Analytical solutions for consolidation of soft soil improved by air-boosted vacuum preloading considering the varied well resistance of PVDs
LU Mengmeng1，2，SUN Jinxin1，2，LI Chuanxun3，GAO Lang4
(1. School of Mechanics and Civil Engineering，China University of Mining and Technology，Xuzhou，Jiangsu 221116，China；2. State Key Laboratory of Geomechanics and Deep Underground Engineering，China University of Mining and Technology，Xuzhou，Jiangsu 221116，China；3. Faculty of Civil Engineering and Mechanics，Jiangsu University，Zhenjiang，Jiangsu 212013，China；4. 9M Architectural Design Co.，Ltd.，Hangzhou，Zhejiang 310012，China)
Abstract：Air-boosted vacuum preloading(AVP) is a newly emerging soft soil improving technology. The studies on the analytical theories of the consolidation with AVP are at the starting stage for few related reports in the literature. To fill this gap，an analytical model for the consolidation of soft ground improved by AVP is proposed based on the assumptions of equal volumetric strain and Darcy?s law. Firstly，the varied well resistance effect of the prefabricated vertical drains(PVDs) is considered based on an assumption that its permeability coefficient decays exponentially with elapsed time and linearly with depth simultaneously. In addition，the smear effect of PVDs and the coupled radial-vertical seepage within soil are also considered to obtain analytical solutions. Then，the reasonability of the present analytical model is verified by degeneration and comparing it to the existing solution and applying it to analyze two field tests. Finally，the present solution with instantaneously loading is adopted to investigate the influence of several parameters on the consolidation behavior. The results show that the AVP can accelerate the consolidation rate more effectively，comparing to the conventional vacuum consolidation technique. The consolidation process of the ground will be retarded with consideration of the clogging effect of PVDs. Moreover，the time well resistance factor ?b has a great influence on the consolidation rate in the later stage. The following factors will lead to a faster consolidation of soft ground，such as a denser layout of PVDs，or a larger Poisson?s ratio of soil，or a smaller influence area of air-boosted pipes or a larger pressurized pressure.
卢萌盟1，2，孙锦鑫1，2，李传勋3，高 浪4. 考虑变井阻的增压式真空预压固结解析模型及解答[J]. 岩石力学与工程学报, 2023, 42(5): 1259-1272.
LU Mengmeng1，2，SUN Jinxin1，2，LI Chuanxun3，GAO Lang4. Analytical solutions for consolidation of soft soil improved by air-boosted vacuum preloading considering the varied well resistance of PVDs. , 2023, 42(5): 1259-1272.
[1] 蔡袁强. 吹填淤泥真空预压固结机制与排水体防淤堵处理技术[J]. 岩土工程学报，2021，43(2)：201–225.(CAI Yuanqiang. Consolidation mechanism of vacuum preloading for dredged slurry and anti-clogging method for drains[J]. Chinese Journal of Geotechnical Engineering，2021，43(2)：201–225.(in Chinese))
[2] KJELLMAN W. Consolidation of clay by means of atmospheric pressure[C]// Proceedings of the Conference on Soil Stabilization. Boston：Massachusetts Institute of Technology，1952：258–263.
[3] CHU J，YAN S，YANG H. Soil improvement by the vacuum preloading method for an oil storage station[J]. Geotechnique，2000，50(6)：625–632.
[4] BARAL P，RUJIKIATKAMJORN C，INDRARATNA B，et al. Radial consolidation characteristics of soft undisturbed clay based on large specimens[J]. Journal of Rock Mechanics and Geotechnical Engineering，2018，10(6)：1 037–1 045.
[5] 孙立强，闫澍旺，李 伟，等. 超软土真空预压室内模型试验研究[J]. 岩土力学，2011，32(4)：984–990.(SUN Liqiang，YAN Shuwang，LI Wei，et al. Study of super-soft soil vacuum preloading model test[J]. Rock and Soil Mechanics，2011，32(4)：984–990.(in Chinese))
[6] LEI H，LU H，LIU J，et al. Experimental study of the clogging of dredger fills under vacuum preloading[J]. International Journal of Geomechanics，2017，17(12)：04017117.
