Effects of phosphorus limitation on sinking velocities of phytoplankton during summer in the Changjiang River Estuary

The sinking of phytoplankton is critical to organic matter transportation in the ocean and it is an essential process for the formation of coastal hypoxic zones.This study was based on a field investigation conducted during the summer of 2022 in the Changjiang River(Yangtze River) Estuary(CJE) and its adjacent waters.The settling column method was employed to measure the sinking velocity(SV) of different size fractions of phytoplankton at the surface of the sea and to analyze their environmental control mechanisms.The findings reveal significant spatial variation in phytoplankton SV(-0.55-2.41 m/d) within the CJE.High-speed sinking was predominantly observed in phosphate-depleted regions beyond the CJE front.At the same time,an upward trend was more commonly observed in the phosphate-rich regions near the CJE mouth.The SV ranges for different sizefractionated phytoplankton,including micro-(>20 μm),nano-(2-20 μm),and picophytoplankton(0.7-2 μm),were-0.50-4.74 m/d,-1.04-1.59 m/d,and-1.24-1.65 m/d,respectively.Correlation analysis revealed a significant negative correlation between SV and dissolved inorganic phosphorus(DIP),implying that the influence of DIP contributes to SV.The variations in phytoplankton alkaline phosphatase activity suggested a significant increase in SV across all size fractions in the event of phosphorus limitation.Phytoplankton communities with limited photo synthetic capacity(maximum photochemical efficience,Fv/Fm <0.3) were found to have higher SV than that of communities with strong capacity,suggesting a link between sinking and alterations in physiological conditions due to phosphate depletion.The findings from the in situ phosphate enrichment experiments confirmed a marked decrease in SV following phosphate supplementation.These findings suggest that phosphorus limitation is the primary driver of elevated SV in the CJE.This study enhances the comprehension of the potential mechanisms underlying hypoxic zone formation in the CJE,providing novel insights into how nearshore eutrophication influences organic carbon migration.

Effects of nutrient limitations on the sinking velocity of Thalassiosira weissflogii

The sinking of diatoms is critic al to the formation of oceanic biological pumps and coastal hypoxic zones.However,little is known about the effects of different nutrient restrictions on diatom sinking.In this study,we measured the sinking velocity(SV) of Thalassiosira weissflogii using a new phytoplankton video observation instrument and analyzed major biochemical components under varying nutrient conditions.Our results showed that the SV of T.weissflogii under different nutrient limitation conditions varied substantially.The highest SV of(1.77±0.02) m/d was obtained under nitrate limitation,signific antly surpassing that under phosphate limitation at(0.98±0.13) m/d.As the nutrient limitation was released,the SV steadily decreased to(0.32±0.03) m/d and(0.15±0.05) m/d,respectively.Notably;under conditions with limited nitrate and phosphate concentrations,the SV values of T.weissflogii significantly positively correlated with the lipid content(P <0.001),with R^(2) values of 0.86 and 0.69,respectively.The change of the phytoplankton SV was primarily related to the intracellular compo sition,which is controlled by nutrient conditions but did not significantly correlate with transparent extracellular polymer and biosilica contents.The results of this study help to understand the regulation of the vertical sinking process of diatoms by nutrient restriction and provide new insights into phytoplankton dynamics and their relationship with the marine nutrient structure.

基于局部密度聚类的WSN多Sink节点部署研究

针对无线传感器网络中传感器节点能量受限,网络生命周期短的问题,在考虑网络成本的情况下,提出一种基于节点局部密度聚类的多Sink节点优化部署算法。首先,基于多属性因子构建聚类决策函数确定Sink节点部署位置,完成传感器节点聚类;然后,根据下一跳节点与Sink节点间距离最短准则搜索并形成数据传输路径;最后,以网络生命周期成本比最大化为依据确定最优的Sink节点数目,实现多Sink节点优化部署。仿真结果表明:与已有算法相比,所提算法能够有效延长网络生命周期,具有较高的网络生命周期能效比。

跳数受限下的传感云网络多Sink节点重选址方法

当传感云网络中的Sink节点处于静止状态时,分布在其周围的邻居节点极易出现“能量空洞”,导致能量消耗不均,节点出现不同的网络生存期,影响节点间数据正常传输。为此,在限制节点跳数的前提下,提出一种多Sink节点重选址方法。基于Sink节点寿命和传感云网络代价函数引入质心理论,建立质点系并确定质心位置;将Sink节点向流量大的节点移动,并与其他Sink节点相互协作、避免发生冲突,直至到达质心位置,实现多Sink节点重选址。结果表明,所提方法重选址的节点生存时间最高为1 000 s为,数据包交付率为98%,节点平均剩余能量值高于0.6 J。

