Effects of mixing velocity on anaerobic fixed film reactors

Four laboratory-model upflow anaerobic fixed film reactors (AFFR 1, 2, 3 and 4) treating landfill leachate were subject to identical volumetric organic load (7 kg COD m⁻³ d⁻¹) and hydraulic retention time (3d), but the contents in each unit were continuously recirculated for 10 months at four different velocities, respectively, of 21, 66, 680 and 3063 cm h⁻¹. The objective was to assess the effects of such mixing velocities (ν) on COD removal efficiencies (E), mean cell residence time (MCRT) and substrate utilization rate (U expressed as g COD removed d⁻¹ g⁻¹ VSS). The results showed that the relationships between E and ν and MCRT and ν were inverted U-shaped curves. The two middle reactors (AFFR 2 and 3) had near-optimum velocities (ν₂ and ν₃) with maximum E values of 88–89%. AFFR 4 had a high value of ν scouring biofilm on the biorings, resulting in higher concentrations of SS, VSS and COD in the effluent. All four reactors had nearly similar values of U (1.85–2.14 g COD d⁻¹ g⁻¹ VSS). The value of ν₁ (AFFR 1) was too low to enhance performance and ν₄ was too high to retain the biomass. The optimum recycle velocity, under the test conditions, was in the range of 66–680 cm h⁻¹.     

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.     

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.     

Glucose mineralization activity and the use of the heterotrophic activity method in an acidified lake

This paper concerns bacterial glucose mineralization in Silver Lake sampled during the summer; specifically, whether or not it occurs, and whether or not the “heterotrophic activity method” can be used to measure it, in this acidified lake.For Sampling I, linearity between turnover time (t/f) and added substrate concentration (A) did not exist at the in situ pH (3.2) or the experimental pH's (5.5 and 7.0), even though time studies showed that glucose was being mineralized at measurable rates. For Sampling II, modifications were made to the concentrations of labelled glucose and the incubation time. A highly significant linear relationship between t/f and A was demonstrated, and the turnover time and V_max were calculated to be 472.3 h and 0.005 μm l⁻¹ h⁻¹, respectively. For Sampling III, even though the environmental conditions were similar to those for the previous sampling, a statistically-significant relationship between t/f and A did not result.     

Sensitivity and importance measures in structural reliability

In multivariate reliability problems, which depend on one or more parameters τ, a sensitivity factor α_E[τ] is defined as the derivative of the equivalent reliability index β_E(τ)=?φ^?1[P _f (τ)] with P _f (τ) the failure probability. α_E[τ] expresses the change of α_E(τ) due to small variations of τ. Since the numerical evaluation of α_E[τ] is usually impractical, an approximation α_E[τ]≈α[τ] is derived, which is asymptotically exact for extreme reliability levels. Simple formulae for α[τ] are given. The approximation α_E[τ]:a[τ] also provides the basis for a better understanding of the commonly used alpha values α_i=?1/βu i? as importance measures for stochastic variables.     

Axial strength of circular concrete-filled steel tube columns — DOE approach

This paper presents the effect of changes in diameter of the steel tube (D), wall thickness of the steel tube (t), strength of in-fill concrete (f_cu), and length of the tube (L) on ultimate axial load (P_ue) and axial shortening at the ultimate point (δ_ue) of circular Concrete Filled steel Tubes (CFT). Taguchi’s approach with an L9 orthogonal array is used to reduce the number of experiments. With the help of initial experiments, linear regression models are developed to predict the axial load and the axial shortening at the ultimate point. A total of 243 circular CFT samples are tested to verify the accuracy of these models at three factors with three levels. The experimental results are analyzed using Analysis Of Variance to investigate the most influencing factor on strength and axial shortening of CFT samples. Comparisons are made with predicted column strengths using the existing design codes, AISC-LRFD-2005 and EC4-1994.     

Generalized crack initiation and crack damage stress thresholds of brittle rock masses near underground excavations

The rock mass failure process is characterized by several distinct deformation stages which include crack initiation, crack propagation and coalescence. It is important to know the stress levels associated with these deformation stages for engineering design and practice.Extensive theoretical, experimental and numerical studies on the failure process of intact rocks exist. It is generally understood that crack initiation starts at 0.3 to 0.5 times the peak uniaxial compressive stress. In confined conditions, the constant-deviatoric stress criterion was found to describe the crack initiation stress level.Here, generalized crack initiation and crack damage thresholds of rock masses are proposed. The crack initiation threshold is defined by σ₁−σ₃=A σ_cm and the crack damage threshold is defined by σ₁−σ₃=B σ_cm for jointed rock masses, where A and B are material constants and σ_cm is the uniaxial compressive strength of the rock masses. For a massive rock mass without joints, σ_cm is equal to σ_cd, the long-term uniaxial strength of intact rock. After examining data from intact rocks and jointed rock masses, it was found that for massive to moderately jointed rock masses, the material constants A and B are in the range of 0.4 to 0.5, 0.8 to 0.9, respectively, and for moderately to highly jointed rock masses, A and B are in the range of 0.5 to 0.6, 0.9 to 1.0, respectively. The generalized crack initiation and crack damage thresholds, when combined with simple linear elastic stress analysis, assist in assessing the rock mass integrity in low confinement conditions, greatly reducing the effort needed to obtain the required material constants for engineering design of underground excavations.     

