Energy analysis of stability of twin shallow tunnels based on nonlinear failure criterion

Based on nonlinear Mohr-Coulomb failure criterion, the analytical solutions of stability number and supporting force on twin shallow tunnels were derived using upper bound theorem of limit analysis. The optimized solutions were obtained by the technique of sequential quadratic programming. When nonlinear coefficient equals 1 and internal friction angle equals 0, the nonlinear Mohr-Coulomb failure criterion degenerates into linear failure criterion. The calculated results of stability number in this work were compared with previous results, and the agreement verifies the effectiveness of the present method. Under the condition of nonlinear Mohr-Coulomb failure criterion, the results show that the supporting force on twin shallow tunnels obviously increases when the nonlinear coefficient, burial depth, ground load or pore water pressure coefficients increase. When the clear distance is 0.5to 1.0 times the diameter of tunnel, the supporting force of twin shallow tunnels reaches its maximum value, which means that the tunnels are the easiest to collapse. While the clear distance increases to 3.5 times the diameter of tunnel, the calculation for twin shallow tunnels can be carried out by the method for independent single shallow tunnel. Therefore, 3.5 times the diameter of tunnel serves as a critical value to determine whether twin shallow tunnels influence each other. In designing twin shallow tunnels,appropriate clear distance value must be selected according to its change rules and actual topographic conditions, meanwhile, the influences of nonlinear failure criterion of soil materials and pore water must be completely considered. During the excavation process, supporting system should be intensified at the positions of larger burial depth or ground load to avoid collapses.     

Energy analysis of stability on shallow tunnels based on non-associated flow rule and non-linear failure criterion

On the basis of upper bound theorem, non-associated flow rule and non-linear failure criterion were considered together.The modified shear strength parameters of materials were obtained with the help of the tangent method. Employing the virtual power principle and strength reduction technique, the effects of dilatancy of materials, non-linear failure criterion, pore water pressure,surface loads and buried depth, on the stability of shallow tunnel were studied. In order to validate the effectiveness of the proposed approach, the solutions in the present work agree well with the existing results when the non-associated flow rule is reduced to the associated flow rule and the non-linear failure criterion is degenerated to the linear failure criterion. Compared with dilatancy of materials, the non-linear failure criterion exerts greater impact on the stability of shallow tunnels. The safety factor of shallow tunnels decreases and the failure surface expands outward when the dilatancy coefficient decreases. While the increase of nonlinear coefficient, the pore water pressure coefficient, the surface load and the buried depth results in the small safety factor. Therefore, the dilatancy as well as non-linear failure criterion should be taken into account in the design of shallow tunnel supporting structure. The supporting structure must be reinforced promptly to prevent potential mud from gushing or collapse accident in the areas with abundant pore water, large surface load or buried depth.     

Upper bound limit analysis of roof collapse in shallow tunnels with arbitrary cross sections under condition of seepage force

The analytical solutions for predicting the exact shape of collapse mechanisms in shallow tunnels with arbitrary excavation profiles were obtained by virtue of the upper bound theorem of limit analysis and variation principle according to Hoek-Brown failure criterion. The seepage force was included in the upper bound limit analysis, and it was computed from the gradient of excess pore pressure distribution. The seepage was regarded as a work rate of external force. The numerical results of roof collapse in square and circular tunnels with different rock parameters were derived and discussed, which proves to be valid in comparison with the previous work. The influences of different parameters on the shape of collapsing blocks were also discussed.     

Upper bound solution for supporting pressure acting on shallow tunnel based on modified tangential technique

Based on the nonlinear failure criterion and the upper bound theorem, the modified tangential technique method was proposed to derive the expression of supporting pressure acting on shallow tunnel. Instead of the same stress state, different normal stresses on element boundaries were used. In order to investigate the influence of different factors on supporting pressures, the failure mechanism was established. The solution of supporting pressure, with different parameters, was obtained by optimization theory. The corresponding failure mechanism and numerical results were presented. In comparison with the results using the single tangential technique method, it is found that the proposed method is effective, and the good agreement shows that the present solution of supporting pressure is reliable.     

