To evaluate the columnar jointed basalts in the dam site of Baihetan hydropower station in southwest China, we developed a basic conceptual model of single jointed rock mass. Considering that the rock mass deformation...To evaluate the columnar jointed basalts in the dam site of Baihetan hydropower station in southwest China, we developed a basic conceptual model of single jointed rock mass. Considering that the rock mass deformation consists of rock block deformation and joints deformation, the linear mechanical characteristics of the cell (including the elastic joints and the nonlinear mechanical behaviors of the cell) with a combined frictional-elastic interface were analyzed. We developed formulas to calculate the rock block deformation, which can be adapted for multiple jointed rock mass and columnar jointed basalts. The formulas are effective in calculating the equivalent modulus of multiple jointed rock mass, and precisely reveal the anisotropic properties of columnar jointed basalts. Furthermore, the in situ rigid bearing plate tests were analyzed and calculated, and the types of loading-unloading curves and the equivalent modulus along different directions of columnar jointed basalts were obtained. The analytical results are in close compliance with the test results.展开更多
The unified hardening(UH)model proposed by Yao et al.(Geotechnique 2009)is the constitutive model which can consider the influence of the complex stress path and stress history on the deformation and strength of clays...The unified hardening(UH)model proposed by Yao et al.(Geotechnique 2009)is the constitutive model which can consider the influence of the complex stress path and stress history on the deformation and strength of clays reasonably.Firstly,the loading-unloading criterion of material model is defined as the change law of the intersection of current yield surface and the p axis,which makes the loading-unloading in the process of hardening and softening can be unified considered in UH model.Then,the Newton-Raphson method is adopted to attain the nonlinear problems solution in the finite element method of UH model,and the semi-implicit return mapping method is adopted to update stress.The application of the UH model in the finite element is realized.And then,the analyses of triaxial test are performed using the unit prediction and finite element method.The results of the unit prediction method are compared with the experimental results to illustrate the rationality of the UH model.Comparing the results with the unit prediction method and the finite element method,the correctness of the finite element program of the UH model is iUusttated.Further,Ae three-dimensional firdte element andysis of embankment on soft soil is performed by the program.The comparison between the results calculated by the UH model and the modified Cam-clay(MCC)model and the experimental data shows that the UH model is rational in analyzing the actual embankment engineering on soft soil.展开更多
In the process of engineering construction such as tunnels and slopes,rock mass is frequently subjected to multiple levels of loading and unloading,while previous research ignores the impact of unloading rate on the s...In the process of engineering construction such as tunnels and slopes,rock mass is frequently subjected to multiple levels of loading and unloading,while previous research ignores the impact of unloading rate on the stability of rock mass.A number of uniaxial multi-level cyclic loading-unloading experiments were conducted to better understand the effect of unloading rate on the deformation behavior,energy evolution,and damage properties of rock-like material.The experimental results demonstrated that the unloading rate and relative cyclic number clearly influence the deformation behavior and energy evo-lution of rock-like samples.In particular,as the relative cyclic number rises,the total strain and reversible strain both increase linearly,while the total energy density,elastic energy density,and dissipated energy density all rise nonlinearly.In contrast,the irreversible strain first decreases quickly,then stabilizes,and finally rises slowly.As the unloading rate increases,the total strain and reversible strain both increase,while the irreversible strain decreases.The dissipated energy damage was examined in light of the aforementioned experimental findings.The accuracy of the proposed damage model,which takes into account the impact of the unloading rate and relative cyclic number,is then confirmed by examining the consistency between the model predicted and the experimental results.The proposed damage model will make it easier to foresee how the multi-level loading-unloading cycles will affect the rock-like materials.展开更多
Using in-situ measurements from the Cassini spacecraft in 2013, we report an Earth substorm-like loading-unloading process at Saturn's distant magnetotail. We found that the loading process is featured with two di...Using in-situ measurements from the Cassini spacecraft in 2013, we report an Earth substorm-like loading-unloading process at Saturn's distant magnetotail. We found that the loading process is featured with two distinct processes: a rapid loading process that was likely driven by an internal source and a slow loading process that was likely driven by solar wind. Each of the two loading processes could also individually lead to an unloading process. The rapid internal loading process lasts for ~ 1-2 hours; the solar wind driven loading process lasts for ~ 3-18 hours and the following unloading process lasts for ~1-3 hours. In this letter, we suggest three possible loadingunloading circulations, which are fundamental in understanding the role of solar wind in driving giant planetary magnetospheric dynamics.展开更多
