Effect of rock mass quality on construction time in a road tunnel

On the basis of the existing NTNU (Norwegian University of Science and Technology) advance rate model and field experiences, an estimation model which can analyze construction time for a broad range of works related to tunnel construction by drill and blast has been established. The model includes the time spent for excavation, rock support, various installations in the tunnel, and site preparation. The model is developed as a spreadsheet. Furthermore, by the use of the model, analyses on various effects of rock mass quality on construction time and advance rate for four Q-values of 0.01, 0.1, 1.0 and 10.0 on seven sizes of road tunnels applied in Norway were made. The results show that construction time increases up to 30–40% with cross sectional area varying from T5 (35.2 m²) to T12 (86.9 m²) under the assumption that the same Q-value is applicable to the entire tunnel length. Standard advance rate considering the effect of rock mass quality may be about 50% lower for Q = 0.01 than in the case of not considering the same effect in a 3 km tunnel. The gap between the two standard advance rates is gradually decreasing with increased Q-value.     

Crack coalescence in a rock-like material containing two cracks

This paper investigates the pattern of crack coalescence and strength of a sandstone-like material containing two parallel inclined frictional cracks under uniaxial compression, with changing values of inclination of preexisting cracks α, bridge angle β (inclination between the inner tips of the two preexisting cracks), and the frictional coefficient μ on the surfaces of the preexisting cracks. Three main modes of crack coalescence are observed: the shear (S) mode (shear cracking between the two preexisting cracks); the mixed shear/tensile (M) mode (propagation of both wing and shear cracks within the bridge area); and the wing tensile (W) mode (coalescence of wing cracks from the tips of the preexisting cracks). The M-mode and W-mode of crack coalescence can further be divided into two and six types, respectively. Simple regime classifications of coalescence in the α–β space are proposed for different values of μ (=0.6, 0.7 and 0.9). In general, the S-mode mainly occurs when α=β or when β<β*(α, μ)=a−bα, with both a and b depending on μ; the M-mode dominates when β_L>β>β*(α, μ) (where β_L≈82.5°); and the W-mode is only observed when β>β_L. However, more experiments are still required to refine the classification. The observed peak strength, in general, increases with μ. Our results show that the peak strength predicted by the Ashby and Hallam (1986) model basically agrees with experiments. A minimum occurs at about α=65° when the peak strength is plotted against α. For α>45°, the peak strength is essentially independent of the bridge angle β.     

A three-dimensional hybrid boundary element method for non-linear analysis of a weak plane near an underground excavation

A three-dimensional hybrid boundary element method is developed for the analysis of non-linear behaviour of weak planes near underground excavations. The hybrid model adopts the fictitious stress method for the simulation of underground excavation and the displacement discontinuity method for the weak planes. Besides, the hybrid model employs linear elastic behaviour for the rock and the Barton-Bandis non-linear model for the weak plane. The developed model was verified and applied to analyze the problem of a tunnel penetrating a weak plane, in which the geometrical and material parameters were adopted from a tunnel project in central Taiwan. For the problem with the strike of the weak plane perpendicular to the tunnel axis, the numerical results show that: (1) the smaller the approaching angle, between the tunnelling direction and the dip direction of the weak plane, the larger the failure zone and the roof deformation; (2) the larger the RMR value, the smaller the deformation and failure zone; and (3) the larger the K (= σ_h/σ_u) ratio the larger failure zone will occur around the tunnel.     

