ECS), integrating various functions based on commands and conditions The Q-system is utilized to assess the rock mass quality around tunnels, facilitating the evaluation of support systems including bolts and shotcrete Key parameters calculated during construction include bolt spacing (Sbs), bolt length (Lb), number of bolts (Nb), shotcrete thickness (Ts), and shotcrete volume (Vs), among others.
The tunnel profile calculated in the ECS is D-shaped, characterized by its span (B) and radius (R) Based on the rock quality assessed using the Q-system, support options during excavation include: 1) support for the roof only; 2) support for the roof and half of the wall; and 3) support for both the roof and the wall (refer to Figure 2.1).
Figure 2.1 Types of supporting 1) Only roof; 2) Roof and a half of wall;
The type of support for a tunnel, such as bolts or shotcrete, depends on the rock quality and the required span During excavation, the owner has the authority to assess rock quality and modify support parameters based on their experience This can lead to significant differences between initial estimates using the Q-system and the adjusted results The ESC was designed to include calculation sheets for both the Q-system and the owner's adjustments, allowing for a comparative analysis of these results.
Digitalizing Q-system
To make more convenient during digitalization of Q-system, a number of specific points on the Q graph was signed by a lot of letters and digits such as:
The graph features numbered lines from 1 to 19, indicating their names and functions, such as graph 1-2, graph 2-3, and graph 4-5 Key points on the Q axis are labeled with capital letters A, B, and C, while points on the Span or height/ESR axis are designated using Roman numerals like I.
II and III, etc The location of specific points was illustrated on Q graph in Figure 2.2
Figure 2.2 Remarked points on Q graph [3]
To utilize the Rock Tunnelling Quality Index (Q-system) in Excel, the highlighted points in Figure 2.2 will be transformed into the Cartesian coordinate system (xOy) The line graph will be digitized into functions, represented as lines or curves, which will categorize the Q-graph into distinct fields Subsequently, the Q-system will be redefined as the Q*-system within the Cartesian coordinate framework (xOy).
The Q*-system (xOy) has an origin (0; 0) which sames point A on Q-system
In other words, Q and Q*-system has the origin point together
The coordinate of points on Q-system was converted to Q*-system as:
Table 2.1 Coordinates of points in Q-system and Q*-system
Point Value in Q-system Value in Q*-system (x0y)
The line graph, named according to the endpoints shown in Figure 2.2, was created by digitalizing the data points and categorizing them into pairs such as 1-2, 2-3, 4-5, and so on, up to 18-19 The purpose of the line graph was to illustrate function approximations derived from the coordinates listed in Table 2.1, with the corresponding graphs of these approximations displayed below.
Figure 2.3 Line graph 1 - 2 in Q*-system
Figure 2.4 Line graph 2 - 3 in Q*-system
Figure 2.5 Line graph 4 - 5 in Q*-system
Figure 2.6 Line graph 6 - 7 in Q*-system
Figure 2.7 Line graph 8 - 9 in Q*-system
Figure 2.8 Line graph 10 - 11 in Q*-system
Figure 2 9 Line graph 12 - 13 in Q*-system
Figure 2.10 Line graph 14 - 15 in Q*-system
Figure 2.11 Line graph 16 - 17 in Q*-system
Figure 2.12 Line graph 18 - 19 in Q*-system
Because the coordinate system of Q has not same scale with coordinate system of Q* (xOy), it is necessary to convert the axis scales between Q-system and Q*-system
To identify the Q-system, we need to determine two key parameters: the Q value and the B/ESR ratio Essentially, the Q-system is defined by the coordinates of a random point, represented as R (Q; B/ESR) This random point in the Q-system is then transformed into the Q*-system as R (xR; yR) Consequently, two conversion phases are required: first, converting the Q value into the xR coordinate, and second, converting the B/ESR ratio into the yR coordinate.