Compressive and sealing characteristics of PTFE under cyclic loading-unloading at room temperature are studied in order to evaluate the cyclic sealing performance of control valve comprehensively. The unloading charac...Compressive and sealing characteristics of PTFE under cyclic loading-unloading at room temperature are studied in order to evaluate the cyclic sealing performance of control valve comprehensively. The unloading characteristics are different from the loading ones, therefore there is hysteresis between the unloading and loading curves. Compressive hysteresis is the main factor that causes sealing hysteresis. The leakage rate of PTFE complies with the power law before it enters the relatively stable region. Lastly, the effect of working pressure on the compressive and sealing characteristics is discussed. The experimental results show that the working pressure has little effect on compressive deformation but has a great influence on leakage rate.展开更多
To investigate the effects of water and cyclic loading on dolomite’s mechanical properties during deep mining,mechanical experiments on non-pressure water absorption and cyclic loading were conducted.The findings rev...To investigate the effects of water and cyclic loading on dolomite’s mechanical properties during deep mining,mechanical experiments on non-pressure water absorption and cyclic loading were conducted.The findings reveal that the elastic modulus and Poisson ratio of dolomite fluctuate with increasing water content.The mass of water absorption is positively correlated with time and the water absorption stage can be divided into three stages:accelerated,decelerated,and stabilized stages.During this process,the number of pores in dolomite increases,while the pore diameter initially decreases and then fluctuates.Microscopic analysis shows that the proportion of mesopores first increases and then decreases,while micropores exhibit the opposite trend,and the proportion of macropores fluctuates around 0%.A model diagram of structural evolution during water absorption has been developed.Additionally,the softening process of dolomite’s water absorption strength is categorized into three stages:a relatively stable stage,an accelerated softening stage dominated by mesopore water absorption,and a decelerated softening stage characterized by micropore water absorption.A uniaxial damage constitutive model for dolomite under water influence was established based on the Weibull distribution and Mohr-Coulomb strength criterion,and experimental validation indicates its strong applicability.展开更多
The peak elastic strain energy consumption ratio(PEECR)is a rock brittleness index proposed by Gong and Wang.In the present study,based on the linear energy storage law of rock under triaxial compression,a new method ...The peak elastic strain energy consumption ratio(PEECR)is a rock brittleness index proposed by Gong and Wang.In the present study,based on the linear energy storage law of rock under triaxial compression,a new method was proposed to calculate the PEECR.The PEECR uses a simplified method to calculate the peak elastic strain energy.To solve this problem accurately,triaxial cyclic loading-unloading compression tests were carried out on shale.Strain energy parameters were calculated from the test curves.The results show that there is a linear relationship between the elastic strain energy and input strain energy,indicating that the linear energy storage law in rock is applicable to triaxial compression state.The universality of the linear energy storage law of rock under triaxial compression is also verified by the data in the published literature.Then,the peak elastic strain energy can be accurately determined using the linear energy storage law,and the PEECR is improved based on this.Finally,the PEECR and the improved PEECR were compared using the triaxial cyclic loading-unloading compression tests on three rocks(shale,red sandstone and granite),and the improved PEECR was compared with 11 existing energy-based brittleness indexes.The results show that the improved PEECR can further reflect the rock brittleness more accurately.展开更多
To study the energy storage and dissipation characteristics of deep rock under two-dimensional compression with constant confining pressure,the single cyclic loading-unloading two-dimensional compression tests were pe...To study the energy storage and dissipation characteristics of deep rock under two-dimensional compression with constant confining pressure,the single cyclic loading-unloading two-dimensional compression tests were performed on granite specimens with two height-to-width(H/W)ratios under five confining pressures.Three energy density parameters(input energy density,elastic energy density and dissipated energy density)in the axial and lateral directions of granite specimens under different confining pressures were calculated using the area integral method.The experimental results show that,for the specimens with a specific H/W ratio,these three energy density parameters in the axial and lateral directions increase nonlinearly with the confining pressure as quadratic polynomial functions.Under constant confining pressure compression,the linear energy storage law of granite specimens in the axial and lateral directions was founded.Using the linear energy storage law in different directions,the elastic energy density in various directions(axial elastic energy density,lateral elastic energy density and total elastic energy density)of granite under any specific confining pressures can be calculated.When the H/W ratio varies from 1:1 to 2:1,the lateral compression energy storage coefficient increases and the corresponding axial compression energy storage coefficient decreases,while the total compression energy storage coefficient is almost independent of the H/W ratio.展开更多
