As a rapid and effective ground improvement method is urgently required for the booming land reclamation in China's coastal area, this study proposes a new combined method of electroosmosis, vacuum preloading and sur...As a rapid and effective ground improvement method is urgently required for the booming land reclamation in China's coastal area, this study proposes a new combined method of electroosmosis, vacuum preloading and surcharge preloading. A new type of electrical prefabricated vertical drain (ePVD) and a new electroosmotic drainage system are suggested to allow the application of the new method. This combined method is then field-tested and compared with the conventional vacuum combined with surcharge preloading method. The monitoring and foundation test results show that the new method induces a settlement 20% larger than that of the conventional vacuum combined with surcharge preloading method in the same treatment period, and saves approximately half of the treatment time compared with the vacuum combined with surcharge preloading method according to the finite element prediction of the settlement. The proposed method also increases the vane shear strength of the soil significantly. The bearing capacity of the ground improved by use of the new proposed method raises 118%. In comparison, there is only a 75% rise when using the vacuum combined with surcharge preloading method during the same reinforcement period. All results indicate that the proposed combined method is effective and suitable for reinforcing the soft clay ground. Besides, the voltage applied between the anode and cathode increases exponentially versus treatment time when the output current of power supplies is kept constant. Most of the voltage potential in electroosmosis is lost at electrodes, leaving smaller than 50% of the voltage to be effectively transmitted into the soil.展开更多
Vacuum combined surcharge preloading is an effective method which has been used in ground treatment. This study presents the analytical solution of vertical drains with vacuum combined surcharge preloading. The surcha...Vacuum combined surcharge preloading is an effective method which has been used in ground treatment. This study presents the analytical solution of vertical drains with vacuum combined surcharge preloading. The surcharge was considered to be time-dependent preloading due to its reflection of the real situation.Moreover,the free strain,instead of equal strain hypothesis of the surface,was adopted for the mathematical rigor. Both vertical and horizontal drainages,along with the well resistance were considered.Besides,the time-dependent surcharge preloading was resolved with the impulse theorem which has been presented in the study,and the solutions for pore water pressure and degree of consolidation were derived by applying the approach of separation of variables.Furthermore,the solution is compared with previous solutions and numerical solutions,and the results verify the correctness of the proposed model.展开更多
Municipal sludge is a sedimentation waste produced during the wastewater process in sewage treatment plants.Among recent studies,pilot and field tests showed that chemical conditioning combined with vacuum preloading ...Municipal sludge is a sedimentation waste produced during the wastewater process in sewage treatment plants.Among recent studies,pilot and field tests showed that chemical conditioning combined with vacuum preloading can effectively treat municipal sludge.To further understand the drainage and consolidation characteristics of the conditioning sludge during vacuum preloading,a large deformation nonlinear numerical simulation model based on the equal strain condition was developed to simulate and analyze the pilot and field tests,whereas the simulation results were not satisfactory.The results of the numerical analysis of the pilot test showed that the predicted consolidation degree was greater than that measured by the field tests,which is attributed to the relatively low permeability layer formed during the preloading process of the prefabricated vertical drain.To better reflect the consolidation process of the conditioned sludge,a simplified analysis method considering the low permeability layer around the prefabricated vertical drain was proposed.The initial permeability coefficient of the low permeability layer is determined via numerical simulations using finite difference method.The predicted settlement curve was in good agreement with the measured results,which indicated that the numerical simulation based on the equal strain condition considering the relatively low permeability layer can better analyze the consolidation process of ferric chloride-conditioning sludge with vacuum preloading.展开更多
A new triaxial apparatus was designed and manufactured. It is able to applysurcharge and combined vacuum-surcharge pressures on soil samples, and allows for monitoring ofexcess pore-water pressure, axial strain or set...A new triaxial apparatus was designed and manufactured. It is able to applysurcharge and combined vacuum-surcharge pressures on soil samples, and allows for monitoring ofexcess pore-water pressure, axial strain or settlement, and volumetric strain during the process ofconsolidation. Tests were performed using the apparatus on undisturbed soft clayey soil samples,which were collected from Wenzhou, Zhejiang Province, China, at average natural water content 72. 5%. The consolidation behavior of theclay has no rigorous difference, whether it is consolidatedunder the vacuum, surcharge, or combined vacuum-surcharge preloading. The study shows that somephysical properties of the soft clayey soils are changed and mechanical properties are improved tosupport excessive loads transferred to the soil foundation due to construction.展开更多