Stress characteristics of surrounding rocks for inner water exosmosis in high-pressure hydraulic tunnels

Seepage and stress redistribution are the main factors affecting the stability of surrounding rock in high-pressure hydraulic tunnels.In this work,the effects of the seepage field were firstly simplified as a seepage factor acting on the stress field,and the equilibrium equation of high pressure inner water exosmosis was established based on physical theory.Then,the plane strain theory was used to solve the problem of elasticity,and the analytic expression of surrounding rock stress was obtained.On the basis of criterion of Norway,the influences of seepage,pore water pressure and buried depth on the characteristics of the stress distribution of surrounding rocks were studied.The analyses show that the first water-filling plays a decisive role in the stability of the surrounding rock; the influence of seepage on the stress field around the tunnel is the greatest,and the change of the seepage factor is approximately consistent with the logarithm divergence.With the effects of the rock pore water pressure,the circumferential stress shows the exchange between large and small,but the radial stress does not.Increasing the buried depth can enhance the arching effect of the surrounding rock,thus improving the stability.     

Elasto-plastic analysis of the surrounding rock mass in circular tunnel based on the generalized nonlinear unified strength theory

The present paper aims to establish a versatile strength theory suitable for elasto-plastic analysis of underground tunnel surrounding rock. In order to analyze the effects of intermediate principal stress and the rock properties on its deformation and failure of rock mass, the generalized nonlinear unified strength theory and elasto-plastic mechanics are used to deduce analytic solution of the radius and stress of tunnel plastic zone and the periphery displacement of tunnel under uniform ground stress field. The results show that: intermediate principal stress coefficient b has significant effect on the plastic range,the magnitude of stress and surrounding rock pressure. Then, the results are compared with the unified strength criterion solution and Mohr–Coulomb criterion solution, and concluded that the generalized nonlinear unified strength criterion is more applicable to elasto-plastic analysis of underground tunnel surrounding rock.     

Equal perimeter yield criterion and its specific plastic work rate: Development,validation and application

In order to overcome the nonlinearity of Mises criterion, a new linear yield criterion with a dodecagon shape of the same perimeter as Mises criterion was derived by means of geometrical analysis. Its specific plastic work rate expressed as a linear function of the yield stress, the maximum and minimum strains was also deduced and compared with that of Mises criterion. The physical meaning of the proposed yield criterion is that yielding of materials begins when the shear yield stress τs reaches the magnitude of 0.594σs. By introducing the Lode parameter, validation of evolution expressions of the proposed yield criterion with those based on Tresca, Mises and TSS criteria as well as available classical yield experimental results of various metals shows that the present results intersect with Mises results and coincide well with experimental data. Moreover, further application to the limit analysis of circle plate as an example is performed to demonstrate the effectiveness of the proposed yield criterion, and the subsequent comparison of limit loads with the Tresca analytical solutions and Mises numerical results shows that the present results are higher than the Tresca analytical results, and are in good agreement with the Mises numerical results.     

A new numerical method for determining collapse load-carrying capacity of structure made of elasto-plastic material简

Determination of collapse load-carrying capacity of elasto-plastic material is very important in designing structure. The problem is commonly solved by elasto-plastic finite element method （FEM）. In order to deal with material nonlinear problem involving strain softening problem effectively, a new numerical method-damped Newton method was proposed. The iterative schemes are discussed in detail for pure equilibrium models. In the equilibrium model, the plasticity criterion and the compatibility of the strains are verified, and the strain increment and plastic factor are treated as independent unknowns. To avoid the stiffness matrix being singularity or condition of matrix being ill, a damping factor a was introduced to adjust the value of plastic consistent parameter automatically during the iterations. According to the algorithm, the nonlinear finite element program was complied and its numerical example was calculated. The numerical results indicate that this method converges very fast for both small load steps and large load steps. Compared with those results obtained by analysis and experiment, the predicted ultimate bearing capacity from the proposed method is identical.     