[7] WANG P，HAN Y，ZHOU Y，et al. Apparent clogging effect in vacuum-induced consolidation of dredged soil with prefabricated vertical drains[J]. Geotextiles and Geomembranes，2020，48(4)：524–531.
[8] DENG Y F，LIU L，CUI Y J，et al. Colloid effect on clogging mechanism of hydraulic reclamation mud improved by vacuum preloading[J]. Canadian Geotechnical Journal，2019，56(5)：611–620.
[9] 金亚伟，金亚君，蒋君南. 增压真空预压固结处理软土地基/尾矿渣/ 湖泊淤泥的方法[P]. 中国：CN101418566，2009–04–29.(JIN Yawei，JIN Yajun，JIANG Junnan. Pressurized vacuum preloading consolidation method for soft soil foundation/ tailing slag/ lake mud[P]. China：CN101418566，2009–04–29.(in Chinese))
[10] LEI H Y，QI Z Y，ZHANG Z P. New vacuum-preloading technique for ultrasoft-soil foundations using model tests[J]. International Journal of Geomechanics，ASCE，2017，17(9)：04017049.
[11] WANG J，CAI Y Q，MA J J，et al. Improved vacuum preloading method for consolidation of dredged clay-slurry fill[J]. Journal of Geotechnical and Geoenvironmental Engineering，2016，142(11)：1–5.
[12] 沈宇鹏，余 江，刘 辉，等. 增压式真空预压处理站场软基效果试验研究[J]. 铁道学报，2011，33(5)：97–103.(SHEN Yupeng，YU Jiang，LIU Hui，et al. Experimental study on the effect of pressurized vacuum preloading treatment of station yard soft foundation[J]. Journal of the China Railway Society，2011，33(5)：97–103.(in Chinese))
[13] 朱 平，孙立强，闫澍旺，等. 可控通气真空预压室内模型试验及其机制分析[J]. 岩石力学与工程学报，2011，30(增1)：3 041–3 148. (ZHU Ping，SUN Liqiang，YAN Shuwang，et al. Laboratory model test and mechanism analysis of controlled ventilation vacuum precompression[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(Supp.1)：3 041–3 148.(in Chinese))
[14] CAI Y Q，XIE Z W，WANG J，et al. New approach of vacuum preloading with booster prefabricated vertical drains(PVDs) to improve deep marine clay strata[J]. Canadian Geotechnical Journal，2018，55(10)：1 359–1 371.
[15] 雷华阳，胡 垚，雷尚华，等. 增压式真空预压加固吹填超软土微观结构特征分析[J]. 岩土力学，2019，40(增1)：32–40.(LEI Huayang，HU Yao，LEI Shanghua，et al. Analysis of microstructure characteristics of air-booster vacuum preloading for ultra-soft dredger fills[J]. Rock and Soil Mechanics，2019，40(Supp.1)：32–40.(in Chinese))
[16] 屠红珍，徐衍徽，谢立全. 软基真空预压加固的注气增效机制与数值分析[J]. 岩土力学，2014，35(增2)：600–606.(TU Hongzhen，XU Yanhui，XIE Liquan. Mechanism and numerical analysis of effect of air injection on vacuum preloading for weak foundation improvement[J]. Rock and Soil Mechanics，2014，35(Supp.2)：600–606.(in Chinese))
[17] 史 吏，胡东东，蔡袁强，等. 增压式真空预压吹填淤泥超静孔隙水压力实时响应及加固机制初探[J]. 岩土力学，2020，41(1)：1–10.(SHI Li，HU Dongdong，CAI Yuanqiang，et al. Preliminary study on real-time pore water pressure response and reinforcement mechanism of dredged slurry treated by air-booster vacuum preloading[J]. Rock and Soil Mechanics，2020，41(1)：1–10.(in Chinese))
[18] FENG S X，LEI H Y，LIN C. Analysis of ground deformation development and settlement prediction by air-boosted vacuum preloading[J]. Journal of Rock Mechanics and Geotechnical Engineering，2022，14(1)：272–288.