In this work, three-dimensional molecular dynamics simulation is carried out to elucidate the nanoindentation behaviour of single crystal Ni. The substrate indenter system is modelled using hybrid interatomic potentia...In this work, three-dimensional molecular dynamics simulation is carried out to elucidate the nanoindentation behaviour of single crystal Ni. The substrate indenter system is modelled using hybrid interatomic potentials including the manybody potential （embedded atom method） and two-body Morse potential. The spherical indenter is chosen, and the simulation is performed for different loading rates from 10 m/s to 200 m/s. Results show that the maximum indentation load and hardness of the system increase with the increase of velocity. The effect of indenter size on the nanoindentation response is also analysed. It is found that the maximum indentation load is higher for the large indenter whereas the hardness is higher for the smaller indenter. Dynamic nanoindentation is carried out to investigate the behaviour of Ni substrate to multiple loading-unloading cycles. It is observed from the results that the increase in the number of loading unloading cycles reduces the maximum load and hardness of the Ni substrate. This is attributed to the decrease in recovery force due to defects and dislocations produced after each indentation cycle.展开更多
To investigate the static compressive properties and mechanical damage evolution of rubber cement-based materials(RCBMs) with dry-and wet-curing conditions, uniaxial compression and cyclic loading-unloading tests were...To investigate the static compressive properties and mechanical damage evolution of rubber cement-based materials(RCBMs) with dry-and wet-curing conditions, uniaxial compression and cyclic loading-unloading tests were carried out on rubber cement mortar(RCM). The mechanical properties of the uniaxial compression specimens cured at 95%(wet-curing) and 50%(dry-curing) relative humidities and cyclic loading-unloading specimens cured at wet-curing were analyzed. Under uniaxial compression, the peak stress loss ratio is higher for dry-curing than for wet-curing. The peak strain decreases with the increase of rubber content, and the peak strain increases with the decrease of curing humidity. Under cyclic loading-unloading, the variation trends of residual strain differences of the normal cement mortar and RCM at each cyclic level with the number of cycles are basically the same, but the failure modes are different. The analysis of the internal mesostructure by a scanning electron microscope(SEM) shows that initial damage is further enhanced by reducing curing humidity and adding rubber aggregate. The damage constitutive model based on strain equivalence principle and statistical theories was used to describe the uniaxial compression characteristics of RCM, and the law of mechanical damage evolution was predicted.展开更多
The pore structure of caprock plays an important role in underground gas storage security, as it significantly influences the sealing capacity of caprock. However, the pore structure evolution of caprock with the cycl...The pore structure of caprock plays an important role in underground gas storage security, as it significantly influences the sealing capacity of caprock. However, the pore structure evolution of caprock with the cyclic stress perturbations triggered by the cyclic gas injection or extraction remains unclear. In this study, the pore structure changes of mudstone caprock under cyclic loading and unloading were obtained by the nuclear magnetic resonance (NMR) tests system, then the influence of the changes on the breakthrough pressure of caprock was discussed. The results indicated that the pore structure changes are depending on the stress loading-unloading path and stress level. In the first cyclic, at the loading stage, with the increase of confining stress, the NMR T2 spectrum curve moved to the left, the NMR signal amplitude of the first peak increased, while the amplitude of the second peak decreased gradually. This indicated that the larger pores of mudstone are compressed and transformed into smaller pores, then the number of macropores decreased and the number of micro- and mesopores increased. For a certain loading-unloading cycle, the porosity curve of mudstone in the loading process is not coincide with that in the unloading process, the porosity curve in the loading process was located below that in the unloading process, which indicated that the pore structure change is stress path dependent. With the increase of cycle numbers, the total porosity shown an increasing trend, indicating that the damage of mudstone occurred under the cyclic stress load-unload effects. With the increase of porosity, the breakthrough pressure of mudstone decreased with the increase of the cyclic numbers, which may increase the gas leakage risk. The results can provide significant implication for the underground gas storage security evaluation.展开更多
基金Project (Nos. 50911130366 and 2011CB013504) supported by the National Natural Science Foundation of Chinathe Postdoctoral Advanced Research Programs Class Ⅱ of Zhejiang Province (No. BSH1302013), China
文摘To evaluate the columnar jointed basalts in the dam site of Baihetan hydropower station in southwest China, we developed a basic conceptual model of single jointed rock mass. Considering that the rock mass deformation consists of rock block deformation and joints deformation, the linear mechanical characteristics of the cell (including the elastic joints and the nonlinear mechanical behaviors of the cell) with a combined frictional-elastic interface were analyzed. We developed formulas to calculate the rock block deformation, which can be adapted for multiple jointed rock mass and columnar jointed basalts. The formulas are effective in calculating the equivalent modulus of multiple jointed rock mass, and precisely reveal the anisotropic properties of columnar jointed basalts. Furthermore, the in situ rigid bearing plate tests were analyzed and calculated, and the types of loading-unloading curves and the equivalent modulus along different directions of columnar jointed basalts were obtained. The analytical results are in close compliance with the test results.