Dynamics and vibration reduction performance of asymmetric tristable nonlinear energy sink

With its complex nonlinear dynamic behavior,the tristable system has shown excellent performance in areas such as energy harvesting and vibration suppression,and has attracted a lot of attention.In this paper,an asymmetric tristable design is proposed to improve the vibration suppression efficiency of nonlinear energy sinks(NESs)for the first time.The proposed asymmetric tristable NES(ATNES)is composed of a pair of oblique springs and a vertical spring.Then,the three stable states,symmetric and asymmetric,can be achieved by the adjustment of the distance and stiffness asymmetry of the oblique springs.The governing equations of a linear oscillator(LO)coupled with the ATNES are derived.The approximate analytical solution to the coupled system is obtained by the harmonic balance method(HBM)and verified numerically.The vibration suppression efficiency of three types of ATNES is compared.The results show that the asymmetric design can improve the efficiency of vibration reduction through comparing the chaotic motion of the NES oscillator between asymmetric steady states.In addition,compared with the symmetrical tristable NES(TNES),the ATNES can effectively control smaller structural vibrations.In other words,the ATNES can effectively solve the threshold problem of TNES failure to weak excitation.Therefore,this paper reveals the vibration reduction mechanism of the ATNES,and provides a pathway to expand the effective excitation amplitude range of the NES.

A viscoelastic nonlinear energy sink with an electromagnetic energy harvester:Narrow-band random response

Nonlinear energy sink is a passive energy absorption device that surpasses linear dampers, and has gained significant attention in various fields of vibration suppression. This is owing to its capacity to offer high vibration attenuation and robustness across a wide frequency spectrum. Energy harvester is a device employed to convert kinetic energy into usable electric energy. In this paper, we propose an electromagnetic energy harvester enhanced viscoelastic nonlinear energy sink(VNES) to achieve passive vibration suppression and energy harvesting simultaneously. A critical departure from prior studies is the investigation of the stochastic P-bifurcation of the electromechanically coupled VNES system under narrowband random excitation. Initially, approximate analytical solutions are derived using a combination of a multiple-scale method and a perturbation approach. The substantial agreement between theoretical analysis solutions and numerical solutions obtained from Monte Carlo simulation underscores the method's high degree of validity. Furthermore, the effects of system parameters on system responses are carefully examined. Additionally, we demonstrate that stochastic P-bifurcation can be induced by system parameters, which is further verified by the steady-state density functions of displacement. Lastly,we analyze the impacts of various parameters on the mean square current and the mean output power, which are crucial for selecting suitable parameters to enhance the energy harvesting performance.

Dynamic performance and parameter optimization of a half-vehicle system coupled with an inerter-based X-structure nonlinear energy sink

Inspired by the demand of improving the riding comfort and meeting the lightweight design of the vehicle, an inerter-based X-structure nonlinear energy sink(IXNES) is proposed and applied in the half-vehicle system to enhance the dynamic performance. The X-structure is used as a mechanism to realize the nonlinear stiffness characteristic of the NES, which can realize the flexibility, adjustability, high efficiency, and easy operation of nonlinear stiffness, and is convenient to apply in the vehicle suspension, and the inerter is applied to replacing the mass of the NES based on the mass amplification characteristic. The dynamic model of the half-vehicle system coupled with the IX-NES is established with the Lagrange theory, and the harmonic balance method(HBM) and the pseudo-arc-length method(PALM) are used to obtain the dynamic response under road harmonic excitation. The corresponding dynamic performance under road harmonic and random excitation is evaluated by six performance indices, and compared with that of the original half-vehicle system to show the benefits of the IX-NES. Furthermore, the structural parameters of the IX-NES are optimized with the genetic algorithm. The results show that for road harmonic and random excitation, using the IX-NES can greatly reduce the resonance peaks and root mean square(RMS) values of the front and rear suspension deflections and the front and rear dynamic tire loads, while the resonance peaks and RMS values of the vehicle body vertical and pitching accelerations are slightly larger.When the structural parameters of the IX-NES are optimized, the vehicle body vertical and pitching accelerations of the half-vehicle system could reduce by 2.41% and 1.16%,respectively, and the other dynamic performance indices are within the reasonable ranges.Thus, the IX-NES combines the advantages of the inerter, X-structure, and NES, which improves the dynamic performance of the half-vehicle system and provides an effective option for vibration attenuation in the vehicle engineering.

