Frost heaving force considering synchronous damage to tunnel lining and surrounding rocks under freeze—thaw cycles

In areas with seasonal freezing,when the tunnel lining concrete is saturated with water infiltrating the interior,the lining and the surrounding rocks will simultaneously freeze.However,the current calculation of the frost heaving force fails to consider the synchronous damage to the lining and surrounding rocks under freeze-thaw cycles.Therefore,as per the elastic calculation model of the frost heaving force and model of steady-state heat transfer of circular tunnels,this study introduces the frost heaving rate of lining and surrounding rocks.First,the analytical solution of frost heaving force is obtained for simultaneous frost heaving of lining and surrounding rocks under any steady-state temperature field.Then,based on the fracture theory and meso-damage mechanics,the damage variables of lining and surrounding rocks under freeze-thaw cycles are extracted,representing their elastic modulus and porosity.Finally,the formula of frost heaving force for synchronous damage to the lining and surrounding rocks at any steady-state temperature field is obtained.The calculation results demonstrate that the lower the temperature inside the lining,the greater the frost heaving force.With the increasing number of freeze-thaw cycles,frost heaving force tends to gradually increase initially,reaching a peak value at 85 freeze-thaw cycles,decreasing to 80%of the peak value at 140 cycles before reaching a constant value.The lining participates in frost heaving,increasing the frost heaving force.The initial increase rate of frost heaving force is 15.7%.Changing the fitting coefficients s1 and s2 of the lining and surrounding rocks can effectively control the magnitude of the frost heaving force in the tunnels.

Influence of thermal insulation layer schemes on the frost heaving force in tunnels

In extreme cold regions,a thermal insulation layer(TIL)is commonly employed to mitigate the detrimental effects of frost heaving forces in tunnels.Optimizing the laying scheme of TIL,specifically minimizing frost heaving forces,holds considerable importance in the prevention of frost damage.This research developed a two-dimensional unsteady temperature field of circular tunnels by using the difference method(taking the off-wall laying method as an example)based on the law of conservation of energy.Then,the frozen circle and water migration coefficient were introduced to establish the relationship between the temperature field and frost heaving forces,and a reliable methodology for calculating these forces under the specific conditions of TIL installation was developed.Then(i)the influence of the air layer thickness of the off-wall laying method,(ii)different laying methods of TIL,(iii)the TIL thickness,(iv)the thermal conductivity of the TIL,and(v)the freeze-thaw cycles on the frost heaving force were investigated.The results showed that the frost heaving force served as a reliable and effective metric for evaluating the insulation effect in tunnels.In order to avoid frost damage in compliance with the design requirements,the insulation effects from various laying methods were established,in descending efficacy order as follows:off-wall laying,double layer laying,surface laying,and sandwich laying.Our findings revealed that the optimal thickness for the air layer in the offwall laying method was 0.10 m.The insulation effect of materials with a thermal conductivity below 0.047 W/(m·℃)was furthermore found to be good.Under freeze-thaw cycle conditions,it is concluded that to prevent frost damage,the TIL thickness should be the sum of the thickness r1 of the first freeze-thaw cycle without frost heaving forces and an additional reserve value 0.06r1 of the TIL thickness.

New semi-analytical approach for ice lens heaving during artificial freezing of fine-grained material

The calculation of frost heaving with ice lens formation is still not standard for construction projects using artificial ground freezing(AGF).In fine-grained material,ice lenses may initiate and lead to significant heaving at the ground surface,which should be considered in advance.However,the complex processes during ice lens formation are still not fully understood and difficult to capture in a simple approach.In the past,the semi-analytical approach of Konrad and Morgenstern used one soil constant,the“segregation potential(SP)”.It has been mainly and most successfully applied to the heave calculation of natural-induced soil freezing in cold regions.Its application to AGF has been so far unsuccessful.To solve this,a new semi-analytical approach is presented in this paper.It includes AGF conditions such as bottom-up freezing,temperature gradients to reach great freezing velocities,and a distinction between two freezing states.One is the freezing-up state until a certain frost body thickness is reached(thermal transient state),and the other is a holding phase where the frost body thickness is kept constant(thermal quasi-steady state).To test its ability,the results are applied to another freezing direction,the top-down freezing.The new approach is validated using two different frost-susceptible soils and,in total,50 frost heave tests.In the thermal transient region,where the SP is applicable,the two semi-analytical approaches are compared,showing improved performance of the current method by about 15%.