Numerical analysis of tunnel reinforcing influences on failure process of surrounding rock under explosive stress waves

Based on mesoscopic damage mechanics, numerical code RFPA2D （dynamic edition） was developed to analyze the influence of tunnel reinforcing on failure process of surrounding rock under explosive stress waves. The results show that the propagation phenomenon of stress wave in the surrounding rock of tunnel and the failure process of surrounding rock under explosive stress waves are reproduced realistically by using numerical code RFPA2O; from the failure process of surrounding rock, the place at which surrounding rock fractures is transferred because of tunnel reinforcing, and the rockfall and collapse caused by failure of surrounding rock are restrained by tunnel reinforcing; furthermore, the absolute values of peak values of major principal stress, and the minimal principal stress and shear stress at center point of tunnel roof are reduced because of tunnel reinforcing, and the displacement at center point of runnel roof is reduced as well, consequently the stability of tunnel increases.     

Stress dilatancy analysis of shallow tunnels subjected to unsymmetrical pressure

Numerical simulation using finite differential code was conducted for the single line railway and four-lane road shallow tunnels subjected to unsymmetrical pressure. The mechanical behavior of weak rock mass was studied considering the influences of stress dilatancy on the failure mechanisms, and the results of numerical simulation were compared with the analytical solutions in specifications. The results show that the dilatancy angle has great influences on the surrounding rock displacement and the shape of failure face for the shallow tunnels. When the dilatancy angle equals zero, the failure face of the surrounding rock forms and extends to the ground surface. With the dilatancy angle increasing, the loose region decreases gradually, and failure surface discontinues. When the dilatancy angle equals the friction angle, the loose region is only distributed in a small range around the crown and sidewalls. On the side of smaller buried depth, the difference of break angle between numerical simulation and the code is less than 10% for single line railway tunnels with the dilatancy angle of zero. However, for the four-lane road tunnels, the difference reaches 20.8%. On the side of larger buried depth, the break angles are smaller than those by the code, the difference reaches 16.8% for single line railway tunnels, and 13.8% for four-lane road tunnels. With the dilatancy angle increasing, especially the dilatancy angle approximating to internal friction angle, it is on safe side to calculate the break angle using the analytical solution method of specifications. Therefore, the influence of stress dilatancy should be considered while determining the failure mechanisms of shallow tunnels subjected to unsymmetrical pressure in weak rocks.     

Preparation and visible-light photocatalytic property of nanostructu- red Fe-doped TiO2 from titanium containing electric furnace molten slag

Nanostructured Fe-doped titanium dioxide was synthesized from titanium containing electric furnace molten slag （TCEFMS） by using an alkali fusion, followed by a hydrolyzation-acidolysis-cMcination route. The effects of Mkali/slag mass ratio, calcinating temperature, calcinating time, and water/slag mass ratio on the extraction efficiency and purity of products were systematically studied in this paper. It is indicated that the best extraction efficiency of nanostructured Fe- doped titanium dioxide is 99.35%, when the molten slag is calcinated at 700℃ for 1 h with the mass ratio of alkali/molten slag of 1.5：1. The influence of alkali/slag mass ratio on the photocatalytic activity of final products was evaluated by the photodegradation of methyl blue under visible light irradiation. A maximum photodegradation efficiency of 88.12% over 30 min was achieved under the optimum conditions.     

Martensitic transformation and magnetic properties of aged Ni-Fe-Ga-Ti shape memory alloy

This article reports the effect of ageing on the microstructure, martensitic transformation, magnetic properties, and mechanical properties of Ni51FelsGa27Ti4 shape memory alloy. There are five specimens of this alloy aged at 573 up to 973 K for 3 h per each. This range of ageing temperature greatly affects the microstructure of the alloy. As the ageing temperature increased from 573 up to 973 K, the microstructure of Ni51FelsGa27Ti4 alloy gradually changed from the entirely martensitic matrix at 573 K to the fully austenitic microstructure at 973 K. The volume fraction of precipi- tated Ni3Ti particles increased with the ageing temperature increasing from 573 to 773 K. Further increasing the ageing temperature to 973 K decreased the content of Ni3Ti in the microstructure. The martensitic transformation tempera- ture was decreased steadily by increasing the ageing temperature. The magnetization saturation, remnant magnetization, and coercivity increased with the ageing temperature increasing up to 773 K. A further increase in ageing temperature decreased these raagnetic properties. Moreover, the hardness values were gradually increased at first by increasing the ageing temperature to 773 K, and then dramatically decreased to the lowest value at 973 K.     