The xR coordinate of R random point was calculated by based on the Q value The xR coordinate was determine by interpolation linearly methods For example:
4 − 1 (18.074 − 15.034)] = 17.061 Where xJ and xK are the abscissae of J and K point respectively
Moreover, it is easy to see on the Q-axis of Q-system that the line segments
AB, DF, GI, JK, LN, OP and line segments BD, FG, IJ, KL, NO, PQ have a same
XQ* - System length respectively Hence, it is easy to time the number of same line segments and add the interpolation linearly part during exchanges to obtain xR coordinate
Figure 2.14 The relationship between Q value and xR coordinate
In addition to linear interpolation methods, the conversion of Q value to xR can be effectively achieved using the logarithmic function, represented by the equation xR = 2.1966.ln(Q) + 15.117 This relationship demonstrates a strong correlation between Q value and xR coordinate, with an R-squared value of 0.9995 (refer to Figure 2.14).
2.2.3.2 Convert B/ESR ratio to y R coordinate
Using same methods for xR coordinate, the yR coordinate was exchanged from B/ESR ratio as:
The yR coordinate was calculated using equal line segments, specifically I-II = IV-V, II-III = V-VII, and III-IV = VII-VIII, in conjunction with the determination of the xR coordinate The formula for xR is xR = 2.1966ln(Q) + 15.117.
Figure 2.15 The relationship between B/ESR ratio and yR coordinate
In addition, the yR coordinate could be determined by a logarithmic function yR = 3.3312.ln(B/ESR) – 0.0026 with R-squared as 0.9999 (see Figure 2.15)
After converting the Q-system to the Q*-system, each random point was characterized using the Descartes coordinate system (xR; yR) The determination of reinforcement categories relied on these two coordinates and specific restrictions on xR and yR Given that the fields for reinforcement categories are confined to the intersection areas of graphs and are represented as discontinuous functions, they can be accurately divided along the Oy-axis, defined by the equation yR = 3.3312ln(B/ESR) - 0.0026.
Figure 2.16 Divided fields in Q-system Reinforcement categories in Q-system included nine categories as:
4) Systematic bolting, (and reinforced concrete, 4 - 19 cm);
5) Fiber reinforced concrete and bolting, 5 - 9 cm;
6) Fiber reinforced shotcrete and bolting, 9 - 12 cm;
7) Fiber reinforced shotcrete and bolting, 12 - 15 cm;
8) Fiber reinforced shotcrete > 15 cm, reinforced ribs of shotcrete and bolting;
A random point R (xR; yR) placed in a category if it meets the boundary conditions of this category For example:
If a random point R meets a complex boundary condition
𝑦 𝑅 6−7 ≤ 𝑦 𝑅 ≤ 𝑦 𝑅 4−5 so point R will belong to category 8
Where yR 6-7 and yR 4-5 are values of functions y6-7 and y4-5 when x = xR respectively (see Figure 2.5 and Figure 2.6) The boundary conditions of other fields are also constituted similarly
2.2.5 Determine bolt spacing in shotcreted area (S bs )
In the Q-system, bolt spacing in shotcreted areas (Sbs) is defined by specific values: 1.0 m, 1.2 m, 1.3 m, 1.5 m, 1.7 m, 2.1 m, 2.3 m, and 2.5 m, which are solely dependent on the Q value This allows for linear interpolation of bolt spacing based on the Q value Consequently, a single bolt spacing value, such as 1.5 m, can correspond to multiple B/ESB ratios under varying conditions, including B/ESB values of 5, 10, and 20.
Using interpolation methods likes above, bolt spacing in shotcreted area in Q*-system will be determined by xR abscissa For example,
2.2.6 Determine bolt spacing in unshotcreted area (S bus )
Bolt spacing in unshotcreted areas (Sbus) is determined when the R (xR; yR) coordinates satisfy the boundary conditions of category 1 (Unsupport) Specifically, the Sbus value is calculated under the conditions xI ≤ xR ≤ xO (where 0.4 ≤ Q ≤ 100) and 0 ≤ yR.
0 ≤ 𝑦 𝑅 ≤ 𝑦 𝑅 18−19 Bolt spacing in unshotcreted area (Sbus) was also calculated depending on interpolation linearly between available Sbus values in unshotcreted area (1.0 m, 1.3 m, 1.6 m, 2.0 m, 3.0 m and 4.0 m)
For example, with Q = 50 and B/ESR = 7 were converted to Q*-system as xR
= 23.5595 and yR = 7.1248 respectively in Descartes coordinate system A random point R meets boundary conditions of category 1 so Sbus was calculated by equations:
The bolt length (Lb) in the Q-system is determined solely by the tunnel span and the ESR ratio, indicating that it relies exclusively on the yR coordinates within the Q*-system Lb can be calculated using linear interpolation methods or the equation provided.