Problems continue to be encountered concerning the traditional vacuum preloading method in field during the treatment of newly deposited dredger fills.In this paper,an improved multiple-vacuum preloading method was de...Problems continue to be encountered concerning the traditional vacuum preloading method in field during the treatment of newly deposited dredger fills.In this paper,an improved multiple-vacuum preloading method was developed to consolidate newly dredger fills that are hydraulically placed in seawater for land reclamation in Lingang Industrial Zone of Tianjin City,China.With this multiplevacuum preloading method,the newly deposited dredger fills could be treated effectively by adopting a novel moisture separator and a rapid improvement technique without sand cushion.A series of model tests was conducted in the laboratory for comparing the results from the multiple-vacuum preloading method and the traditional one.Ten piezometers and settlement plates were installed to measure the variations in excess pore water pressures and moisture content,and vane shear strength was measured at different positions.The testing results indicate that water dischargeetime curves obtained by the traditional vacuum preloading method can be divided into three phases:rapid growth phase,slow growth phase,and steady phase.According to the process of fluid flow concentrated along tiny ripples and building of larger channels inside soils during the whole vacuum loading process,the fluctuations of pore water pressure during each loading step are divided into three phases:steady phase,rapid dissipation phase,and slow dissipation phase.An optimal loading pattern which could have a best treatment effect was proposed for calculating the water discharge and pore water pressure of soil using the improved multiple-vacuum preloading method.For the newly deposited dredger fills at Lingang Industrial Zone of Tianjin City,the best loading step was 20 kPa and the loading of 40-50 k Pa produced the highest drainage consolidation.The measured moisture content and vane shear strength were discussed in terms of the effect of reinforcement,both of which indicate that the multiple-vacuum preloading method has a better treatment effect not only in decreasing the moisture content and increasing the bearing capacity,but also in increasing the process uniformity at different depths of foundation.展开更多
A laboratory test was performed to assess the effectiveness of vacuum preloading incorporated with electroosmotic (EOM) treatment on silty clay (combined method) for reclamation projects like new disposal ponds, where...A laboratory test was performed to assess the effectiveness of vacuum preloading incorporated with electroosmotic (EOM) treatment on silty clay (combined method) for reclamation projects like new disposal ponds, where the horizontal electrode configurations beneath the soil layer were possible and the drainage pipes and the prefabricated vertical drains (PVDs) system could be easily installed in advance before the sludge dragged from sea bed or river bed was filled into the site. Three groups of tests were conducted on the silty clay from Qinhuai River in Nanjing, China. The model is able to apply vacuum pressure at the bottom of the soil layer and a direct current electric field simultaneously. It is also possible to measure the pore pressures at different depths of soil column, and the changes in settlement and volume with the elapsed time. In this study, the vacuum preloading method, vacuum preloading applied at the bottom (VAB method), was applied and the cathodes were installed beneath the soil layer. The results obtained indicate substantial reduction in water content, and increases in dry density and undrained shear strength in comparison with those obtained by the vacuum preloading only, particularly at the positions close to the anode. The combined method utilizes the vertical drainage flow created by the electroosmosis integrating the horizontal drainage flow created mostly by the vacuum pressure. The total drainage flow can be calculated as a result of the vertical drainage flow by electroosmosis only and the horizontal drainage flow by the vacuum preloading only. The way of placement of the cathode and the anode in the combined method also overcomes the disadvantage of EOM method itself, i.e. the appearance of cracks between the anode and the surrounding soil. Moreover, it is observed that the vacuum preloading plays a primary role in earlier stage in deduction of free pore water; meanwhile, the electroosmotic method is more efficient in later stage for absorbing water in the diffused double layers of soil.展开更多