A comprehensive review on microchannel heat sinks for electronics cooling

The heat generation of electronic devices is increasing dramatically,which causes a serious bottleneck in the thermal management of electronics,and overheating will result in performance deterioration and even device damage.With the development of micro-machining technologies,the microchannel heat sink(MCHS)has become one of the best ways to remove the considerable amount of heat generated by high-power electronics.It has the advantages of large specific surface area,small size,coolant saving and high heat transfer coefficient.This paper comprehensively takes an overview of the research progress in MCHSs and generalizes the hotspots and bottlenecks of this area.The heat transfer mechanisms and performances of different channel structures,coolants,channel materials and some other influencing factors are reviewed.Additionally,this paper classifies the heat transfer enhancement technology and reviews the related studies on both the single-phase and phase-change flow and heat transfer.The comprehensive review is expected to provide a theoretical reference and technical guidance for further research and application of MCHSs in the future.

Effects of urbanization and forest type on species composition and diversity,forest characteristics,biomass carbon sink,and their associations in Changchun,Northeast China:implications for urban carbon stock improvement

Differences in forest attributes and carbon sequestration of each organ and layer between broadleaved and conifer forests of central and outer urban areas are not well-defined,hindering the precise management of urban forests and improvement of function.To clarify the effect of two forest types with different urbanization intensities,we determined differences in vegetation composition and diversity,structural traits,and carbon stocks of 152 plots(20 m×20 m)in urban park forests in Changchun,which had the largest green quantity and carbon density effectiveness.We found that 1.1-fold thicker and healthier trees,and 1.6-to 2.0-fold higher,healthier,denser,and more various shrubs but with sparser trees and herbs occurred in the central urban forests(p<0.05)than in the outer forests.The conifer forests exhibited 30–70%obviously higher tree aboveground carbon sequestration(including stem and leaf)and 20%bigger trees,especially in the outer forests(p<0.05).In contrast,1.1-to 1.5-fold higher branch stocks,healthier and more diverse trees were found in broadleaved forests of both the inner and outer forests(p<0.05).Plant size and dominant species had similarly important roles in carbon stock improvement,especially big-sized woody plants and Pinus tabuliformis.In addition,a higher number of deciduous or needle species positively affected the broadleaved forest of the central urban area and conifer forest of the outer urban area,respectively.These findings can be used to guide precise management and accelerate the improvement of urban carbon function in Northeast China in the future.

A vertical track nonlinear energy sink

Eliminating the effects of gravity and designing nonlinear energy sinks(NESs)that suppress vibration in the vertical direction is a challenging task with numerous damping requirements.In this paper,the dynamic design of a vertical track nonlinear energy sink(VTNES)with zero linear stiffness in the vertical direction is proposed and realized for the first time.The motion differential equations of the VTNES coupled with a linear oscillator(LO)are established.With the strong nonlinearity considered of the VTNES,the steady-state response of the system is analyzed with the harmonic balance method(HBM),and the accuracy of the HBM is verified numerically.On this basis,the VTNES prototype is manufactured,and its nonlinear stiffness is identified.The damping effect and dynamic characteristics of the VTNES are studied theoretically and experimentally.The results show that the VTNES has better damping effects when strong modulation responses(SMRs)occur.Moreover,even for small-amplitude vibration,the VTNES also has a good vibration suppression effect.To sum up,in order to suppress the vertical vibration,an NES is designed and developed,which can suppress the vertical vibration within certain ranges of the resonance frequency and the vibration intensity.