基金supported by the National Natural Science Foundation of China(Grants 11672015,51808547,and 51808548)the Central University Basic Scientific Research Business Expenses Funded Project(Grant 3122014C014)+1 种基金the Civil Aviation University Airport Engineering Base Open Fund(Grant JCGC2019KFJJ003)Tianjin Municipal Education Commission Scientific Research Project(Grant 2019KJ124)。
文摘The unified hardening(UH)model proposed by Yao et al.(Geotechnique 2009)is the constitutive model which can consider the influence of the complex stress path and stress history on the deformation and strength of clays reasonably.Firstly,the loading-unloading criterion of material model is defined as the change law of the intersection of current yield surface and the p axis,which makes the loading-unloading in the process of hardening and softening can be unified considered in UH model.Then,the Newton-Raphson method is adopted to attain the nonlinear problems solution in the finite element method of UH model,and the semi-implicit return mapping method is adopted to update stress.The application of the UH model in the finite element is realized.And then,the analyses of triaxial test are performed using the unit prediction and finite element method.The results of the unit prediction method are compared with the experimental results to illustrate the rationality of the UH model.Comparing the results with the unit prediction method and the finite element method,the correctness of the finite element program of the UH model is iUusttated.Further,Ae three-dimensional firdte element andysis of embankment on soft soil is performed by the program.The comparison between the results calculated by the UH model and the modified Cam-clay(MCC)model and the experimental data shows that the UH model is rational in analyzing the actual embankment engineering on soft soil.
基金the Water Conservancy Science and Technology Major Project of Hunan Province,China(Project XSKJ2019081-10)the China Scholarship Council(Grant No.202006370344)the First-class Project Special Funding of Yellow River Laboratory,China(Grant No.YRL22YL07).
文摘In the process of engineering construction such as tunnels and slopes,rock mass is frequently subjected to multiple levels of loading and unloading,while previous research ignores the impact of unloading rate on the stability of rock mass.A number of uniaxial multi-level cyclic loading-unloading experiments were conducted to better understand the effect of unloading rate on the deformation behavior,energy evolution,and damage properties of rock-like material.The experimental results demonstrated that the unloading rate and relative cyclic number clearly influence the deformation behavior and energy evo-lution of rock-like samples.In particular,as the relative cyclic number rises,the total strain and reversible strain both increase linearly,while the total energy density,elastic energy density,and dissipated energy density all rise nonlinearly.In contrast,the irreversible strain first decreases quickly,then stabilizes,and finally rises slowly.As the unloading rate increases,the total strain and reversible strain both increase,while the irreversible strain decreases.The dissipated energy damage was examined in light of the aforementioned experimental findings.The accuracy of the proposed damage model,which takes into account the impact of the unloading rate and relative cyclic number,is then confirmed by examining the consistency between the model predicted and the experimental results.The proposed damage model will make it easier to foresee how the multi-level loading-unloading cycles will affect the rock-like materials.