[19] XIE Z，WANG J，FU H，et al. Effect of pressurization positions on the consolidation of dredged slurry in air-booster vacuum preloading method[J]. Marine Georesources and Geotechnology，2020，38(1)：122–131.
[20] ANDA R，FU H，WANG J，et al. Effects of pressurizing timing on air booster vacuum consolidation of dredged slurry[J]. Geotextiles and Geomembranes，2020，48(4)：491–503.
[21] KE S，WANG P，HU X，et al. Effect of the pressurized duration on improving dredged slurry with air booster vacuum preloading[J]. Marine Georesources and Geotechnology，2020，38(8)：970–979.
[22] 雷华阳，王 鹏，刘 旭，等. 基于气体运移规律的增压式真空预压法加固机制分析[J]. 岩土力学，2021，42(4)：943–953.(LEI Huayang，WANG Peng，LIU Xu，et al. Influence of gas migration patterns on reinforcement of dredged slurry by air-booster vacuum preloading method[J]. Rock and Soil Mechanics，2021，42(4)：943–953.(in Chinese))
[23] BARRON R A. Consolidation of fine-grained soils by drain wells by drain wells[J]. Transactions of the American Society of Civil Engineers，1948，113(1)：718–742.
[24] HANSBO S. Consolidation of fine-grained soils by prefabricated drains[C]// 10th International Conference on Soils Mechanics and Foundation Engineering. [S. l.]：[s. n.]，1980：677–682.
[25] 谢康和，曾国熙. 等应变条件下的砂井地基固结解析理论[J]. 岩土工程学报，1989，11(2)：3–17.(XIE Kanghe，ZENG Guoxi. Analytical theory for consolidation of sand drain under equal strain assumption[J]. Chinese Journal of Geotechnical Engineering，1989，11(2)：3–17.(in Chinese))
[26] TANG X W，ONITSUKA K. Consolidation by vertical drains under time-dependent loading[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2000，24(9)：739–751.
[27] 胡亚元. 不排水桩准饱和复合地基的固结特性[J]. 哈尔滨工业大学学报，2021，53(10)：140–148.(HU Yayuan. Consolidation behavior of nearly saturated composite ground with impervious piles[J]. Journal of Harbin Institute of Technology，2021，53(10)：140–148.(in Chinese))
[28] MOHAMEDELHASSAN E，SHANG J Q. Vacuum and surcharge combined one-dimensional consolidation of clay soils[J]. Canadian Geotechnical Journal，2002，39(5)：1 126–1 138.
[29] INDRARATNA B，SATHANANTHAN I，RUJIKIATKAMJORN C，et al. Analytical and numerical modeling of soft soil stabilized by prefabricated vertical drains incorporating vacuum preloading[J]. International Journal of Geomechanics，2005，5(2)：114–124.
[30] GENG X Y，INDRARATNA B，RUJIKIATKAMJORN C. Analytical solutions for a single vertical drain with vacuum and time-dependent surcharge preloading in membrane and membraneless systems[J]. International Journal of Geomechanics，2012，10(1)：27–42.
[31] TIAN Y，WU W B，JIANG G S，et al. Analytical solutions for vacuum preloading consolidation with prefabricated vertical drain based on elliptical cylinder model[J]. Computers and Geotechnics，2019，116：103202.
[32] 沈宇鹏，董淑海，王云超，等. 增压式真空预压两种固结解析解的对比分析[J]. 岩石力学与工程学报，2019，38(增1)：3 171–3 178. (SHEN Yupeng，DONG Shuhai，WANG Yunchao，et al. Comparative analysis between integral-transform solution and separate variable method for consolidation of the ground by air-boosted vacuum preloading[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(Supp.1)：3 171–3 178.(in Chinese))
[33] KIM R，HONG S J，LEE M J，et al. Time dependent well resistance factor of PVD[J]. Marine Georesources and Geotechnology，2011，29(2)：131–144.