Coupling and Long-term Change Characteristics of Forest Carbon Sink and Forestry Economic Development in China

[Objectives]To analyze the changes in of forest carbon sink and forestry economic development,provide reference for relevant management decisions,ecological governance and resource and environment management,and promote the development of green low-carbon economy in China.[Methods]Based on the data of six forest resource inventories from 1989 to 2018 and related studies,the comprehensive evaluation model of forest carbon sink and forestry economic development,the coupling degree model of forest carbon sink and forestry economic development,and the coupling coordination degree model of forest carbon sink and forestry economic development were adopted.The coupling degree of forest carbon sink and forestry economic development from 1992 to 2018 was analyzed.Stepwise regression and ARIMA model were used to analyze the influencing factors and lagging characteristics of forest carbon sink.The coupling degree between forest carbon sink and forestry economic development in China from 2019 to 2030 was predicted by autoregression and ADF test.The coupling between forest carbon sink and forestry economic development in China and its long-term change characteristics were also discussed in this study.[Results](i)The investment of ecological construction and protection,the actual investment of forestry key ecological projects,GDP and the import of forest products had a significant impact on forest resources carbon stock.The total output value of forestry industry,the actually completed investment of forestry key ecological projects and the export volume of forest products had a significant impact on the forest carbon sink,and the actually completed investment of forestry key ecological projects has the greatest impact on the two.(ii)The impact of actually completed investment of forestry key ecological projects had a lag of 2 years on the forest resources carbon stock and a lag of 1 year on the forest carbon sink.When investing in forest carbon sink,it is necessary to make a good plan in advance,and do a good job in forest resources management and time optimization.(iii)From 1992 to 2018,the coupling degree of forest resources carbon stock,forest carbon sink and long-term development of forestry economy in China was gradually increasing.Although there were some fluctuations in the middle time,the coupling degree of forest resources carbon stock and the long-term development of forestry economy increased by 9.24%annually,and the degree of coupling coordination increased from"serious imbalance"in 1992 to"high-quality coordination"in 2018.From 1993 to 2018,the coupling degree of forest carbon sink and long-term development of forestry economy increased by 9.63%annually,slightly faster than the coupling coordination degree of forest resources carbon stock and long-term development of forestry economy.The coordination level also rose from level 2 in 1993 to level 10 in 2018.(iv)The prediction shows that the coupling coordination degree of forest resources carbon stock,forest carbon sink and the long-term development of forestry economy would increase from 2019 to 2030.The coupling coordination degree(D)values of both were close to 1,the coordination level was also 10 for a long time,and the degree of coupling coordination was also maintained at the"high-quality coordination"level for a long time.[Conclusions]Forest has multiple benefits of society,economy and ecology,and forest carbon sink is only a benefit output.The long-term coupling analysis of forest carbon sink and forestry economic development is a key point to multiple benefit analysis.The analysis shows that the spillover effect and co-evolution effect of forest carbon sink in China are significant.From 1992 to 2018,the coupling coordination degree of forest carbon sink and forestry economic development was gradually rising.The prediction analysis also indicate that the coupling coordination degree between the forest carbon sink and the long-term development of forestry economy will remain at the level of"high-quality coordination"for a long time from 2019 to 2030.Therefore,improving the level of forest management and maintaining the current trend of increasing forest resources are the key to achieving the goal of carbon peaking and carbon neutrality in China.

Heat dissipation enhancement method for finned heat sink for AGV motor driver's IGBT module

With the widespread use of high-power and highly integrated insulated gate bipolar transistor(IGBT),their cooling methods have become challenging.This paper proposes a liquid cooling scheme for heavy-duty automated guided vehicle(AGV)motor driver in port environment,and improves heat dissipation by analyzing and optimizing the core component of finned heat sink.Firstly,the temperature distribution of the initial scheme is studied by using Fluent software,and the heat transfer characteristics of the finned heat sink are obtained through numerical analysis.Secondly,an orthogonal test is designed and combined with the response surface methodology to optimize the structural parameters of the finned heat sink,resulting in a 14.57%increase in the heat dissipation effect.Finally,the effectiveness of heat dissipation enhancement is verified.This work provides valuable insights into improving the heat dissipation of IGBT modules and heat sinks,and provides guidance for their future applications.

Sinking型和Sourcing型数字信号I/O接口应用

当为控制系统选择数字信号输入/输出模块的接口类型时,正确理解Sinking Current(灌电流)和Sourcing Current(拉电流)的概念是非常重要的。讨论数字信号输入/输出接口/连接电路时会经常使用这些术语,在设计与负载连接的电路时,除了考虑电压、电流、功率等匹配外,更要注意灌电流型和拉电流型DI/O的区别,以使得连接电路更合理、可靠,逻辑表达更清楚和正确。

Establishing Submersed Macrophytes via Sinking and Colonization of Shoot Fragments Clipped off Manually