基金supported by the National Science Foundation of China (41525016,41404117)
文摘Using in-situ measurements from the Cassini spacecraft in 2013, we report an Earth substorm-like loading-unloading process at Saturn's distant magnetotail. We found that the loading process is featured with two distinct processes: a rapid loading process that was likely driven by an internal source and a slow loading process that was likely driven by solar wind. Each of the two loading processes could also individually lead to an unloading process. The rapid internal loading process lasts for ~ 1-2 hours; the solar wind driven loading process lasts for ~ 3-18 hours and the following unloading process lasts for ~1-3 hours. In this letter, we suggest three possible loadingunloading circulations, which are fundamental in understanding the role of solar wind in driving giant planetary magnetospheric dynamics.
基金Funded by the Fund of the State Key Laboratory of Technologies in Space Cryogenic Propellants(No.SKLTSCP1210)
文摘Compressive and sealing characteristics of PTFE under cyclic loading-unloading at room temperature are studied in order to evaluate the cyclic sealing performance of control valve comprehensively. The unloading characteristics are different from the loading ones, therefore there is hysteresis between the unloading and loading curves. Compressive hysteresis is the main factor that causes sealing hysteresis. The leakage rate of PTFE complies with the power law before it enters the relatively stable region. Lastly, the effect of working pressure on the compressive and sealing characteristics is discussed. The experimental results show that the working pressure has little effect on compressive deformation but has a great influence on leakage rate.
基金Project(IMRI23005)supported by Ordos Science and Technology Bureau,ChinaProjects(52174096,52304110)supported by the National Natural Science Foundation of China。
文摘To investigate the effects of water and cyclic loading on dolomite’s mechanical properties during deep mining,mechanical experiments on non-pressure water absorption and cyclic loading were conducted.The findings reveal that the elastic modulus and Poisson ratio of dolomite fluctuate with increasing water content.The mass of water absorption is positively correlated with time and the water absorption stage can be divided into three stages:accelerated,decelerated,and stabilized stages.During this process,the number of pores in dolomite increases,while the pore diameter initially decreases and then fluctuates.Microscopic analysis shows that the proportion of mesopores first increases and then decreases,while micropores exhibit the opposite trend,and the proportion of macropores fluctuates around 0%.A model diagram of structural evolution during water absorption has been developed.Additionally,the softening process of dolomite’s water absorption strength is categorized into three stages:a relatively stable stage,an accelerated softening stage dominated by mesopore water absorption,and a decelerated softening stage characterized by micropore water absorption.A uniaxial damage constitutive model for dolomite under water influence was established based on the Weibull distribution and Mohr-Coulomb strength criterion,and experimental validation indicates its strong applicability.
基金supported by the National Natural Science Foundation of China(Grant No.42077244).
文摘The peak elastic strain energy consumption ratio(PEECR)is a rock brittleness index proposed by Gong and Wang.In the present study,based on the linear energy storage law of rock under triaxial compression,a new method was proposed to calculate the PEECR.The PEECR uses a simplified method to calculate the peak elastic strain energy.To solve this problem accurately,triaxial cyclic loading-unloading compression tests were carried out on shale.Strain energy parameters were calculated from the test curves.The results show that there is a linear relationship between the elastic strain energy and input strain energy,indicating that the linear energy storage law in rock is applicable to triaxial compression state.The universality of the linear energy storage law of rock under triaxial compression is also verified by the data in the published literature.Then,the peak elastic strain energy can be accurately determined using the linear energy storage law,and the PEECR is improved based on this.Finally,the PEECR and the improved PEECR were compared using the triaxial cyclic loading-unloading compression tests on three rocks(shale,red sandstone and granite),and the improved PEECR was compared with 11 existing energy-based brittleness indexes.The results show that the improved PEECR can further reflect the rock brittleness more accurately.
基金Projects(41877272,51974359)supported by the National Natural Science Foundation of China。
文摘To study the energy storage and dissipation characteristics of deep rock under two-dimensional compression with constant confining pressure,the single cyclic loading-unloading two-dimensional compression tests were performed on granite specimens with two height-to-width(H/W)ratios under five confining pressures.Three energy density parameters(input energy density,elastic energy density and dissipated energy density)in the axial and lateral directions of granite specimens under different confining pressures were calculated using the area integral method.The experimental results show that,for the specimens with a specific H/W ratio,these three energy density parameters in the axial and lateral directions increase nonlinearly with the confining pressure as quadratic polynomial functions.Under constant confining pressure compression,the linear energy storage law of granite specimens in the axial and lateral directions was founded.Using the linear energy storage law in different directions,the elastic energy density in various directions(axial elastic energy density,lateral elastic energy density and total elastic energy density)of granite under any specific confining pressures can be calculated.When the H/W ratio varies from 1:1 to 2:1,the lateral compression energy storage coefficient increases and the corresponding axial compression energy storage coefficient decreases,while the total compression energy storage coefficient is almost independent of the H/W ratio.