Influence of intermediate principal stress on rock fracturing and strength near excavation boundaries—Insight from numerical modeling

The influence of the intermediate principal stress on rock fracturing and strength near excavation boundaries is studied using a FEM/DEM combined numerical tool. A loading condition of σ₃=0 and σ₁≠0, and σ₂≠0 exists at the tunnel boundary, where σ₁, σ₂, and σ₃, are the maximum, intermediate, and minimum principal stress components, respectively. The numerical study is based on sample loading testing that follows this type of boundary stress condition. It is seen from the simulation results that the generation of tunnel surface parallel fractures and microcracks is attributed to material heterogeneity and the existence of relatively high intermediate principal stress (σ₂), as well as zero to low minimum principal stress (σ₃) confinement. A high intermediate principal stress confines the rock in such a way that microcracks and fractures can only be developed in the direction parallel to σ₁ and σ₂. Stress-induced fracturing and microcracking in this fashion can lead to onion-skin fractures, spalling, and slabbing in shallow ground near the opening and surface parallel microcracks further away from the opening, leading to anisotropic behavior of the rock. Hence, consideration of the effect of the intermediate principal stress on rock behavior should focus on the stress-induced anisotropic strength and deformation behavior of the rocks. It is also found that the intermediate principal stress has limited influence on the peak strength of the rock near the excavation boundary.     

Experimental study on face instability of shield tunnel in sand

Face stability is critical for ground settlement and construction safety control in shield tunneling. In this paper, a series of 3D large-scale model tests with a tunnel of 1 m diameter were conducted in dry sand for various cover-to-diameter ratios C/D = 0.5, 1, and 2 (i.e., relative depth; C is the cover depth and D is the diameter of tunnel). Each test provided a measurement of the support pressure and the ground settlement with the advance of face displacement. The evolution of soil arching during face failure was investigated by monitoring the redistribution of earth pressure in front of the face in the test case of C/D = 2. In the displacement-controlled face failure tests in the medium density sands, the support pressure dropped steeply to the minimum value, then increased to a steady state with the continuing increase in the face displacement. Relationships between the support pressure and face displacement for various cover depths were also verified by the numerical analysis using the finite difference program, FLAC^3D (Itasca, 2005). The limit support pressure increases with the increase of the relative depth C/D and then tends to be constant. A significant rotation of principal stress axes in the upward arches in the soil during face failure was found in the tests. A two-stage failure pattern is proposed based on the observation of earth pressure. The theoretical and empirical formulas for estimating limit support pressure were verified by the tests results.     

Analysis on microseismic characteristics and stability of the access tunnel in the main powerhouse,Shuangjiangkou hydropower station,under high in situ stress

Access tunnel in the main powerhouse of Shuangjiangkou hydropower station was deep buried with high in situ stress and complex geological conditions. Microseismic monitoring technology was established to monitor microcrack evolution process inside the surrounding rock in early excavation stage. Serious falling blocks in the left spandrel of the tunnel were predicted in a timely manner by delimiting major damage areas in the tunnel. Based on comparative analysis on microseismic activity law and field failure characteristics of the access tunnel, a quantitative index was supposed between slight rockburst like falling blocks and microseismic events. Moreover, the change law of daily average apparent stress difference and b value were analyzed based on microseismic event data. In addition, a three-dimensional numerical simulation software (RFPA3D) was used to simulate the damage distribution around the tunnel, and a relationship between spatial position of tunnel damage and direction of the maximum principal stress was qualitatively analyzed. The study results showed that advance speed of the tunnel working face was an important factor affecting the state of stress redistribution in surrounding rock mass, and the change law of b values of microseismic events could be used to predict activity state inside the surrounding rock effectively, which reflected mechanical properties and stress state of surrounding rock. In particular, field falling blocks became more serious with increasing b value, and field surrounding rock was relatively stable with minor b value. A risk of surrounding rock instability was relatively high with small b values. It provided an efficient method of predicting and assessing slight rockburst like falling blocks. The study results can provide significant guidance for field construction and later construction planning.