ESR is Excavation Support Ratio
In the Q-system, shotcrete thickness (Ts) has only been established for categories 4, 5, 6, 7, and 8 The Ts value is determined when the coordinates of the R point in the Q*-system satisfy the boundary conditions of these categories To calculate the Ts value for random points within categories 4 to 8, interpolation of the boundary functions for each category is utilized.
Figure 2.18 Determine shotcrete thickness (Ts) For example, a random point R (xR; yR) placed in category 8, the Ts value at
For other random points at other location, the Ts value was also interpolated similarly.
Calculated sheet in Excel
The Q-system parameters were inputted into the Excel Calculated Sheet (ECS) with specific functions and restrictions The Q*-system within the ECS consists of four calculated sheets that facilitate various procedures, including Plotting the Q-system, Estimating the Q value, Geometrical Input, and Temporary Rock Support Parameters.
Figure 2.19 The interface of Q-system sheet
Figure 2.22 Temporary Rock Support Parameters sheet
The Q value is crucial for estimating rock mass quality, taking into account the key elements discussed in section 1.2 Upon calculation, the results yield a Minimum Q value, Average Q value, and Maximum Q value One of these Q values will be chosen for inclusion in the Rock Support Parameters sheet.
The Geometrical input sheet requires several key data points, including the length of the segment (z), the Q value based on the Q-system or user evaluation, the span of the cross-section (B), the height of the cross-section (H), the Excavation Support Ratio (ERS), and the supported profile.
The input data was processed using various functions and calculated methods related to Temporary Rock Support parameters, yielding significant results.
+ Rock mass quality: Rock classes and Categories
+ Bolt parameters: Bolt length (Lb); Bolt spacing in shotcrete area/ Bolt spacing in unshotcrete area (Sbs/Sbus); Total bolts in plane (N1); Total blots in a segment (N2); Total bolts (N = N1 + N2)
+ Shotcrete parameters: Thickness of shotcrete (Ts); Volume of shotcrete per
1 m in length (V1); Volume of shotcrete in a segment (V2); Total volume of shotcrete (V)
Estimate the precise degree
The Q*-system differs significantly from the Q-system due to the coordinate measurement uncertainty arising from the approximate selection of points This uncertainty affects the precise degree of R (xR; yR) within the Q*-system Additionally, other values in the Q-system are linearly interpolated, which means that the coordinate measurement uncertainty of R ultimately impacts the overall measurement uncertainty throughout the Q*-system.
The Q*-system functions are based on coordinate interpolation methods using points along the line graph, where the precision of these functions is directly influenced by the number of selected points As more points are chosen, the accuracy of the Q*-system increases Figure 2.23 demonstrates the precision comparison between the Q*-system and the Q-system.
Figure 2.23 The precise degree of points and functions in Q*-system
Figure 2.23 illustrates that the critical ending points of the Q-system and Q*-system show minimal deviations, indicating that the precision of points between the two systems is acceptable.
The Q*-system line graph displayed slight deviations compared to the Q-system, particularly noticeable at the boundaries between categories 7 and 8 Overall, the precision among the line graphs was not significantly different In practice, the Q-system evaluation of rock mass quality was primarily conducted visually, leading to minimal distinction between the direct tracking results and the computed outcomes from the Q*-system (ECS).
Discussion
The main work performances included the calculated sheets that were constituted to estimate the Q value and the support parameters of Q-system
Building the calculated sheets will help the evaluating Q value and support parameters quickly and conveniently during excavations
Bases on Rock Tunnelling Quality Index, Q-system, the calculated sheet in Excel program was used to calculate Q values of rock mass The outputs included minimum, average and maximum Q value
This thesis highlights the significant task of transforming the Q-system presented in the paper into the Q*-system using Excel by appropriately adjusting the coordinate systems As a result, the inputs from the Q-system, specifically Q and B/ESR, were converted to the coordinates of R (xR; yR) in the Q*-system.