文摘In this work, three-dimensional molecular dynamics simulation is carried out to elucidate the nanoindentation behaviour of single crystal Ni. The substrate indenter system is modelled using hybrid interatomic potentials including the manybody potential （embedded atom method） and two-body Morse potential. The spherical indenter is chosen, and the simulation is performed for different loading rates from 10 m/s to 200 m/s. Results show that the maximum indentation load and hardness of the system increase with the increase of velocity. The effect of indenter size on the nanoindentation response is also analysed. It is found that the maximum indentation load is higher for the large indenter whereas the hardness is higher for the smaller indenter. Dynamic nanoindentation is carried out to investigate the behaviour of Ni substrate to multiple loading-unloading cycles. It is observed from the results that the increase in the number of loading unloading cycles reduces the maximum load and hardness of the Ni substrate. This is attributed to the decrease in recovery force due to defects and dislocations produced after each indentation cycle.
基金Projects(52008003,52074009)supported by the National Natural Science Foundation of ChinaProject(201904a07020081)supported by the Key Research and Development Program Project of Anhui Province,ChinaProject(1908085QE213)supported by the Nature Science Foundation of Anhui Province,China。
文摘To investigate the static compressive properties and mechanical damage evolution of rubber cement-based materials(RCBMs) with dry-and wet-curing conditions, uniaxial compression and cyclic loading-unloading tests were carried out on rubber cement mortar(RCM). The mechanical properties of the uniaxial compression specimens cured at 95%(wet-curing) and 50%(dry-curing) relative humidities and cyclic loading-unloading specimens cured at wet-curing were analyzed. Under uniaxial compression, the peak stress loss ratio is higher for dry-curing than for wet-curing. The peak strain decreases with the increase of rubber content, and the peak strain increases with the decrease of curing humidity. Under cyclic loading-unloading, the variation trends of residual strain differences of the normal cement mortar and RCM at each cyclic level with the number of cycles are basically the same, but the failure modes are different. The analysis of the internal mesostructure by a scanning electron microscope(SEM) shows that initial damage is further enhanced by reducing curing humidity and adding rubber aggregate. The damage constitutive model based on strain equivalence principle and statistical theories was used to describe the uniaxial compression characteristics of RCM, and the law of mechanical damage evolution was predicted.
基金the National Natural Science Foundation of China(Grant No.52174107)the Basic Research and Frontier Exploration Projects in Chongqing(No.cstc2021 yszx-jcyjX0010).
文摘The pore structure of caprock plays an important role in underground gas storage security, as it significantly influences the sealing capacity of caprock. However, the pore structure evolution of caprock with the cyclic stress perturbations triggered by the cyclic gas injection or extraction remains unclear. In this study, the pore structure changes of mudstone caprock under cyclic loading and unloading were obtained by the nuclear magnetic resonance (NMR) tests system, then the influence of the changes on the breakthrough pressure of caprock was discussed. The results indicated that the pore structure changes are depending on the stress loading-unloading path and stress level. In the first cyclic, at the loading stage, with the increase of confining stress, the NMR T2 spectrum curve moved to the left, the NMR signal amplitude of the first peak increased, while the amplitude of the second peak decreased gradually. This indicated that the larger pores of mudstone are compressed and transformed into smaller pores, then the number of macropores decreased and the number of micro- and mesopores increased. For a certain loading-unloading cycle, the porosity curve of mudstone in the loading process is not coincide with that in the unloading process, the porosity curve in the loading process was located below that in the unloading process, which indicated that the pore structure change is stress path dependent. With the increase of cycle numbers, the total porosity shown an increasing trend, indicating that the damage of mudstone occurred under the cyclic stress load-unload effects. With the increase of porosity, the breakthrough pressure of mudstone decreased with the increase of the cyclic numbers, which may increase the gas leakage risk. The results can provide significant implication for the underground gas storage security evaluation.