     

Towards a better understanding of high rate biological film flow reactor theory

On the assumption that performance of biological film flow reactors is independent of oxygen transfer, a theoretical extension of a mathematical model (after Ames) is described. This predictive and interpretive model incorporates both mass transfer-limitations between biomass and liquid film, and kinetic biological reaction rate of organic “food” utilization.Given general boundary conditions for the differential equations describing the mass transfer process, it is shown that: C_e = C_r + (C_l − C_r.exp(−K_m D/Q) where by definition: C_t = α C_s + C_r1/K_m = 1/K_LA_γ + α/Kx.For an influent concentration biochemical oxygen demand (C_i) and resultant effluent concentration (C_e) obtained during film flow through a packed media depth (D), the Model proposes that the residual concentration (C_r) is a function of surface irrigation rate (Q) and biomass activity. If this term is negative, adsorption occurs; while if positive, desorption from the biomass film at concentration (C_s) takes place.An overall mass transfer coefficient (K_m) is defined by a series equation where the usual mass transfer coefficient (K_L) is primarily a function of Reynolds Number [surface irrigation rate (Q) and specific surface area (A_V)], Schmidt Number (diffusivity of organic “Food”) and concentration. “Food” utilization at active sites on the biological film is governed by a specific adsorption coefficient (α) and explained by a Langmuir analogy. Biological conversion of “food” is described by a kinetic rate constant (K), while the necessary oxygen is defined by (X).This predictive model was developed from a wide range of pilot plant data, successfully tested further on a variety of published results and on actual full scale operating plants.Parameters derived from this Model, in terms of Height of Transfer Unit and Kinetic Reaction coefficient, characterize organic “treatability” for a variety of wastes.     

Coefficient of restitution and rotational motions of rockfall impacts

This paper presents experimentally obtained results for the coefficient of restitution for spherical boulders impacting on rock slopes. Plaster modeling material is used for casting both the boulders and slopes. It is observed that the normal component of the coefficient of restitution (R_n) increases with the slope angle α, which agrees with Wu's observations (Trans. Res. Rec. 1–5 (1985) 1031). However, there appears to be no clear correlation between the tangential component of the coefficient of restitution (R_t) and the slope angle α. When the ratio of the resultant velocities and the ratio of the kinetic energies before and after impacts are used to define the coefficient of restitution (i.e. R_V and R_E), a very clear increasing trend in the coefficient of restitution with α is observed. When all data are plotted onto the R_t−R_n space, our laboratory data fall into the rock slope regime proposed by Fornaro et al. (In: D.G. Price (Ed.), Proceedings of the Sixth International Congress IAEG, Amsterdam, Balkema, Rotterdam, 1990, p. 2173) and also agree with those data gleaned from literature. In addition, the rotational kinetic energy E_r, induced at each impact, increases with the slope angle α, achieves a maximum at about α=40°, before decreasing again to a negligible value at α=70°. A simple theoretical model is proposed to explain this observation based on the locking between the boulder and the slope during impact. The α-dependence of E_r differs from the recommendation by the Japanese Railway Association that the induced rotational energy is about 10% of that of the translational kinetic energy.     

The flattened Brazilian disc specimen used for testing elastic modulus, tensile strength and fracture toughness of brittle rocks: analytical and numerical results

The flattened Brazilian disc specimen is proposed for determination of the elastic modulus E, tensile strength σ_t and opening mode fracture toughness K_IC for brittle rocks in just one test. This paper is concerned with the theoretical analysis as well as analytical and numerical results for the formulas. According to the results of stress analysis and Griffith's strength criteria, in order to guarantee crack initiation at the centre of the specimen, which is considered to be crucial for the test validity, the loading angle corresponding to the flat end width must be greater than a critical value (2α20°). The analysis shows that, based on the recorded complete load–displacement curve of the specimen (the curve should include the ‘fluctuation’ section after the maximum load), E can be determined by the slope of the section before the maximum load, σ_t by the maximum load, and K_IC by the local minimum load immediately subsequent to the maximum load. The relevant formulas for the calculation of E, σ_t, K_IC are obtained, and the key coefficients in these formulas are calibrated by finite-element analysis. In addition, some approximate closed-form formulas based on elasticity are provided, and their accuracy is shown to be adequate by comparison with the finite-element results.     