The line graphs in the Q-system were digitized into functions within the Q*-system These functions' values at each coordinate (xR; yR) were utilized to calculate support parameters and assess the quality of the rock mass.
The calculated sheets enable users to effortlessly adjust the Q-system factors and support profiles, including options for only the roof, roof and wall, or roof with half a wall The modified results will be compared against the estimated outcomes in the Q-system.
The comparison between the Q*-system and the Q-system is primarily influenced by the number of selected points and the accuracy of the approximate functions This study reveals that there is minimal difference between the two systems.
The Q*-system in Excel enhances convenience for contractors and owners in estimating rock mass and support Additionally, it assists students in quickly tracking the Q-system during their studies and research.
This thesis demonstrates several errors, particularly in the ineffective use of the Q-system The issues are evident in the calculated sheet, which fails to account for time and cost based on the parameters obtained from the Q*-system.
The thesis's calculated sheets lack user-friendliness and require enhancements in interface and functionality for improved user convenience By integrating digital methods from the Q-system with programming languages such as Visual Basic, C++, and Matlab, the Q-system can be significantly upgraded to achieve a more professional standard.
ESTIMATING THE RADIAL DISPLACEMENT ON THE
Introduction
The Rock Tunnelling Index (Q-system), developed by Barton et al in 1974, is a valuable tool for assessing rock mass quality and determining the necessary support for tunnels and rock caverns In the past 10 to 15 years, numerous studies have expanded the Q-system's applications, highlighting its advantages However, like other rock mass classification systems, it has limitations Plamstrom et al (2002) identified that the effective working range of the Q-system spans from 0.1 to 40 in Q value, which corresponds to a (Span or Height)/ESR ratio of 2.5 to 35, as illustrated in the highlighted rectangular area in Figure 3.1.
The stability of supported tunnels assessed using the Q-system has not been adequately addressed, particularly in its effective working area N Barton (1981) developed a back-calculation method to estimate the average deformation modulus of rock masses classified by the Q-system in large caverns Utilizing the finite element method, the study established a correlation between the Q value and the average deformation modulus, enabling predictions of tunnel deformation Additionally, the study identified that the deformations of the tunnel's arch, wall, and invert are influenced by the Q/Span or Q/Height ratio, as well as the dimensions of the excavations However, it's important to note that these findings stemmed from well-instrumented underground power stations and did not encompass the deformation of smaller tunnels excavated in rock masses with high Q values.
In Bieniawski's 1974 research, the analysis of in-situ deformation measurements was conducted by classifying rock masses according to the Q-system The deformation modulus of the in-situ rock mass served as a valuable reference linked to the Q value, essential for numerical studies on stress distribution and displacement around tunnels However, the findings primarily focused on the deformation modulus, neglecting the implications for tunnel stability within the effective working area of the Q-system.
This study evaluates the stability of rock masses in the effective working area of the Q-system by analyzing the radial displacement of tunnel boundaries derived from a numerical model The findings will enhance the application of the Q-system in tunneling, particularly in forecasting tunnel stability.
Efficient working area of Q-system
Q-system was constituted by the plenty of data that was collected from tunnels in Norway and other countries before Based on Q-system, the parameters about rock supports as bolts and shotcrete were determined by Rock mass quality in terms of Q value and (Span or Height)/ESR ratio (Equivalent Dimension, De)
Palmstrom and Broch (2006) conducted elaborately a survey about Q-system and showed that actually the Q-system worked best within a certain range of parameters
[1] This range was illustrated by a rectangle in Figure 3.1
The best working area of Q-system fluctuated between 0.1 and 40 in Q value corresponding to the (Span or Height)/ESR ratio varied from 2.5 to 35
When data falls outside the specified range, it is essential to employ supplementary calculated methods to improve the reliability of determining appropriate rock supports in tunneling.
Figure 3.1 Limitation of Q-system for rock support Outside this area supplementary methods/evaluations/calculations should be applied (reproduced from Palmstrom and Broch, 2006) [1]
Ensuring the stability of a tunnel after rock support is crucial While the Q-system provides empirical methods for framing rock support, it fails to adequately quantify tunnel stability Specifically, the radial displacement at the tunnel boundary within the effective working area of the Q-system has not been sufficiently addressed.