Some aspects of unsaturated flow in jointed rock

The applicability of Darcy's Law to two-phase flow has been discussed. Specialised triaxial equipment has been employed to separately inject two pore fluid components (air and water) into fractured rock specimens, so that two-phase flow behaviour can be studied at high axial and confining stresses. Improvements to recently developed two-phase high-pressure triaxial apparatus have enabled the authors to continue their study of air–water (i.e. unsaturated) flow in intact and fractured rock specimens under a wide range of stress conditions, similar to those encountered in underground mining operations. In this paper, a simplified stratified two-phase flow model is also presented that satisfactorily predicts flow behaviour in an inclined rock fracture over a range of linear laminar flow for particular capillary pressure relationships. The mathematical model is based upon the principles of conservation of mass and momentum, and relates the fracture aperture (e_t) to phase permeability (k_i) using Poiseuille's law and the proposed ‘phase height’, h_i(t), for water and air phases. The experimental approach used to verify the model predictions is described and the predicted results compared with the measurements. The experimental data confirmed the relationship between relative permeability and flow rate, with respect to two-phase flow conditions.     

Effects of loading rate on rock fracture

By means of a wedge loading applied to a short-rod rock fracture specimen tested with the MTS 810 or SHPB (split Hopkinson pressure bar), the fracture toughness of Fangshan gabbro and Fangshan marble was measured over a wide range of loading rates, =10⁻²–10⁶ MPa m^1/2 s⁻¹. In order to determine the dynamic fracture toughness of the rock as exactly as possible, the dynamic Moiré method and strain–gauge method were used in determining the critical time of dynamic fracture. The testing results indicated that the critical time was generally shorter than the transmitted wave peak time, and the differences between the two times had a weak increasing tendency with loading rates. The experimental results for rock fracture showed that the static fracture toughness K_Ic of the rock was nearly a constant, but the dynamic fracture toughness K_Id of the rock ( ≥10⁴ MPa m^1/2 s⁻¹) increased with the loading rate, i.e. log(K_Id)=a log +b. Macroobservations for fractured rock specimens indicated that, in the section (which was perpendicular to the fracture surface) of a specimen loaded by a dynamic load, there was clear crack branching or bifurcation, and the higher the loading rate was, the more branching cracks occurred. Furthermore, at very high loading rates ( ≥10⁶ MPa m^1/2 s⁻¹) the rock specimen was broken into several fragments rather than only two halves. However, for a statically fractured specimen there was hardly any crack branching. Finally, some applications of this investigation in engineering practice are discussed.     

Simplified P–M interaction curve for square steel tube filled with high-strength concrete

The purpose of this study is to propose simplified strength equations that can be conveniently used to establish a P–M interaction curve of square concrete filled tubes (CFTs) with concrete strength of up to 100 MPa. The method presented in the author's previous study [Choi Y-H, Foutch DA, LaFave JM. New approach to AISC P–M interaction curve for concrete filled tube beam-columns. Eng Struct 2006;28(11):1586–98] was used as a basic unified formula for pure steel members and CFT ones, and a parametric study was performed to determine the contribution of the concrete, which were expressed by two variables: a normalized maximum moment, α, and the axial load ratio at the maximum moment, β. The two variables were formulated with respect to tube width-to-thickness ratio (b/t) and relative concrete compressive strength to yield strength of the steel tube (f′_c/F_y). Then, the proposed method were compared to experimental data found in literatures, which showed greatly improved results in terms of accuracy and amount of computation, when compared to the current AISC design methods.     

Numerical simulation of the excavation damaged zone around an opening in brittle rock

The micromechanics-based damage model proposed by Golshani et al. [A micromechanical model for brittle failure of rock and its relation to crack growth observed in triaxial compression tests of granite. Mech Mater 2006;38:287–303] is extended so that time-dependent behavior of brittle material can be taken into account, with special attention to the numerical analysis of an excavation damaged zone (EDZ) around an opening, which is a major concern in assessing the safety of underground repositories. The present model is capable of reproducing the three characteristic stages of creep behavior (i.e., primary, secondary, and tertiary creep) commonly observed in the laboratory creep tests. The sub-critical microcrack growth parameters (i.e., n and A) can be determined for Inada granite by fitting the numerical results of elapse time to failure versus the creep stress ratio curve with the experimental data under both dry and wet conditions. It is found that moisture has a significant influence on the parameter A rather than the parameter n. Use of the extended model makes it possible to analyze not only the extension of microcrack length, but also the development of EDZ around an opening as a function of time. The damaged zones mainly develop in the sidewalls of the opening in the case that the vertical stress σ₂₂ is larger than the horizontal stress σ₁₁.     