Compaction of flocculated material

The device used in the experiment consists of a flat-bottomed graduated cylinder and a coaxial plunger. A suspension flocculated with chemicals is sedimented after being mechanically worked within the graduate, and the supernatant water is removed with a pipette. The plunger is thrust into the sludge at a constant speed. The sludge is not only compressed but also flows into the annular gap between the plunger and the graduate, resulting in liberation of water. The liberated water is accumulated on the sludge in the annular gap. The “sludge bulkiness” β is used to describe the volumetric proportion of sludge and solids in it. The sludge bulkiness values before and after the “plunger test” are denoted as β_i and β_f, respectively. The values of β_i and β_j have been explored as a function of the time of the mechanical working. As a result, there is a definite time lag between the maximum value of β_i and the minimum value of β_f. The minimum value of β_j is obtained when the sludge consists of “pelleted flocs”.     

Flow-induced vibration of two circular cylinders in tandem arrangement. Part 2: Suppression of vibrations

This paper presents an experimental investigation on suppression of cross-flow vibrations of two circular cylinders in tandem arrangement, conducted at the fluid mechanics laboratory of Kitami Institute of Technology, Japan. To suppress the vibrations of the cylinders, tripping wires were deployed, attached symmetrically about the leading stagnation lines of the cylinders. Five spacing ratios were examined, i.e., L/D=0.1, 0.3, 0.8, 2.0 and 3.2 (L is the gap spacing between the two cylinders; D is the diameter of cylinder), which are representative for five Regimes I (0.1≤L/D<0.2), II (0.2≤L/D<0.6), III (0.6≤L/D<2), IV (2≤L/D<2.7) and V (L/D≥2.7), respectively, as classified in Part 1 [Kim et al., 2009. Flow-induced vibrations of two circular cylinders in tandem arrangement (part 1: characteristics of vibration). Journal of Wind Engineering and Industrial Aerodynamics, submitted together for publication]. Tripping wire position θ measured from the leading stagnation lines of the cylinders was changed from 20° to 60° to determine the optimum range of θ for suppressing structural vibrations. The shear layers separated from the two cylinders were investigated based on flow visualization. The main findings are: (i) the flow-induced vibration on the two cylinders depends strongly on θ, (ii) at θ=20–30° the vibrations on both cylinders are almost completely suppressed for all regimes except V, and (iii) for θ≥40° the vibration amplitudes of both cylinders are considerably larger than those of the plain cylinders, particularly at θ=40°, where the vibration of the upstream cylinder becomes divergent.     

Cracking mechanism of secondary lining for a shallow and asymmetrically-loaded tunnel in loose deposits

Tunnels constructed in loose deposits with low strength and complex composition are usually subjected to asymmetrical stresses at the entrance and exit. The secondary tunnel lining is prone to excessive deformation, cracking, or even collapse, seriously affecting the safety of tunnel construction and operation. In this paper, a large shallow highway tunnel in loose deposits is used as an example to study the cracking mechanism of secondary lining. Triaxial consolidated-drained shear tests are carried out on large remolded specimens to obtain the mechanical parameters of the surrounding soil. Three-dimensional numerical modeling is conducted based on the field monitoring data to simulate the process of tunnel construction and to analyze the mechanical mechanism of cracking in the secondary lining. It is shown that even with the 30 m advance pipe roof at the tunnel entrance, the apparent difference in stiffness between the retaining wall and the surrounding soil results in an obvious stress concentration at the spring of the secondary lining near the end of the retaining wall, due to the effect of highly asymmetrical stresses. In addition, loose deposits are very sensitive to construction disturbances. Large horizontal deformation towards the lower topography occurs during tunnel construction. With increasing overburden depth, the stress concentration at the spring level and the horizontal deformation in the secondary lining increases, which are the main reasons for cracking in the secondary lining. These findings can be useful for tunnel design and construction in the similar type of loose deposits.     