Frost-heaving pressure in geotechnical engineering materials during freezing process

Energy and resources including coal, oil, and gas are in demand all over the world. Because these resources near the earth's surface have been exploited for many years, the extraction depth has increased.As mining shafts in the coal extraction process become deeper, especially in western China, an artificial freezing method is used and is concentrated in the fractured rock mass. The frost-heaving pressure(FHP)is directly related to the degree of damage of the fractured rock mass. This paper is focused on FHP during the freezing process, with emphasis on the frost-heaving phenomenon in engineering materials. A review of the frost phenomenon in the geotechnical engineering literature indicates that:(1) During the soil freezing process, the ice content that is influenced by unfrozen water and the freezing rate are the determining factors of FHP;(2) During the freezing process of rock and other porous media, the resulting cracks should be considered because the FHP may damage the crack structure;(3) The FHP in a joint rock mass is analyzed by the joint deformation in field and experimental tests and can be simulated by the equivalent expansion method including water migration and joint deformation.

Effect of Cambering on the Aerodynamic Performance of Heaving Airfoils

In the present work,a parametric numerical study is conducted in order to assess the effect of airfoil cambering on the aerodynamic performance of rigid heaving airfoils.The incompressible Navier-Stokes equations are solved in their velocity-pressure formulation using a second-order accurate in space and time finite-difference scheme.To tackle the problem of moving boundaries,the governing equations are solved on overlapping structured grids.The numerical simulations are performed at a Reynolds number of Re=1100 and at different values of Strouhal number and reduced frequency.The results obtained show that the airfoil cambering geometric parameter has a strong influence on the average lift coefficient,while it has a smaller impact on the average thrust coefficient and propulsive efficiency of heaving airfoils.

Effects of Heaving Motion on the Aerodynamic Performance of a Double-Element Wing in Ground Effect

The broad implication of the paper is to elucidate the significance of the dynamic heaving motion in the aerodynamic performance of multi-element wings,currently considered as a promising aspect for the improvement of the aerodynamic correlation between CFD,wind tunnel and track testing in race car applications.The relationship between the varying aerodynamic forces,the vortex shedding,and the unsteady pressure field of a heaving double-element wing is investigated for a range of mean ride heights,frequencies,and amplitudes,using a two-dimensional(2D)unsteady Reynolds-averaged Navier-Stokes(URANS)approach and an overset mesh method for modelling the moving wing.The analysis of the results shows that at high frequencies,i.e.,k≥5.94 and amplitudes a/c≥0.05 the interaction of the shear vorticity between the two elements results in the generation of cohering leading and trailing edge vortices on the flap,associated to the rapid variation of thrust and downforce enhancement.Both the occurrence and intensity of these vortices are dependent upon the frequency,amplitude,and mean ride height of the heaving wing.The addition of the flap significantly alters the frequency of the shed vortices in the wake and maintains the generation of downforce for longer time in ground proximity.The comparison with the static wing provides evidence that the dynamic motion of a race car wing can be beneficial in terms of performance,or detrimental in terms of aerodynamic correlation.

Zonal overturning circulation and heat flux induced by heaving modes in the world oceans

Zonal overturning circulation （ZOC） and its associated zonal heat flux （ZHF） are important components of the oceanic circulation and climate system, although these conceptions have not received adequate attentions. Heaving induced by inter-annual and decadal wind stress perturbations can give rise to anomalous ZOC and ZHF. Based on a simple reduced gravity model, the anomalous ZOC and ZHF induced by idealized heaving modes in the world oceans are studied. For example, in a Pacific-like model basin intensified equatorial easterly on decadal time scales can lead to a negative ZOC with a non-negligible magnitude （-0.3×10^6 m^3/s） and a considerable westward ZHF with an amplitude of -11.2 TW. Thus, anomalous ZOC and ZHF may consist of a major part of climate signals on decadal time scales and thus play an important role in the oceanic circulation and climate change.