The author performed a numerical investigation utilizing RS2 software from Rocscience to assess the stability of a tunnel This assessment focused on radial displacement measured at three critical points along the tunnel boundary: the crown of the tunnel, the top of the tunnel wall, and the tunnel floor, as illustrated in Figure 3.3.
Case study and Model parameters
Based on the efficient working area of the Q-system proposed by Palmstrom and Broch (2006), this study selects cases of rock mass quality and support structures that lie on the mutual boundary between categories, as illustrated in Figure 3.2.
Figure 3.2 presents the adopted case studies, identified based on two key parameters: Q value and the (Span or Height)/ESR ratio This study encompasses a total of 28 numerical calculations, with all case parameters detailed in Table 3.1.
Table 3.1 Parameters of case study
Case Q value GSI B/ESR Bolt spacing
Tunnelling presents a complex three-dimensional challenge influenced by the advancing process of the tunnel face However, the tunnel analyzed in this study is significantly longer than its cross-sectional dimensions, allowing for the use of two-dimensional models instead of three-dimensional ones for simplicity.
The 2D model features dimensions of 160 meters in both height and width, chosen through parametric analysis to minimize the impact of boundary conditions on numerical calculation outcomes.
The numerical model analyzed features D-shaped tunnels, with the height (H) equal to the width (B) as illustrated in Figure 3.2 The Excavation Stability Rating (ESR) was established at 1 (category D) for various structures, including power stations, major road and railway tunnels, civil defense chambers, and portal intersections, following the recommendations of Barton et al (1974).
The numerical model layout, depicted in Figure 3.3, includes monitored points (1), (2), and (3), which were established based on vertical displacement at points (1) and (3), and horizontal displacement at point (2) The model was discretized into finite elements, specifically triangular elements with six nodes each Its sufficiently large size ensured that the influence of model dimensions on stress and displacement in the surrounding rock mass was minimized Additionally, the model's external boundary was constrained in the x and y directions, as illustrated in Figure 3.3.
In this study, the initial stresses in the rock mass were simulated by considering the effects of gravity on the model Key parameters included the vertical stress derived from the unit weight of the overlying rock mass (γ), the depth of the tunnel (H), and the lateral earth pressure (K0) It was assumed that the tunnel's depth plays a significant role in these stress calculations.
100 m, rock's unit weight (γ) equals 0.026 MN/m 3 and lateral earth pressure (K0) was set as 0.5 for whole cases
Evaluation of rock mass and rock support parameters
The constitutive model using Hoek-Brown failure criterion has been adopted for the rock mass surrounding tunnel [11] The deformation modulus of intact rock
Ei was evaluated as follows [12]
Where: MR - Modulus ratio, MR = 500; σci - Uniaxial compressive strength, σci = 50 MPa
The deformation modulus of rock mass (Erm) was calculated on the basis of the following relationship:
(3.2) Where: D - Disturbance factor, assumed D = 0; GSI - Geological Strength Index
The reduced value of material constant (mb) was calculated based on the Hoek - Brown failure criterion [11] m b = m i exp (GSI − 100
For each case in Figure 3.2 just has produced Q value Consequently, Q value and Rock Mass Rating (RMR) value of rock mass was transferred by the relationship [6]
In addition, the relationship between Q value and RMR value was determined by a logarithmic function as following [2]
Therefore, GSI value can be calculated as:
In the Q-system for tunnel support, bolts and shotcrete serve as essential rock reinforcement methods Key parameters such as bolt spacing, bolt length, and shotcrete thickness were established based on case studies outlined in Table 3.1 Additional specifications for the bolts and shotcrete utilized in the models are detailed in Table 3.2.
Results
The results of a simulation involving 28 case studies, conducted using RS2 software by Rocscience, revealed the radial displacement on the boundary at three key points: the top of the crown, the top of the wall, and the middle of the road, as illustrated in Figures 3.4, 3.5, and 3.6.