Critical ventilation velocity for tunnel fires occurring near tunnel exits

Ventilation is an effective method for controlling smoke during a tunnel fire. The “critical ventilation velocity” u_cr is generally defined as the minimum velocity at which smoke is prevented from spreading against the longitudinal ventilation flow in tunnel fire situations. This study conducted small-scale experiments to investigate u_cr for situations when tunnel fire occurs near tunnel exits. The model tunnel was 4 m long, 0.6 m wide and 0.6 m tall, and the fires were located at 0.5 m, 1.0 m and 1.5 m from the tunnel exit. 6.3×6.3 cm² and 9.0×9.0 cm² square asoline fuel pans were used as fire source. Results show that u_cr decreases as the fire approaches the tunnel exit.     

A stable CS-FEM for the static and seismic stability of a single square tunnel in the soil where the shear strength increases linearly with depth

A numerical procedure using a stable cell-based smoothed finite element method (CS-FEM) is presented for estimation of stability of a square tunnel in the soil where the shear strength increases linearly with depth. The kinematically admissible displacement fields are approximated by uniform quadrilateral elements in conjunction with the strain smoothing technique, eliminating volumetric locking issues and the singularity associated with the Mohr–Coulomb model. First, a rich set of simulations was performed to compute the static stability of a square tunnel with different geometries and soil conditions. The presented results are in excellent agreement with the upper and lower bound solutions using the standard finite element method (FEM). The stability charts and tables are given for practical use in the tunnel design, along with a newly proposed formulation for predicting the undrained stability of a single square tunnel. Second, the seismic stability number was computed using the present numerical approach. Numerical results reveal that the seismic stability number reduces with an increasing value of the horizontal seismic acceleration (α_h), for both cases of the weightless soil and the soil with unit weight. Third, the link between the static and seismic stability numbers is described using corrective factors that represent reductions in the tunnel stability due to seismic loadings. It is shown from the numerical results that the corrective factor becomes larger as the unit weight of soil mass increases; however, the degree of the reduction in seismic stability number tends to reduce for the case of the homogeneous soil. Furthermore, this advanced numerical procedure is straightforward to extend to three-dimensional (3D) limit analysis and is readily applicable for the calculation of the stability of tunnels in highly anisotropic and heterogeneous soils which are often encountered in practice.     

Evaluation of common TBM performance prediction models based on field data from the second lot of Zagros water conveyance tunnel (ZWCT2)

Zagros water conveyance tunnel (ZWCT) is a 49 km tunnel designed for conveying 70 m³/s water from Sirvan River southward to Dashte Zahab plain in western Iran. This long tunnel has been divided in 3 Lots namely 1A, 1B, 2. By November 2014, about 22 km of the Lot 2 (with a total length of 26 km) has been excavated by two double shield TBMs from two southern and northern portals. The bored section of tunnel passed through different geological units of 3 main formations of Zagros mountain ranges which mainly consist of weak to moderately strong argillaceous-carbonate sedimentary rocks. In this paper, the operating and as-built geological data collected during construction phase of the Lot 2 of ZWCT project was used to compare the calculated machine performance by empirical methods such as the Hassanpour et al. (2011), Q_TBM, NTNU, Palmstrom, and theoretical model of Colorado School of Mines or CSM. The predicted penetration rates were then compared with the observed field performance of the machine and the variations of predicted rates were examined by statistical analysis. The results showed that the site-specific model, which was based on TBM performance in similar formations can provide estimates closer to actual machine performance.     