Estimation of the tensile elastic modulus using Brazilian disc by applying diametrically opposed concentrated loads

The tensile elastic modulus E_t of a rock is different from the compressive elastic modulus E_c, due to inhomogeneity and microcracks. There is no convenient method to obtain E_t except using direct tension tests. However, the direct tension test for rock materials is difficult to perform, because of stress concentrations, and the difficulty of preparing specimens. We have developed a new method to determine E_t of rock materials easily and conveniently. Two strain gauges are pasted at the center part of a Brazilian disc's two side faces along the direction perpendicular to the line load to record tensile strain, and a force sensor is used to record the force applied; then the stress–strain curve can be obtained; finally the E_t can be calculated according to those related formulas which are derived on the basis of elasticity theory. Our experimental results for marble, sandstone, limestone and granite indicate that E_t is less than E_c, and their ratio is generally between 0.6 and 0.9.     

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.     

Finite element modelling of concrete-filled lean duplex stainless steel tubular stub columns

This paper presents a finite element (FE) study on concrete-filled lean duplex slender stainless steel tubular (CFDSST) stub columns of square and L-, T-, and +-shape (Non-Rectangular Sections or NRSs) sections under pure axial compression. The effect of cross-sectional shape and concrete compressive strength, by considering equal steel consumption (i.e. equal cross-sectional area) for all the square and NRSs sections have been reported. In CFDSST stub columns, the axial deformation (δ _u ) at ultimate load (P _u ) decreases with increasing concrete strengths, but increases as the sections changes from Square→L→T→+-shape. For normal concrete strength (≤40 MPa), NRSs appear to have similar or slightly enhanced P _u , in comparison with the representaive square section. But in the case of a high strength concrete core (i.e. >40 MPa), NRSs are clearly at a disadvantage as far as the values of P _u is concerned, however as the NRSs are lighter by 37%, they still offer an attractive option for the designers. The FE strengths over predicts the EN 1994-1-1 (2004) specification by about an average of 21, 19, 14, and 4% for the square, L, T, and +-shape sections, respectively.     

Fracture resistance on aggregate bridging crack in concrete

Fracture toughening exhibited in quasi-brittle materials such as concrete is often mainly related to the action of aggregate bridging, which leads to the presence of a fracture process zone ahead of stress-free cracks in such materials. In this investigation, the fracture resistance induced by aggregate bridging, denoted by G _I-bridging, in the primary focus. In order to quantitatively determine it, a general analytical formula is firstly developed, based on the definition of fracture energy by Hillerborg. After this, we further present the calculated procedures of determining this fracture resistance from the recorded load vs. crack opening displacement curve. Then, both numerical simulations and fracture experiments are performed on concrete three-point bending beams. Utilizing the obtained load against crack opening displacement curve, the value of G _I-bridging at any crack extension as well as the change of G _I-bridging with the crack extension is examined. It is found that G _I-bridging will firstly increase with the development of crack and then stay constant once the initial crack tip opening displacement reaches the characteristic crack opening displacement w ₀. The effects of material strength and specimen depth on this fracture resistance are also investigated. The results reveal that the values of G _I-bridging of different specimens at any crack propagation are strongly associated with the values of fracture energy of specimens. If the values of fracture energy between different specimens are comparable, the differences between G _I-bridging are ignored. Instead, if values of fracture energy are different, the G _I-bridging will be different. This shows that for specimens with different strengths, G _I-bridging will change greatly whereas for specimens that are different in depth, whether G _I-bridging exhibits size effect depends on whether the fracture energy of specimens considered in the calculation of G _I-bridging is assumed to be a size-dependent material parameter.     