In this paper, sinking and growth of apexes and mid-stems of Myriophyllum spicatum L., Hydrilla verticillata （L.f.） Royle and Ceratophyllum demersum L. in concrete ponds containing eutrophic water and sediment were investigated. Sinking rates of apexes and mid-stems reached 34.8% and 4.4% at the 6 th day and 91.1% and 66.7% at the 22 nd day for M. spicatum, 57.8% and 55.6% at the 6 th day and 100% and 97.8% at the 22 nd day for H. vertieillata, 18.9% and 86.7% at the 6 th day and 95.6% and 100% at the 22 nd day for C. demersum, respectively. Most sunken fragments established themselves successfully with significant growth. Total shoot length ofplantlets developed from apexes and mid-stems increased by 399% and 61% for M. spicatum, 593% and 256% for H. vertieillata and 114% and 104% for C. demersum, respectively. The results showed that it was feasible to establish submersed macrophytes via sinking and colonization of shoot fragments clipped off manually.

Temporal variation in biodeposit organic content and sinking velocity in long-line shellfish culture

We measured the organic content and sinking velocities of biodeposits from two scallop species(Chlamys farreri,Patinopecten yessoensis) and abalone(Haliotis discus hannai) that were cultured on suspended long-lines.Measurements were conducted every two months from April 2010 to February 2011.The shellfish were divided into three size groups(small,middle,and big sizes).At each sample point,we assessedbiodeposit organic content,average sinking velocity,the frequency distribution of sinkingvelocities,and the correlation between organic content and sinking velocity.The organic content of biodeposits varied significantly among months(P<0.05) and the pattern of change varied among species.Sinking velocities varied significantly,ranging from <0.5 cm/s to >1.9 cm/s.The sinking velocities of biodeposits from C.farreri and P.yessoensis were 0.5-1.5 cm/s and from H.discus hannai were <0.7 cm/s.The organic content was significantly negatively correlated to the sinking velocity of biodeposits in C.farreri(P<0.001) and P.yessoensis(P<0.05).

Application of Numerical Simulation for Analysis of Sinking Characteristics of Purse Seine

This study applies the mass-spring system to model the dynamic behavior of a submerged net panel similar to the shooting process in actual purse seine fishing operation. Modeling indicates that there is insufficient stretching with the net panel under the floatline in the prophase of the shooting process. Sinkers at different locations along the leadline descend successively after submergence, and the sinking speed decreases gradually with elapsed time until attainment of a stable state. Designs with different current speeds and sinker weights are executed to determine the dimensional shape and sinking characteristics of the net. The net rigged with greater sinker weight gains significantly greater sinking depth without water flow. Compared with the vertical spread of the net wall in static water, the middle part of the netting presents a larger displacement along the direction of current under flow condition. It follows that considerable deformation of the netting occurs with higher current speed as the sinkers affected by hydrodynamic force drift in the direction of current. The numerical model is verified by a comparison between simulated results and sea measurements. The calculated values generally coincide with the observed ones, with the former being slightly higher than the latter. This study provides an implicit algorithm which saves computational loads for enormous systems such as purse seines, and ensures the accuracy and stability of numerical solutions in a repetitious iteration process.

The inner circulation mechanism in sinking column formation in North China coal field ——A case study in Fengfeng mining areas

Sinking columns are one of the most hazardous geological structures in north Chine typed coal fields. To understand the sinking column formation, to judge if the columns are hazardous or not, the inner circle mechanism of groundwater in forming sinking columns in the relatively isolated areas was proposed according to the investigation on formation or distribution of sinking columns in some north China typed coal fields, such as Fengfeng, Xiangtai, Huaibei, Yangquan and so on. The heat generated by magma energized groundwater circulation and developed limestone karst in the relatively isolated areas. The CaCO3 solution accelerated by geothermal abnormality, the effect of high content of CO2 on dissolution and saturation of CaCO3 were discussed. Compared the forming conditions of the sinking columns developed in other coal mining areas in north China coal field, the paper deduced that the above factors collude karst development and sinking column formation, the columns in current geothermal areas are permeable and those in high coal rank areas or in paleo abnormally geothermal areas. The paper suggested that the sinking columns in the current abnormally geothermal areas were permeable, but those in the areas with high coal rank were not on contract.