Figure 3.4 Vertical displacement at Point 1
Figure 3.5 Vertical displacement at Point 3
The analysis of radial displacement at points (1), (2), and (3) within the effective working area of the Q-system indicates a gradual decline in radial displacement as the Q value increases and the (Span or Height)/ESR ratio decreases This suggests that tunnels supported by bolts and shotcrete, in accordance with the Q-system recommendations, exhibit greater stability with improved rock mass quality and reduced tunnel span For instance, at a Q value of 0.1 and a B/ESR of 25, the radial displacement at point 1 measures 4.4 cm, while an increase to a Q value of 0.3 and a B/ESR of 20 results in a reduced radial displacement of 3 cm.
The analysis in Figure 3.5 reveals that the radial displacement at point 3 significantly exceeds that of other points Specifically, when the Q value is set at 0.3 and the (Span or Height)/ESR ratio is 20, point 3, located in the middle of the road, experiences a radial displacement of 7.2 cm In contrast, points 1 and 2 show radial displacements of only 3.0 cm and 1.4 cm, respectively.
Figure 3.7 demonstrates how the Q/De ratio influences radial displacement at Points 1, 2, and 3 along the tunnel boundary, revealing a consistent downward trend in radial displacement across all three locations.
The Q/De ratio exhibited an exponential increase, as illustrated by the dependency of Radial Displacement across 28 cases, represented in Figure 3.7 Notably, the Radial Displacement at Point 3 demonstrated a significantly higher dependency compared to other points.
Figure 3.7 Radial displacement at Point 1, Point 2 and Point 3
The tunnel's road lacked structural support, allowing the rock mass to move freely into the tunnel space In contrast, at Points 1 and 2, the rock mass exhibited radial movement, but the displacement was less significant than at Point 3 due to the support provided by multiple bolts and a shotcrete layer along the tunnel boundary.
Discussion
This literature review highlights numerous numerical investigations aimed at estimating radial displacement at the tunnel boundary within the effective working area of the Rock Tunnelling Quality Index (Q-system) Key conclusions from the performance study indicate significant insights into the behavior of tunnel boundaries under varying conditions.
The Q-system provides a reliable framework for assessing rock stability in tunneling, thanks to its extensive practical measurements However, outside the Q-system's effective range, additional methods are necessary to accurately determine appropriate rock support designs.
The Radial Displacement at Point 3 consistently exceeds that of other points under similar conditions, indicating that the magnitude of Radial Displacement increases in the following order: Point 1, Point 2, and finally Point 3.
- The Radial Displacement at Point 3 depends significantly on the Q/De ratio compared dependency degree of Radial Displacement at others points
The thesis focused on identifying the appropriate rock support for tunnels using the Q-system, which involved developing calculation sheets and estimating radial displacement at the tunnel boundary within the effective working area of the Q-system.
To utilize Q-system efficiently, the author built calculated sheets in Excel those allowed users to trace Q-system visually, promptly and flexibly to vary input parameters
This thesis establishes proper rock support parameters by digitizing the Q-system and converting it to the Q*-system, enabling practical application The Q*-system evaluates rock supports in three scenarios: only the roof, roof and wall, and roof plus half the wall The results are automatically compiled for each tunnel segment and overall length Utilizing the Q*-system in Excel enhances convenience for contractors and owners in estimating rock mass and support, while also assisting students in quickly tracking the Q-system during their studies and research.
The stability of tunnels utilizing the Q-system is significantly influenced by proper rock supports, as evidenced by the radial displacements observed at various monitored points Notably, Point 3 consistently exhibits greater radial displacement compared to other points under similar conditions Therefore, ensuring adequate rock supports is crucial for maintaining tunnel stability throughout the excavation process The analysis of radial displacements in tunnels supported by effective rock systems is closely tied to the Q/De ratio, revealing substantial variations in displacement across different points, with Point 3 demonstrating a stronger dependence on this ratio than the others.
The thesis highlights that work performance was limited by the D-shaped cross-section, with appropriate rock support only assessed for overall tunnel stability In practice, tunnels can be excavated in various cross-sections to fulfill specific requirements, while the selection of proper supports is influenced by time and cost considerations Additionally, the quality of excavated tunnels in rock mass is affected by multiple factors, including the presence of adjacent tunnels and varying geological conditions These aspects will guide future research directions of the thesis.
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