Experimental Study on the Hydrodynamic Performance of a Heaving Buoy Assembled on a Net Cage Platform

To take advantage of the abundance of both fishery and wave energy resources in offshore sea areas,a novel floating platform with a heaving buoy-based wave energy converter(WEC)assembled with a set of net cages is presented in this work.The floating WEC system provides a power supply,while the net cages are used for aquaculture.It is designed to have an independent and self-operation breeding function.An experimental study is carried out to investigate the hydrodynamic performance of the device in a wave tank considering the factors of net cages,draft depth,and power take-off,and results show that these variables have significant effects on wave energy capture.Incident waves with short periods cause intense interactions that allow the device to undergo large relative motion.The draft depth could be determined according to wave period rather than wave height.This study also explores the response amplitude operator of the device and determines its resonance scope.The experimental results could provide reliable information for future studies on phase differences and the design of two-body WECs.

Simulation of the Power Take-off System for a Heaving Buoy Wave Energy Converter

The heaving buoy wave energy device is popular for wave conditions with small wave heights and short periods. This paper presents the design of a wave energy converter composed of a gyro buoy, a hydraulic power take-off, and an electricity generation system. The energy accumulators are used to improve the output power with different control strategies. The quantity relations between each component are established using theoretical methods. The simulation model describes the energy conversion and calculates the operation time, energy capacity, and output power of the device under different initial pressures, release pressures, and electric resistances. As a result, the capacity is determined by the electronic load, and the maximum output power can be obtained when the accumulators are turned on and off at the same time. This study investigates the factors influencing the electric energy production and can be used to guide the optimization of this type of device.

Hydrodynamic Characteristics of Square Heaving Plates with Opening Under Forced Oscillation

The existence of the heaving plates can improve the heaving motion performance of an offshore structure significantly by providing both extra added mass and damping.In the current research,numerical investigation is carried out on the hydrodynamic characteristics of both isolated square heaving plate and double square heaving plates with opening by an immersed boundary-lattice Boltzmann method.The effects on hydrodynamic performance of plates due to Keulegan-Carpenter(KC)number,frequency number,opening ratio,opening distribution and spacing of plates are examined.It is found that the heaving plates with optimized opening ratio can provide additional damping compared with the plates without opening.Better hydrodynamic characteristics of double plates can be obtained with the increase of plate spacing.

Model test study of frost heaving pressures in tunnels excavated in fractured rock mass in cold regions

Based on the similarity theory, taking the horseshoe, city-gate and round linings as examples, the value and distribution regularities of normal frost heaving pressures （hereinafter as frost heaving pressures） in tunnels excavated in fractured rock mass in cold regions under different constraints and freezing depths were studied by a test model. It was found that the larger the frozen depth, the larger the frost heaving pressure, and the stronger the top constraint, the larger the frost heaving pressure. For the horseshoe lining and city-gate lining, the top constraint has a greater effect on the frost heaving pressures on the arch and the inverted arch. For the round lining, the influences of the top constraint on the frost heaving pressure in all linings are almost the same. The frost heaving pressure is maximum on the city-gate lining and minimal on the round lining. The largest frost heaving pressure all occur near the foot of the inverted arch for the three kinds of lining. Thus, the test data basically coincide with the observed in situ data.