Effects of blast induced vibrations on the fresh concrete lining of a shaft

During shaft excavation, blast induced vibrations can cause micro-cracks in the fresh concrete lining and decrease its strength. The traditional method to reduce the vibration effect is to control the scale of blasting and apply temporary support to protect the fresh concrete. Recent research was conducted to study the effects of the blast induced vibration on the fresh concrete. Shaft sinking operations (drilling, blasting and concrete lining) were simulated in a laboratory model. Additives of triethanolamine – TEA (N(C₂H₄OH)₃) and sodium chloride (NaCL) in varying proportions were added to the concrete lining to increase the early strength. Vibration was generated by small scale blasting. The experimental results show that the blast induced vibration has negative and positive effects on the strength of the fresh concrete depending on the curing time at blasting. Vibration can increase the strength within the first 1–2 days. After that period, vibration can cause cracks in the fresh concrete and reduce the strength. Still later, it has no more effect. The time windows vary with the magnitude of vibration and the strength of the concrete at the time of blasting. It was also found that both additives increased the early strength of concrete lining and expanded the time windows. These results indicate that proper timing of blasting and use of additives can change the negative effect of the blast induced vibration into a positive effect and increase the strength of a concrete lining.     

Tunnel roof deflection in blocky rock masses as a function of joint spacing and friction – A parametric study using discontinuous deformation analysis (DDA)

The stability of underground openings excavated in a blocky rock mass was studied using the discontinuous deformation analysis (DDA) method. The focus of the research was a kinematical analysis of the rock deformation as a function of joint spacing and friction. Two different opening geometries were studied: (1) span B = h_t; (2) B = 1.5h_t; where the opening height was h_t = 10 m for both configurations. Fifty individual simulations were performed for different values of joint spacing and friction angle. It was found that the extent of loosening above the excavation was predominantly controlled by the spacing of the joints, and only secondarily by the shear strength. The height of the loosening zone h_r was found to be dependent upon the ratio between joint spacing and excavation span S_j/B: (1) h_r < 0.56B for S_j/B  2/10; (2) stable arching within the rock mass for S_j/B  3/10. The results of this study provide explicit correlation between geometrical features of the rock mass, routinely collected during site investigation and excavation, and the expected extent of the loosening zone at the roof, which determines the required support.     

Effects of lime addition on geotechnical properties of sedimentary soil in Curitiba,Brazil

The soil of the Guabirotuba geological formation(Paraná Basin, Brazil) has physico-mechanical properties which are not suitable for its utilization in pavement construction, in protection of hillsides and slopes, or as shallow foundation support. Treatment of this soil by lime addition would improve its usability. The present context intends to determine the ratio between the splitting tensile strength(q_t)and the unconfined compressive strength(q_u) of clayey soil in the metropolitan region of Curitiba City,which has been treated with different lime contents and curing times. The control parameters evaluated include lime content(L), curing time(t), moisture content(w), and ratio of porosity to volumetric lime content(η/L_v). It was observed that the q_t/q_u ratio is between 0.17 and 0.2 in relation to the curing time,and an exponential relation exists between them. Meanwhile, the unconfined compressive strength of lime-treated soil was found to be approximately four times the initial value.     

Fracture toughness study for a brittle rock subjected to mixed mode I/II loading

A semi-disk specimen containing an angled edge crack has been used in the past for conducting fracture tests on a brittle rock named Johnstone [Fracture testing of a soft rock with semi-circular specimens under three-point bending. Part 2—mixed mode. Int J Rock Mech Min Sci Geomech Abstr 1994b;31(3):199–212]. The test specimen is appropriate for investigating brittle fracture when the rock samples are subjected to the combined effects of tension and shear along the crack line. However, the experimental results reported in Lim, Johnston, Choi, Boland [Fracture testing of a soft rock with semi-circular specimens under three-point bending. Part 2—mixed mode. Int J Rock Mech Min Sci Geomech Abstr 1994b;31(3):199–212.] are inconsistent with all of the well-known theoretical criteria available for predicting mixed mode brittle fracture. In this paper, a modified criterion is used to provide accurate predictions for the reported experimental results. The modified criterion makes use of a three-parameter model (based on K_I, K_II and T) for describing the crack tip stresses. It is shown that the non-singular stress term T has a significant role when the rock fracture tests are conducted on the semi-disk specimens.     

Design method for checking tensile stresses under service loads in cracked prestressed concrete members with 2,400‐MPa strands

The ACI 318‐14 building code requirements specify that the net tensile stresses of prestressing strands under service loads (Δf_ps ) shall be limited to 250 MPa for proper crack control of prestressed concrete (PC) members which are classified as Class C. However, as high‐strength prestressing strands with a tensile strength of 2,400 MPa have recently been developed and applied to PC members, this requirement needs to be reviewed. In this study, experiments and analysis were carried out in order to investigate the Δf_ps of PC members with the recently developed 2400 MPa strands, and in the test, the strain distributions, flexural crack widths, and stress change in bonded prestressed reinforcement were measured in detail according to the applied loads. In addition, the minimum magnitudes of effective prestress to satisfy the stress limitation of the net tensile stress of prestressing strands specified in the current design code were estimated using a nonlinear flexural analysis model, and a simplified design equation was proposed for a simple calculation of the Δf_ps at the design stage.