To assess the effectiveness of vacuum preloading combined electroosmotic strengthening of ultra-soft soil and study the mechanism of the process, a comprehensive experimental investigation was performed. A laboratory ...To assess the effectiveness of vacuum preloading combined electroosmotic strengthening of ultra-soft soil and study the mechanism of the process, a comprehensive experimental investigation was performed. A laboratory test cell was designed and applied to evaluate the vacuum preloading combined electroosmosis. Several factors were taken into consideration, including the directions of the electroosmotic current and water induced by vacuum preloading and the replenishment of groundwater from the surrounding area. The results indicate that electroosmosis together with vacuum preloading improve the soil strength greatly, with an increase of approximately 60%, and reduce the water content of the soil on the basis of consolidation of vacuum preloading, howeve~ further settlement is not obvious with only 1.7 mm. The reinforcement effect of vacuum preloading combined electroosmosis is better than that of electroosmosis after vacuum preloading. Elemental analysis using X-ray fluorescence proves that the soil strengthening during electroosmotic period in this work is mainly caused by electroosmosis-induced electrochemical reactions, the concentrations of Al2O3 in the VPCEO region increase by 2.2%, 1.5%, and 0.9% at the anode, the midpoint between the electrodes, and the cathode, respectively.展开更多
The rapid development of high-speed transportation infrastructure such as highway and high-speed railway has resulted in the advancement of soft soil improvement techniques. Vacuum preloading combined with vertical dr...The rapid development of high-speed transportation infrastructure such as highway and high-speed railway has resulted in the advancement of soft soil improvement techniques. Vacuum preloading combined with vertical drains has been proved to be an effective method in the treatment of soft foundation. A three-dimensional numerical analysis of the coupled methods was presented, in which the smear zone and the well resistance were taken into account. The variations of the basic soil parameters including the permeability coefficient and the coefficient of volume compressibility were considered in the numerical model. The result of the numerical model was then compared to the measured value. The results indicate that the decrease of coefficient of volume compressibility accelerates the consolidation of the soil while the influence of hydraulic conductivity is insignificant. A cube drain presents the closest result to the real situation compared to the other equivalent methods of prefabricated vertical drain (PVD). The case study indicates that the numerical model with variation of soil parameters is closer to the measured value than the numerical model without variation of soil parameters.展开更多
It is very important to control any risk of instability of embankment during vacuum construction, the simulation vacuum preloading method using tri-axial apparatus is proposed to predict the behavior of soft soil impr...It is very important to control any risk of instability of embankment during vacuum construction, the simulation vacuum preloading method using tri-axial apparatus is proposed to predict the behavior of soft soil improvement in the laboratory, as well as to make this method become familiar and easier in the future. The tri-axial apparatus is used instead of the large-scale one, which has been performed by Bergado (1998) and Indaratna (2008). The tri-axial test on small size specimen can be carried out in one week compared to the large-scale apparatus takes one month for big specimen. In addition, the lateral deformation as well as the shear strength increase with time can determine accurately.展开更多
Vacuum preloading has been widely used to improve soft soils in coastal areas of China.An increasing amount of evidence from field operations has shown that conventional vacuum preloading is prone to clogging in prefa...Vacuum preloading has been widely used to improve soft soils in coastal areas of China.An increasing amount of evidence from field operations has shown that conventional vacuum preloading is prone to clogging in prefabricated vertical drains(PVDs)and demands a large volume of sand fills.In recent years,air-boosted vacuum preloading has been developed to overcome these limitations;however,this method still requires more data to verify its performance.In this study,a field test for air-boosted vacuum preloading was conducted,and a large-strain two-dimensional(2D)finite element(FE)model was developed and validated against the field test data.Then,a series of FE parametric analyses was performed to assess key factors,i.e.the air injection pressure,the injection spacing,and the characteristics of cyclic injection,which affect the performance of the air-boosted vacuum preloading.The results showed that the ground settlement and lateral displacement of the soils increased due to an increase in the injection pressure,a decrease in the injection spacing,or increases in the number and duration of the injection cycles.Based on the parametric analyses,an empirical formula for ground settlement prediction was proposed and compared with a case history reported in the literature,showing good agreement.展开更多
Based on the characteristics and reinforcement mechanism of vacuum preloading applied in high way soft foundation, the theoretical calculation method of vacuum preloading was presented. According to the equivalent met...Based on the characteristics and reinforcement mechanism of vacuum preloading applied in high way soft foundation, the theoretical calculation method of vacuum preloading was presented. According to the equivalent method derived from sand drain foundation subjected to plane and axisymmetric conditions, the three dimensional problem was transformed into plane strain problem. The modified Komala-Huang model was used to model the rheological behavior and the damage theory was also introduced to consider the effect of damage caused by construction disturbance. Numerical simulations were carried out for a high way test section. The results show that simulations of the viscoelastic-plastic-damage model are in good agreement with the field measurements. It suggests that the calculation method, simplified load and boundary condition used in this study are reasonable.展开更多