Microstructural and mechanical properties of A1-4.5wt% Cu rein- forced with alumina nanoparticles by stir casting method

The microstructure and mechanical properties of A1-4.5wt% Cu Mloy reinforced with different volume fractions （1.5vo1%, 3vo1%, and 5vo1%） of alumina nanoparticles, fabricated using stir casting method, were investigated. CMculated amounts of alumina nanoparticles （about ~50 nm in size） were ball-milled with aluminum powders in a planetary ball mill for 5 h, and then the packets of milled powders were incorporated into molten Al-4.5wt% Cu alloy. Microstructural studies of the nanocomposites reveal a uniform distribution of alumina nanoparticles in the A1-4.5wt% Cu matrix. The results indicate an outstanding improvement in compression strength and hardness due to the effect of nanoparticle addition. The aging behavior of the composite is also evaluated, indicating that the addition of alumina nanoparticles can accelerate the aging process of the Mloy, resulting in higher peak hardness values.     

Preparation of CaO-Al2O3-SiO2 system glass from molten blast furnace slag

To use the potential heat of molten blast furnace slag completely, a CaO-Al2O3-SiO2 system glass （MSG） was prepared from the molten industrial slag. The corresponding method proposed in this study utilized both slag and its potential heat, improving the production rate and avoiding the environmental pollution. Using appropriate techniques, an MSG with uniform color and superior performances was produced. Based on the experimental results and phase diagram, the chemical composition of MSG by mass is obtained as follows：CaO 27%-33%, SiO2 42%-51%, Al2O3 11%-14%, MgO 6%-8%, and Na2O＋K2O 1%-4%. Thermodynamic processes of MSG preparation were analyzed, and the phases and microstructures of MSG were investigated by X-ray diffraction （XRD） and scanning electron microscopy （SEM）. The results show that alkali metal oxides serve as the fluxes, calcium oxide serves as the stabilizer, and alumina reinforces the Si-O network. XRD and SEM analyses show that, the prepared MSG displays the glass-feature patterns, the melting process is more complete, and the melt viscosity is lowered with an increase in calcium oxide content;however, a continuous increase in slag content induces the crystalli-zation of glass, leading to the formation of glass subphase. The optimum content of molten slag in MSG is 67.37wt%. With respect to bend-ing strength and acid/alkali resistance, the performance of MSG is better than that of ordinary marble.     

Effect of some operational variables on bubble size in a pilot-scale mechanical flotation machine简

This work aims to provide a relationship of how the key operational variables of frother type and impeller speed affect the size of bubble （D32）. The study was performed using pilot-scale equipment （0.8 m^3） that is up to two orders of magnitude larger than equipment used for studies performed to date by others, and incorporated the key process variables of frother type and impeller speed. The results show that each frother family exhibits a unique CCC95-HLB relationship dependent on n （number of C-atoms in alkyl group） and m （number of propylene oxide group）. Empirical models were developed to predict CCC95 from HLB associated with other two parameters a and ft. The impeller speed-bubble size tests show that D32 is unaffected by increased impeller tip speed across the range of 4.6 to 9.2 m/s （representing the industrial operating range）, although D32 starts to increase below 4.6 m/s. The finding is valid for both coalescing and non-coalescing conditions. The results suggest that the bubble size and bubble size distribution （BSD） being created do not change with increasing impeller speed in the quiescent zone of the flotation.     

Feasibility of developing composite action between concrete and cold-formed steel beam

Cold-formed steel structures are steel structure products constructed from sheets or coils using cold rolling, press brake or bending brake method. These structures are extensively employed in building construction industry due to their light mass, ductility by economic cold forming operations, favorable strength-to-mass ratio and other factors. The utilization of cold formed steel sections with concrete as composite can hugely reduce the construction cost. However, the use of cold formed steel members in composite concrete beams has been very limited. A comprehensive review of developments in composite beam with cold formed steel sections was introduced. It was revealed that employing cold-formed steel channel section to replace reinforcement bars in conventional reinforced concrete beam results in a significant cost reduction without reducing strength capacity. The use of composite beam consisting of cold-formed steel open or close box and filled concrete could also reduce construction cost. Lighter composite girder for bridges with cold-formed steel of U section was introduced. Moreover, types of shear connectors to provide composite action between cold-formed steel beam and concrete slab were presented. However, further studies to investigate the effects of metal decking on the behavior of composite beam with cold-formed steel section and introduction of ductile shear connectors were recommended.     