Shaft resistance of a pile embedded in rock

A rational calculation procedure is proposed for establishing the shaft resistance of a pile embedded in rock, based upon the Hoek and Brown failure model. The state of the art of the calculation of the pile shaft resistance is analysed. Nearly all the recommendations that have appeared in the technical literature, for calculating the ultimate shear strength of a shaft embedded in rock (τ_ult) propose that τ_ult=ασ_c^k(σ_c;τ_ulten MN/m²) where the coefficient α, considered as a constant dimensional value, ranges from 0.1 to 0.8, if the unconfined compressive strength (σ_c) is expressed in MN/m². In most cases, the exponent k is 0.5.A comparison is made between the results yielded and the different empirical theories that have been put forward with respect to this shaft resistance. It can generally be stated that the results obtained with this theory are reasonable for long and deeply socketed piles (high confining pressures) but the results are on the safe side in some cases where short piles (low confining pressures) are involved.This paper is a continuation of the works developed by the same authors with piles working at the tip, socketed in rock.     

Deformation control method of a large cross-section tunnel overlaid by a soft-plastic loess layer: a case study

This paper presents a case study of a large cross-section high-speed railway tunnel overlaid by a Q₂ soft-plastic loess layer. Due to poor engineering properties of the soft-plastic loess, two unexpected collapses occurred. This indicates that there is great difficulty and risk during tunneling. In this paper, the deformation control methods are studied by carrying out a series of numerical simulations and then validating via field tests. The stress and seepage coupling equations are deducted to embed into a 3D fluid-mechanical coupled numerical analysis. The results show that the curtain grouting scheme can effectively control the deformation of surrounding rock, and the real field data of settlement and horizontal convergence are 152 mm and 37 mm, respectively. However, the tunneling advance rate is slow (0.6 m/day) in trial sections because of the mutual interference between construction procedures. It can be used as an alternative scheme for lager deformation. The advanced drainage scheme can lower the ground water table below the excavation outline. The average water content of soft-plastic loess decreases from 26 to 22%, and the state of surrounding rock changes from soft plastic to hard plastic. The in situ settlement and horizontal convergence are 165 mm and 51 mm, respectively. Finally, it is proposed to use advanced drainage in combination with advanced small pipe grouting as a follow-up construction scheme. The successful completion of the whole tunnel proved the effectiveness of the proposed method.

     

Simulation of water-bloom in a eutrophic lake—I. Photosynthetic characteristics of Microsystis aeruginosa

A perspective of how to simulate “emergence and/or disappearance of the water-bloom… dense population of a blue-green alga, Microcystis aeruginosa at the surface of eutrophic waters… ” was presented.The algal photosynthetic activity. Q_o2 as a function of irradiation light intensity. I, could be represented by the Blackman model, taking the algal content. C of chlorophyll-α and water temperature. 0 as parameters.When the cells that had been cultured under dim light were transferred to a new environment, wherein the light intensity was from 0 (dark) to the level much brighter than the dim light, the value of C exhibited various responses against time. Subtracting the rate of chlorophyll-α degradation from that of chlorophyll-α synthesis, the rate of change in C values during the light-adaptation period was studied.     

Interaction of tunnel linings and soft ground

Although soil-lining interaction is highly dependent on the tunnelling technology used, most of the available design methods for tunnel linings fail to take into consideration this important factor. During tunnel excavation, the in-situ stresses are significantly altered, depending on the tunnelling technique as well as the configuration of the tunnel and the characteristics of the soil deposits. The reduced radial stresses are the starting point of the soil-lining interaction at lining activation. This paper presents a method of lining design that considers the details of the excavation procedure and lining installation. Interaction between the tunnel lining and the ground is analysed in two stages—excavation and interaction. The excavation stage is responsible for determining the pre-lining soil deformations and the reduced in-situ stresses. The interaction stage models the soil-lining system together. Soil continuum, tunnel lining, and the interface between them are idealized in the whole system using nonlinear finite-element techniques. The deformations of the soil-lining system, as well as the lining internal forces, and equilibrium soil pressures are determined. Finally, results of the proposed analytical method as well as commonly used procedures are compared with field measurements compiled during the construction of two tunnels in which a precast segmental lining and rib and lagging lining were used.