基金financially supported by the National Natural Science Joint High Speed Railway Key Program Foundation of China(Grant No.U1134207)the Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT1125)the Key Science and Technology Program of the Science and Technology Department of Zhejiang Province(Grant No.2009C03001)
文摘As a rapid and effective ground improvement method is urgently required for the booming land reclamation in China's coastal area, this study proposes a new combined method of electroosmosis, vacuum preloading and surcharge preloading. A new type of electrical prefabricated vertical drain (ePVD) and a new electroosmotic drainage system are suggested to allow the application of the new method. This combined method is then field-tested and compared with the conventional vacuum combined with surcharge preloading method. The monitoring and foundation test results show that the new method induces a settlement 20% larger than that of the conventional vacuum combined with surcharge preloading method in the same treatment period, and saves approximately half of the treatment time compared with the vacuum combined with surcharge preloading method according to the finite element prediction of the settlement. The proposed method also increases the vane shear strength of the soil significantly. The bearing capacity of the ground improved by use of the new proposed method raises 118%. In comparison, there is only a 75% rise when using the vacuum combined with surcharge preloading method during the same reinforcement period. All results indicate that the proposed combined method is effective and suitable for reinforcing the soft clay ground. Besides, the voltage applied between the anode and cathode increases exponentially versus treatment time when the output current of power supplies is kept constant. Most of the voltage potential in electroosmosis is lost at electrodes, leaving smaller than 50% of the voltage to be effectively transmitted into the soil.
基金National Natural Science Foundation of China(No.51578214)
文摘Vacuum combined surcharge preloading is an effective method which has been used in ground treatment. This study presents the analytical solution of vertical drains with vacuum combined surcharge preloading. The surcharge was considered to be time-dependent preloading due to its reflection of the real situation.Moreover,the free strain,instead of equal strain hypothesis of the surface,was adopted for the mathematical rigor. Both vertical and horizontal drainages,along with the well resistance were considered.Besides,the time-dependent surcharge preloading was resolved with the impulse theorem which has been presented in the study,and the solutions for pore water pressure and degree of consolidation were derived by applying the approach of separation of variables.Furthermore,the solution is compared with previous solutions and numerical solutions,and the results verify the correctness of the proposed model.
基金acknowledge the financial support from The National Natural Science Foundation No.Gk321002Foundation of Nanjing Hydraulic Research Institute No.Y320012.
文摘Municipal sludge is a sedimentation waste produced during the wastewater process in sewage treatment plants.Among recent studies,pilot and field tests showed that chemical conditioning combined with vacuum preloading can effectively treat municipal sludge.To further understand the drainage and consolidation characteristics of the conditioning sludge during vacuum preloading,a large deformation nonlinear numerical simulation model based on the equal strain condition was developed to simulate and analyze the pilot and field tests,whereas the simulation results were not satisfactory.The results of the numerical analysis of the pilot test showed that the predicted consolidation degree was greater than that measured by the field tests,which is attributed to the relatively low permeability layer formed during the preloading process of the prefabricated vertical drain.To better reflect the consolidation process of the conditioned sludge,a simplified analysis method considering the low permeability layer around the prefabricated vertical drain was proposed.The initial permeability coefficient of the low permeability layer is determined via numerical simulations using finite difference method.The predicted settlement curve was in good agreement with the measured results,which indicated that the numerical simulation based on the equal strain condition considering the relatively low permeability layer can better analyze the consolidation process of ferric chloride-conditioning sludge with vacuum preloading.
文摘A new triaxial apparatus was designed and manufactured. It is able to applysurcharge and combined vacuum-surcharge pressures on soil samples, and allows for monitoring ofexcess pore-water pressure, axial strain or settlement, and volumetric strain during the process ofconsolidation. Tests were performed using the apparatus on undisturbed soft clayey soil samples,which were collected from Wenzhou, Zhejiang Province, China, at average natural water content 72. 5%. The consolidation behavior of theclay has no rigorous difference, whether it is consolidatedunder the vacuum, surcharge, or combined vacuum-surcharge preloading. The study shows that somephysical properties of the soft clayey soils are changed and mechanical properties are improved tosupport excessive loads transferred to the soil foundation due to construction.
