工程科学学报，第40卷，第7期：783-792,2018年7月 Chinese Journal of Engineering,Vol.40,No.7:783-792,July 2018 DOI:10.13374/j.issn2095-9389.2018.07.003;http://journals.ustb.edu.cn 半透水边界砂井真空联合堆载预压Hansbo固结解 胡亚元区 浙江大学滨海和城市岩土工程研究中心，杭州310058 ☒通信作者，E-mail:huyayuan@(zju.cdu.cm 摘要把砂井地基上下边界视为半透水边界，以研究顶部垫层和底部下卧层透水特性对砂井地基固结过程的影响.根据轴 对称固结方程和等应变假定，利用Hansbo法获得了真空联合堆载预压下半透水边界砂井地基的固结解答，分析了上下边界透 水系数对真空和堆载预压固结度和沉降的影响，比较了真空单独预压下本文解与ndraratna等解答和周琦等解答的联系和差 别.研究表明，(1)不管真空预压还是堆载预压，固结时间因子相同时地基固结度随边界透水系数增大而增大.(2)对于真空 预压，下边界透水系数越大，地基的最终沉降越小，固结期间时间因子相同时的沉降也越小：上边界透水系数越大，固结期间 时间因子相同时的沉降越大.(3)对于堆载预压，不管上边界还是下边界，边界透水系数越大，最终沉降不变，而固结期间时间 因子相同时的沉降越大.(4)当真空预压上边界透水时，周琦等解答的固结度大于本文解答的固结度大于ndraratna等解答的 固结度.为了提高真空预压的最终沉降，需减少地基下边界的透水性 关键词砂井地基：半透水边界：真空联合堆载预压：固结度：沉降 分类号TU472.33 A Hansbo's consolidation solution of sand-drained ground with impeded boundaries under vacuum and surcharge preloading HU Ya-yuan Research Center of Coastal and Urban Geotechnical Engineering,Zhejiang University,Hangzhou 310058,China Corresponding author,E-mail:huyayuan@zju.cdu.cn ABSTRACT The top and bottom boundaries of sand-drained ground were visualized as impeded boundaries to investigate the effects of the pervious behaviors of the cushion above the top and the substratum below the bottom during the consolidation process of sand- drained ground.Based on the axisymmetric consolidation equations and the equal strain assumption,the consolidation solution of sand- drained ground with impeded boundaries was obtained using Hansbo's method for vacuum and surcharge preloading.The effects of the pervious coefficients of top and bottom boundaries on the consolidation degrees and settlements of vacuum preloading and surcharge pre- loading were analyzed.The similarities and differences between the solution and Indraratna et al.,'s solution and Zhou et al.,'s solu- tion were compared under vacuum preloading alone.The results reveal the following:(1)for either vacuum or surcharge preloading, the consolidation degree of the ground increases with the increasing pervious coefficients of the boundaries when the consolidation time factor is the same;(2)for vacuum preloading,the larger the pervious coefficient of the bottom boundary is,the smaller the final settle- ment of the ground is,and the smaller is the settlement at the same time factor during the consolidation process;the larger the pervious coefficient of the top boundary is,the greater is the settlement at the same time factor during the consolidation process;(3)for sur- charge preloading,the larger the pervious coefficient of the bottom or top boundary is,the larger is the settlement at the same time fac- tor during the consolidation process while the final settlement remains constant;(4)when the top boundary is permeable during vacu- um preloading,the consolidation degree of Zhou et al's solution is higher than the consolidation degree of the proposed solution,and 收稿日期：2017-08-14 基金项目：国家自然科学基金资助项目(51178419)工程科学学报,第 40 卷,第 7 期:783鄄鄄792,2018 年 7 月 Chinese Journal of Engineering, Vol. 40, No. 7: 783鄄鄄792, July 2018 DOI: 10. 13374 / j. issn2095鄄鄄9389. 2018. 07. 003; http: / / journals. ustb. edu. cn 半透水边界砂井真空联合堆载预压 Hansbo 固结解 胡亚元苣 浙江大学滨海和城市岩土工程研究中心, 杭州 310058 苣通信作者, E鄄mail: huyayuan@ zju. edu. cn 摘 要 把砂井地基上下边界视为半透水边界,以研究顶部垫层和底部下卧层透水特性对砂井地基固结过程的影响. 根据轴 对称固结方程和等应变假定,利用 Hansbo 法获得了真空联合堆载预压下半透水边界砂井地基的固结解答,分析了上下边界透 水系数对真空和堆载预压固结度和沉降的影响,比较了真空单独预压下本文解与 Indraratna 等解答和周琦等解答的联系和差 别. 研究表明,(1)不管真空预压还是堆载预压,固结时间因子相同时地基固结度随边界透水系数增大而增大. (2)对于真空 预压,下边界透水系数越大,地基的最终沉降越小,固结期间时间因子相同时的沉降也越小;上边界透水系数越大,固结期间 时间因子相同时的沉降越大. (3)对于堆载预压,不管上边界还是下边界,边界透水系数越大,最终沉降不变,而固结期间时间 因子相同时的沉降越大. (4)当真空预压上边界透水时,周琦等解答的固结度大于本文解答的固结度大于 Indraratna 等解答的 固结度. 为了提高真空预压的最终沉降,需减少地基下边界的透水性. 关键词 砂井地基; 半透水边界; 真空联合堆载预压; 固结度; 沉降 分类号 TU472郾 33 收稿日期: 2017鄄鄄08鄄鄄14 基金项目: 国家自然科学基金资助项目(51178419) A Hansbo爷 s consolidation solution of sand鄄drained ground with impeded boundaries under vacuum and surcharge preloading HU Ya鄄yuan 苣 Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou 310058, China 苣Corresponding author, E鄄mail: huyayuan@ zju. edu. cn ABSTRACT The top and bottom boundaries of sand鄄drained ground were visualized as impeded boundaries to investigate the effects of the pervious behaviors of the cushion above the top and the substratum below the bottom during the consolidation process of sand鄄 drained ground. Based on the axisymmetric consolidation equations and the equal strain assumption, the consolidation solution of sand鄄 drained ground with impeded boundaries was obtained using Hansbo爷s method for vacuum and surcharge preloading. The effects of the pervious coefficients of top and bottom boundaries on the consolidation degrees and settlements of vacuum preloading and surcharge pre鄄 loading were analyzed. The similarities and differences between the solution and Indraratna et al. ,爷s solution and Zhou et al. ,爷s solu鄄 tion were compared under vacuum preloading alone. The results reveal the following: (1) for either vacuum or surcharge preloading, the consolidation degree of the ground increases with the increasing pervious coefficients of the boundaries when the consolidation time factor is the same; (2) for vacuum preloading, the larger the pervious coefficient of the bottom boundary is, the smaller the final settle鄄 ment of the ground is, and the smaller is the settlement at the same time factor during the consolidation process; the larger the pervious coefficient of the top boundary is, the greater is the settlement at the same time factor during the consolidation process; (3) for sur鄄 charge preloading, the larger the pervious coefficient of the bottom or top boundary is, the larger is the settlement at the same time fac鄄 tor during the consolidation process while the final settlement remains constant; (4) when the top boundary is permeable during vacu鄄 um preloading, the consolidation degree of Zhou et al 爷s solution is higher than the consolidation degree of the proposed solution, and