Influence of light availability on the specific density,size and sinking loss of Anabaena flos-aquae and Scenedesmus obliquus

Harmful algal blooms in eutrophic waters pose a serious threat to freshwater ecosystems and human health. In-situ light availability control is one of the most commonly used technologies to suppress algae in lakes and reservoirs. To develop a better understanding of the effects of light on algal growth, specific density, colony size and sinking loss, Anabaena flos-aquae(cyanobacteria) and Scenedesmus obliquus(green algae) were evaluated in varying light scenarios. The results showed that the specific density and colony size of these two species varied during growth, and there were obvious differences among the light scenarios. At the end of exponential phase, S. obliquus incubated under light-limited condition maintained a higher specific density and formed larger aggregates, whereas A. flos-aquae formed a longer filament length. Both species exhibited higher sinking loss rates with lower light availability. These results implied that the sinking loss rate was not always constant but should be considered as a variable response to the change of light availability, and in-situ light availability control might result in a significant increase of the sinking loss of algae due to the change of size and specific density, thereby further affecting the algal biomass in the water column.

Concentrations and sinking rates of transparent exopolymer particles(TEPs)in a coastal sea:the Changjiang River(Yangtze River)Estuary

Transparent exopolymer particles(TEPs)are ubiquitous throughout the oceans,and their sedimentation is considered an efficient biological carbon sink pathway.To investigate the role of coastal TEPs in sinking carbon from the upper layer,samples were collected in the spring and summer of 2011 in the Changjiang River(Yangtze River)Estuary,a typical coastal water.The concentrations and sinking rates of TEPs were measured,and potential sedimentation flux of TEPs was estimated.TEPs concentrations ranged from 40.00μg/L to 1040.00μg/L(mean=(209.70±240.93)μg/L)in spring and 56.67μg/L to 1423.33μg/L(mean=(433.33±393.02)μg/L)in summer,and they were higher at bloom stations than at non-bloom stations during both cruises.A significant positive correlation between TEPs concentration and chlorophyll a(Chl a)concentration was detected,suggesting that phytoplankton was the primary source of TEPs in this area.TEPs sinking rates ranged from 0.08 m/d to 0.57 m/d with a mean of(0.28±0.14)m/d in spring and 0.10 m/d to 1.08 m/d with a mean of(0.34±0.31)m/d in summer.The potential sedimentation flux of TEP-C ranged from 4.95 mg/(m2·d)to 29.40 mg/(m2·d)with a mean of(14.66±8.83)mg/(m2·d)in spring and 6.80 mg/(m2·d)to 30.45 mg/(m2·d)with a mean of(15.71±8.73)mg/(m2·d)in summer,which was^17.81%to 138.27%(mean=65.15%±31.75%)of sedimentation flux of phytoplankton cells in the study area.Due to the increase of TEPs concentrations and their sinking rates,sedimentation fluxes of TEPs at the bloom station were obviously higher than at the non-bloom station during both cruises.This study indicates that TEPs serve as a carbon sink in the Changjiang River Estuary,especially during bloom events,and their sedimentation should be taken into account when we study the carbon sedimentation in the coastal sea.

Coupled thermo-hydro-mechanical modeling of frost heave and water migration during artificial freezing of soils for mineshaft sinking

Artificial freezing of water-bearing soil layers composing a sedimentary deposit can induce frost heave and water migration that affect the natural stress-strain state of the soil layers and freezing process.In the present paper,a thermo-hydro-mechanical(THM)model for freezing of water-saturated soil is proposed to study the effects of frost heave and water migration in frozen soils on the formation of a frozen wall and subsequent excavation activity for sinking a vertical shaft.The governing equations of the model are formulated relative to porosity,temperature,and displacement which are considered as primary variables.The relationship between temperature,pore water,and ice pressure in frozen soil is established by the Clausius-Clapeyron equation,whereas the interaction between the stress-strain behavior and changes in porosity and pore pressure is described with the poromechanics theory.Moreover,constitutive relations for additional mechanical deformation are incorporated to describe volumetric expansion of soil during freezing as well as creep strain of soil in the frozen state.The ability of the proposed model to capture the frost heave of frozen soil is demonstrated by a comparison between numerical results and experimental data given by a one-sided freezing test.Also to validate the model in other freezing conditions,a radial freezing experiment is performed.After the validation procedure,the model is applied to numerical simulation of artificial freezing of silt and sand layers for shaft sinking at Petrikov potash mine in Belarus.Comparison of calculated temperature with thermal monitoring data during active freezing stage is presented.Numerical analysis of deformation of unsupported sidewall of a shaft inside the frozen wall is conducted to account for the change in natural stress-strain state of soil layers induced by artificial freezing.