Study of experiment method for triaxial frost heaving constitutive relation of frozen soil

A new experiment method is introduced to study the relations between frost heaving strain and stress of soil or fracture rock under different moisture contents, temperatures and stress states. Based on experiments, a new triaxial frost heaving stress-strain relation is presented aiming at tunnel in cold regions. The experimental equipments are strain-controlled and low temperature buildup, and different restrained conditions are controlled by changing the stiffness of a test-force-ring. Then the frost heaving strain and stress of soil or fracture rock can be obtained under different restrained conditions, and the frost heaving stress-strain relation can be got by regression analysis of some feature points. Experiments of saturated sandy soil conducted by this method show that the triaxial frost heaving stress-strain relation could be expressed by logarithmic curves, and the frost heaving stress changes linearly with the logarithm of the frost heaving strain. The stronger the constraint, the smaller the frost heaving strain and the larger the frost heaving stresses. The frost heaving stresses would tend to a limit value with increasing the constraint intensity. The larger the confining pressure, the larger the frost heaving strain and stress.

Establishment of Field Sites to Study Frost Heaving and Related Landforms in Southern Yakutia,Russia

Frost heaving processes have been a focus of study since the late 19th century.Factors controlling frost heave development were investigated over several decades.The mechanisms involved were identified based on numerous field and experimental evidences. However,despite this long history of frost

Power Absorption of A Two-Body Heaving Wave Energy Converter Considering Different Control and Power Take-off Systems

This study proposed a wave power system with two coaxial floating cylinders of different diameters and drafts.Wavebob’s conceptual design has been adopted in the wave power system.In this study,a basic analysis of the wave energy extraction by the relative motion between two floats is presented.The maximum power absorption was studied theoretically under regular wave conditions,and the effects of both linear and constant damping forces on the power take-off(PTO)were investigated.A set of dynamic equations describing the floats’displacement under regular waves and different PTOs are established.A time-domain numerical model is developed,considering the PTO parameter and viscous damping,and the optimal PTO damping and output power are obtained.With the analysis of estimating the maximum power absorption,a new estimation method called Power Capture Function(PCF)is proposed and constructed,which can be used to predict the power capture under both linear and constant PTO forces.Based on this,energy extraction is analyzed and optimized.Finally,the performance characteristics of the two-body power system are concluded.

Frost heaving in ballast railway tracks

Frost heaving is a well-known phenomenon in cold regions, which may occur in wet clayey grounds during winter. Railway track upheaval occurring in cold regions during the winter is generally understood as frost heaving in the subgrade layer. However, it has been confirmed that upheaval due to frost heaving sometimes occurs in the ballast layer. This un- derstanding has been observed in active railways in northern Japan. The samples collected from ballast and subgrade layers have been examined for frost heave susceptibilities and confirmed that ballast layers which contain fines may heave.

Incident analyses of frost heaving failure of municipal underground gas pipelines in cold regions of northern China

In the cold regions of northern China, incidents of municipal underground gas pipeline rupture and leakage occur quite fi-equently, aaost often in winter. To prevent harm to citizen safety and property, analysis of the causes of such cracking and leakage is therefore valuable. Two incident analyses are discussed here and the reasons why most of these types of cases occur dttring winter are clarified. Fhe effects of vehicle loadings above buried pipelines are calculated and compared with the effects and calculations of frost heaving forces. We demonstrate thtit when the soil layer above a pipeline freezes rapidly, the soil generates repeated frost heaving, which exerts heaving forces on the pipeline that can result in fatigue crack propagation and ultimate pipeline failure. Therefore, the incident induced 9y frost heaving is one of the primary reasons of gas pipeline failure. Based on these analyses, we present some recommendations pertaining to the proper design, construction, and management of gas pipelines.

The Investigation of the Effect of Heaving and Pitching on Wave-Induced Vertical Hull Vibration of a Container Ship in Regular Waves

The aim of this paper is to investigate the effect of heaving and pitching of ship motion due to springing bending moment. The investigation was conducted both experimentally and validated theoretically. Series of experiment were carried out using a container model-ship of which length was 3 meter, and the possibility of the so-called nth resonant springing vibration is tested by taking n from n = 2 to n = 4. The bending moment due- to vibration is also measured. The following conclusions were obtained： （l） Occurance of the higher order resonant vibration between 2nd-4th is recognized experimentally; （2） The results indicated that heaving and pitching of ship motion influenced the springing bending moment accurately.