Effects of Sr2＋ substitution on the structural,dielectric, and piezoelectric properties of PZT-PMN ceramics

This study described the structural, dielectric, and piezoelectric behavior of Pb1-xSrx[（Zr0.52Ti0.48）0.95（Mn1/3Nb2/3）0.05]O3 ceramics （PSZT-PMN, x=0, 0.025, 0.050, and 0.075）, prepared by a semi-wet route. X-ray diffraction, dielectric, and piezoelectric investigations were carried out to analyze the crystal structure. The relative dielectric constant and dielectric loss were both calculated as the functions of temperature. The room-temperature dielectric constant reaches a maximum for a Sr2＋-modified PZT-PMN ceramic with an x value of 0.050, which corresponds to the morphotropic phase boundary （MPB）. Raman spectroscopy studies also confirm the existence of this MPB for x=0.050. The piezoelectric strain coefficients （d33） value shows a maximum response for this composition. In addition, the phase transition temperature decreases significantly when the Sr2＋concentration increases in the PZT-PMN ceramics.     

Interfacial intermetallic compound growth and shear strength of low-silver SnAgCuBiNi//Cu lead-free solder joints

The growth rule of the interfacial intermetallic compound （IMC） and the degradation of shear strength of Sn-0.SAg-0.5Cu-2.0Bi-0.05Ni （SACBN）/Cu solder joints were investigated in comparison with Sn-3.0Ag-0.5Cu （SAC305）/ Cu solder joints aging at 373, 403, and 438 K. The results show that （Cul-x,Nix）6Sn5 phase forms between the SACBN solder and Cu substrate during soldering. The interracial IMC thickens constantly with the aging time increasing, and the higher the aging temperature, the faster the IMC layer grows. Compared with the SAC305/Cu couple, the SACBN/Cu couple exhibits a lower layer growth coefficient. The activation energies of IMC growth for SACBN/Cu and SAC305/Cu couples are 111.70 and 82.35 kJ/mol, respectively. In general, the shear strength of aged solder joints declines continuously. However, SACBN/Cu solder joints exhibit a better shear strength than SAC305/Cu solder joints.     

Pyrolysis characteristics of rubber compositions in medical waste

Thermogravimetric study of rubber compositions （operating glove and catheter） in medical waste was carried out using the thermogravimetric analyser （TGA）,at the heating rate of 20 ℃/min in a stream of N2.The results indicate that the decomposition process of operating glove appears an obvious mass loss stage at 250-485 ℃,while catheter has two obvious stages at 240-510 ℃ and 655-800 ℃,respectively; both samples present endothermic pyrolysis reaction; the decomposition of operating glove and the first mass loss stage of catheter are in agreement with natural rubber pyrolysis; the second mass loss stage of catheter corresponds to CaCO3 decomposition.Based on the experimental results,a novel two-step four-reaction model was established to simulate the whole continuous processes,which could more satisfactorily describe and predict the pyrolysis processes of rubber compositions,being more mechanistic and conveniently serving for the engineering.     

Low temperature sintering and dielectric properties of Ca-Ba-Al-B-Si-O glass/Al2O3 composites for LTCC applications

The effects of various SiO2 contents on both the microstructures and properties of Ca-Ba- A1-B-Si-O glass/Al2O3 cotrtposites were investigated by FTIR, DSC, XRD and SEM. The experimental results show that increasing SiO2 content in the glass leads to the increase of [SIO4] units, increases the continuity of glass network, and decreases the trend to crystallization of composites. The shrinkage of samples rises rapid around the glass softening temperature and the final shrinkage of samples decreases with increasing SiO2 content in the glass. Borosilicate glass/Al2O3 composites with 60wt% SiO2 sintered at 875 ℃ for 15 min show better properties： a bulk density of 3.10 g,cm-3, a porosity of 0.23 %, a er value of 7.55 and a tan 8 value of 0.00053 （measured at 10 MHz） and a well matching with Ag electrodes.