[34] DENG Y B，XIE K H，LU M M，et al. Consolidation by prefabricated vertical drains considering the time dependent well resistance[J]. Geotextiles and Geomembranes，2013，36：20–26.
[35] 江文豪，詹良通，杨 策，等.考虑井阻随时间变化及径–竖向渗流下砂井地基固结的解析解及其分析[J]. 工程力学，2021，38(6)：218–226.(JIANG Wenhao，ZHAN Liangtong，YANG Ce，et al. Analytical solution and analysis for consolidation of sand-drained ground considering the time dependent well resistance and radial-vertical flow[J]. Engineering Mechanics，2021，38(6)：218–226.(in Chinese))
[36] 张玉国，万东阳，郑言林，等. 考虑径向渗透系数变化的真空预压竖井地基固结解析解[J]. 岩土力学，2019，40(9)：3 533–3 541. (ZHANG Yuguo，WAN Dongyang，ZHENG Yanlin，et al. Analytical solution for consolidation of vertical drain under vacuum preloading considering the variation of radial permeability coefficient[J]. Rock and Soil Mechanics，2019，40(9)：3 533–3 541.(in Chinese))
[37] INDRARATNA B，BASACK S，RUJIKIATKAMJORN C. Numerical solution of stone column-improved soft soil considering arching，clogging，and smear effects[J]. Journal of Geotechnical and Geoenvironmental Engineering，2013，139(3)：377–394.
[38] 卢萌盟. 复合地基固结解析理论研究方法与进展[J]. 地基处理，2020，2(6)：451–460.(LU Mengmeng. Research methodologies and advances in analytical theory for consolidation of composite ground[J]. Journal of Ground Improvement，2020，2(6)：451–460.(in Chinese))
[39] LU M M，SLOAN S W，INDRARATNA B，et al. A new analytical model for consolidation with multiple vertical drains[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2016，40(11)：1 623–1 640.
[40] 郭 霄，谢康和，吕文晓，等. 井阻随深度和时间变化的竖井地基固结解析解[J]. 岩土工程学报，2015，37(6)：996–1 001.(GUO Xiao，XIE Kanghe，LU Wenxiao，et al. Analytical solutions for consolidation by vertical drains with variation of well resistance with depth and time[J]. Chinese Journal of Geotechnical Engineering，2015，37(6)：996–1 001.(in Chinese))
[41] LU M M，SUN J X. Analytical model for consolidation of soft ground improved by PVDs with air-boosted system[J]. Computers and Geotechnics，2022，151：104968.
[42] WAN D Y，ZHANG Y G，YANG H Y，et al. The analytical solution for consolidation of vertical drain with vacuum preloading based on equivalent annular drain[C]// IOP Conference Series：Earth and Environmental Science. [S. l.]：IOP Publishing，2019，218(1)：012023.
[43] 雷国辉，许 波，张旭东. 堆载预压径竖向固结等体积应变解答[J]. 岩土工程学报，2013，35(1)：76–84.(LEI Guohui，XU Bo，ZHANG Xudong. Equal volumetric strain solutions for radial and vertical consolidation with vertical drains under surcharge preloading[J]. Chinese Journal of Geotechnical Engineering，2013，35(1)：76–84.(in Chinese))
[44] 沈宇鹏，王云超，董淑海，等. 增压式真空预压处理单层均质土固结理论研究[J]. 铁道学报，2019，41(4)：118–124.(SHEN Yupeng，WANG Yunchao，DONG Shuhai，et al. Study on consolidation theory of single-layer homogeneous soil treated by air-boosted vacuum preloading[J]. Journal of the China Railway Society，2019，41(4)：118–124.(in Chinese))
2023, Vol. 42 