基金the National Natural Science Foundation of China(NSFC)(Grant Nos.51378344 and 51578371)Tianjin Research Program of Application Foundation and Advanced Technology(Grant No.14JCYBJC21700)Beijing-Tianjin-Hebei Special Projects of Cooperation(Grant No.16JCJDJC40000) for their financial supports
文摘Problems continue to be encountered concerning the traditional vacuum preloading method in field during the treatment of newly deposited dredger fills.In this paper,an improved multiple-vacuum preloading method was developed to consolidate newly dredger fills that are hydraulically placed in seawater for land reclamation in Lingang Industrial Zone of Tianjin City,China.With this multiplevacuum preloading method,the newly deposited dredger fills could be treated effectively by adopting a novel moisture separator and a rapid improvement technique without sand cushion.A series of model tests was conducted in the laboratory for comparing the results from the multiple-vacuum preloading method and the traditional one.Ten piezometers and settlement plates were installed to measure the variations in excess pore water pressures and moisture content,and vane shear strength was measured at different positions.The testing results indicate that water dischargeetime curves obtained by the traditional vacuum preloading method can be divided into three phases:rapid growth phase,slow growth phase,and steady phase.According to the process of fluid flow concentrated along tiny ripples and building of larger channels inside soils during the whole vacuum loading process,the fluctuations of pore water pressure during each loading step are divided into three phases:steady phase,rapid dissipation phase,and slow dissipation phase.An optimal loading pattern which could have a best treatment effect was proposed for calculating the water discharge and pore water pressure of soil using the improved multiple-vacuum preloading method.For the newly deposited dredger fills at Lingang Industrial Zone of Tianjin City,the best loading step was 20 kPa and the loading of 40-50 k Pa produced the highest drainage consolidation.The measured moisture content and vane shear strength were discussed in terms of the effect of reinforcement,both of which indicate that the multiple-vacuum preloading method has a better treatment effect not only in decreasing the moisture content and increasing the bearing capacity,but also in increasing the process uniformity at different depths of foundation.
文摘A laboratory test was performed to assess the effectiveness of vacuum preloading incorporated with electroosmotic (EOM) treatment on silty clay (combined method) for reclamation projects like new disposal ponds, where the horizontal electrode configurations beneath the soil layer were possible and the drainage pipes and the prefabricated vertical drains (PVDs) system could be easily installed in advance before the sludge dragged from sea bed or river bed was filled into the site. Three groups of tests were conducted on the silty clay from Qinhuai River in Nanjing, China. The model is able to apply vacuum pressure at the bottom of the soil layer and a direct current electric field simultaneously. It is also possible to measure the pore pressures at different depths of soil column, and the changes in settlement and volume with the elapsed time. In this study, the vacuum preloading method, vacuum preloading applied at the bottom (VAB method), was applied and the cathodes were installed beneath the soil layer. The results obtained indicate substantial reduction in water content, and increases in dry density and undrained shear strength in comparison with those obtained by the vacuum preloading only, particularly at the positions close to the anode. The combined method utilizes the vertical drainage flow created by the electroosmosis integrating the horizontal drainage flow created mostly by the vacuum pressure. The total drainage flow can be calculated as a result of the vertical drainage flow by electroosmosis only and the horizontal drainage flow by the vacuum preloading only. The way of placement of the cathode and the anode in the combined method also overcomes the disadvantage of EOM method itself, i.e. the appearance of cracks between the anode and the surrounding soil. Moreover, it is observed that the vacuum preloading plays a primary role in earlier stage in deduction of free pore water; meanwhile, the electroosmotic method is more efficient in later stage for absorbing water in the diffused double layers of soil.