Numerical Simulation of Fluid Resonance in a Moonpool by Twin Rectangular Hulls with Various Configurations and Heaving Amplitudes

Fluid resonance in a moonpool formed by two identical rectangular hulls during in-phase heaving motion is investigated by employing a two-dimensional numerical wave flume based on OpenFOAM package with Re-Normalization Group(RNG) turbulent model. The focus of the study is to examine the influence of heaving frequency and amplitude with various moonpool configurations on fluid resonant behavior. It is found that the resonant frequency of wave response in moonpool tends to decrease with the increase of moonpool breadth and hulls draft. The decrease of resonant amplitude can be observed for large moonpool breadth. The influence of hulls draft on resonant amplitude is not remarkable, especially for large heaving amplitude. The increase in heaving amplitude results in the decrease of relative resonant amplitude in an approximate power function, implying a complicated dependence of the resonant amplitude on heaving amplitude. Flow patterns in the vicinity of the moonpool are also analyzed, mainly regarding the dependence on the heaving frequency. The negligible influence of vortices on the wave response in moonpool is expected for low-frequency excitation because it is hard to observe the vortex structures. Intensive vortical flow and vortex structure can be identified under resonant condition, which gives rise to significant dissipation and accounts for the smaller relative resonant amplitude in moonpool. As for high-frequency excitation, the vortex motion is rather weak and dissipates rapidly, leading to insignificant effect on wave response amplitude.

A Frost Heaving Prediction Approach for Ground Uplift Simulation Due to Freeze-Sealing Pipe Roof Method

Freeze-sealing pipe roof method is applied in the Gongbei tunnel,which causes the ground surface uplift induced by frost heave.A frost heaving prediction approach based on the coefficient of cold expansion is proposed to simulate the ground deformation of the Gongbei tunnel.The coefficient of cold expansion in the model and the frost heaving rate from the frost heave test under the hydration condition can achieve a good correspondence making the calculation result closer to the actual engineering.The ground surface uplift along the lateral and longitudinal direction are respectively analyzed and compared with the field measured data to validate the model.The results show that a good agreement between the frost heaving prediction model and the field measured data verifies the rationality and applicability of the proposed model.The maximum uplift of the Gongbei tunnel appears at the center of the model,gradually decreasing along with the lateral and longitudinal directions.The curve in the lateral direction presents a normal distribution due to the influence of the constraint of two sides,while the one along the lateral direction shapes like a parabola with the opening downward due to the temperature field distribution.The model provides a reference for frost heaving engineering calculation.

Numerical investigation of edge configurations on piston-modal resonance in a moonpool induced by heaving excitations

The renormalization group (RNG) turbulent model is used to investigate the fluid resonance in a moonpool formed by two identical rectangular hulls under synchronous heaving excitation (e.g., a catamaran or dual pontoon). The numerical model is validated against the available experimental data, and accurate numerical solutions are obtained. The present study focuses on the amplitude of the moving hulls and the edge configuration of the moonpool entrance, as well as their influences on the piston-modal resonant wave in the moonpool. The dependence of the resonant wave amplitude in the moonpool on the heaving amplitude, the characteristic moonpool dimensions and the local velocity magnitude is derived based on a theoretical analysis, and the results are in good agreement with the RNG turbulent solutions. Five different edge profiles are considered, including two convex edges, two concave edges (both with various dimensions), and a sharp edge. Numerical examinations show that the edge configuration has a significant influence on the piston-modal resonant responses, a larger opening size leading to a higher resonant frequency and a larger resonant wave amplitude in the moonpool. Various flow patterns of the piston-modal resonance in the vicinity of the moonpool entrance are also identified, mainly depending on the edge profile. More intensive turbulent and vortical flows give rise to more significant dissipation, accounting for the smaller relative wave amplitude in the moonpool. With the increase of the heaving amplitude, the relative piston-modal resonant amplitude is decreased in an approximate power function. Within the scope of this work, the numerical investigations show that the piston-modal resonant frequency is hardly affected by the heaving amplitude.