基金Project(2009B13014) supported by the Fundamental Research Funds for the Central Universities of ChinaProject(IRT1125) supported by the Program for Changjiang Scholars and Innovative Research Team in University,China
文摘To assess the effectiveness of vacuum preloading combined electroosmotic strengthening of ultra-soft soil and study the mechanism of the process, a comprehensive experimental investigation was performed. A laboratory test cell was designed and applied to evaluate the vacuum preloading combined electroosmosis. Several factors were taken into consideration, including the directions of the electroosmotic current and water induced by vacuum preloading and the replenishment of groundwater from the surrounding area. The results indicate that electroosmosis together with vacuum preloading improve the soil strength greatly, with an increase of approximately 60%, and reduce the water content of the soil on the basis of consolidation of vacuum preloading, howeve~ further settlement is not obvious with only 1.7 mm. The reinforcement effect of vacuum preloading combined electroosmosis is better than that of electroosmosis after vacuum preloading. Elemental analysis using X-ray fluorescence proves that the soil strengthening during electroosmotic period in this work is mainly caused by electroosmosis-induced electrochemical reactions, the concentrations of Al2O3 in the VPCEO region increase by 2.2%, 1.5%, and 0.9% at the anode, the midpoint between the electrodes, and the cathode, respectively.
基金Project(2010THZ021)supported by Tsinghua University,ChinaProject(50978139)supported by the National Natural Science Foundation of ChinaProject(2012CB719804)supported by the National Basic Research Program of China
文摘The rapid development of high-speed transportation infrastructure such as highway and high-speed railway has resulted in the advancement of soft soil improvement techniques. Vacuum preloading combined with vertical drains has been proved to be an effective method in the treatment of soft foundation. A three-dimensional numerical analysis of the coupled methods was presented, in which the smear zone and the well resistance were taken into account. The variations of the basic soil parameters including the permeability coefficient and the coefficient of volume compressibility were considered in the numerical model. The result of the numerical model was then compared to the measured value. The results indicate that the decrease of coefficient of volume compressibility accelerates the consolidation of the soil while the influence of hydraulic conductivity is insignificant. A cube drain presents the closest result to the real situation compared to the other equivalent methods of prefabricated vertical drain (PVD). The case study indicates that the numerical model with variation of soil parameters is closer to the measured value than the numerical model without variation of soil parameters.
文摘It is very important to control any risk of instability of embankment during vacuum construction, the simulation vacuum preloading method using tri-axial apparatus is proposed to predict the behavior of soft soil improvement in the laboratory, as well as to make this method become familiar and easier in the future. The tri-axial apparatus is used instead of the large-scale one, which has been performed by Bergado (1998) and Indaratna (2008). The tri-axial test on small size specimen can be carried out in one week compared to the large-scale apparatus takes one month for big specimen. In addition, the lateral deformation as well as the shear strength increase with time can determine accurately.
基金the National Key Research and Development Program of China(Grant No.2017YFC0805402)the Tianjin Construction Commission Science and Technology Project(financial support No.2017E6-0015)the China Scholarship Council(CSC)(Grant No.201906250153)for their Grant of the study in this paper。
文摘Vacuum preloading has been widely used to improve soft soils in coastal areas of China.An increasing amount of evidence from field operations has shown that conventional vacuum preloading is prone to clogging in prefabricated vertical drains(PVDs)and demands a large volume of sand fills.In recent years,air-boosted vacuum preloading has been developed to overcome these limitations;however,this method still requires more data to verify its performance.In this study,a field test for air-boosted vacuum preloading was conducted,and a large-strain two-dimensional(2D)finite element(FE)model was developed and validated against the field test data.Then,a series of FE parametric analyses was performed to assess key factors,i.e.the air injection pressure,the injection spacing,and the characteristics of cyclic injection,which affect the performance of the air-boosted vacuum preloading.The results showed that the ground settlement and lateral displacement of the soils increased due to an increase in the injection pressure,a decrease in the injection spacing,or increases in the number and duration of the injection cycles.Based on the parametric analyses,an empirical formula for ground settlement prediction was proposed and compared with a case history reported in the literature,showing good agreement.
文摘Based on the characteristics and reinforcement mechanism of vacuum preloading applied in high way soft foundation, the theoretical calculation method of vacuum preloading was presented. According to the equivalent method derived from sand drain foundation subjected to plane and axisymmetric conditions, the three dimensional problem was transformed into plane strain problem. The modified Komala-Huang model was used to model the rheological behavior and the damage theory was also introduced to consider the effect of damage caused by construction disturbance. Numerical simulations were carried out for a high way test section. The results show that simulations of the viscoelastic-plastic-damage model are in good agreement with the field measurements. It suggests that the calculation method, simplified load and boundary condition used in this study are reasonable.