Phân tích vai trò của vải địa kỹ thuật đối với hiệu ứng vòm trong nền đường đắp trên nền đất yếu được gia cố bằng trụ xi măng đất

Bộ CƠNG THƯƠNG ĐẠI HỌC CƠNG NGHIỆP THÀNH PHĨ HỊ CHÍ MINH BÁO CÁO TƠNG KẾT ĐÈ TÀI KHOA HỌC KÉT QUẢ THỰC HIỆN ĐỀ TÀI NGHIÊN CỨU KHÓA HỌCCẤP TRƯỜNG Tên đề tài: Phân tích vai trị vải địa kỹ thuật hiệu ứng vòm đường đắp đất yếu gia cố trụ xi măng đất Mã số đề tài: 22/1XD01 Chủ nhiệm đề tài: Ths Nguyễn Thị Phương Linh Đơn vị thực hiện: Khoa Kỹ thuật Xây dụng, Trường Đại học Cơng Nghiệp TP Hố Chí Minh LỜI CÁM ƠN Nhóm nghiên cứu đề tài “Phân tích vai trị vải địa kỹ thuật hiệu ứng vòm đường đắp đất yếu gia cố trụ xi măng đất” xin chân thành cảm ơn Trường Đại học Cơng Nghiệp TP Hồ Chí Minh hỗ trợ kinh phí cho nhóm hồn thành đề tài nghiên cứu Nhóm nghiên cứu xin chân thành cảm ơn Ban chủ nhiệm quý Thầy Cô Khoa Kỹ thuật Xây dựng động viên để nhóm nghiên cứu hoàn thành đề tài nghiên cứu Xin cảm ơn! PHẦN I THƠNG TIN CHƯNG I Thơng tin tong qt 1.1 Tên đề tài: Phân tích vai trị vải địa kỹ thuật đối vói hiệu ứng vịm đường đắp đất yếu gia cố trụ xi măng đất 1.2 Mã so: 21.2XD01 1.3 Danh sách chủ trì, thành viên tham gia thực đề tài TT Họ tên (học hàm, học vị) Đơn vị cơng tác Vai trị thực đề tài Ths.Nguyễn Thị Phưong Linh Trường Đại học Công Nghiệp TP Hồ Chí Minh Chủ nhiệm đề tài TS Nguyễn Bá Phú Trường Đại học Công Nghiệp TP Hồ Chí Minh Thành viên Ths Trần Minh Hồng Trường Đại học Tơn Đức Thắng Thành viên 1.4 Đơn vị chủ trì: 1.5 Thịi gian thực hiện: 1.5.1 Theo hợp đồng: từ 30 tháng năm 2022 đến 30 tháng năm 2023 1.5.2 Gia hạn (nếu có): Không 1.5.3 Thực thực tế: từ 30 tháng năm 2022 đến 30 tháng năm 2023 1.6 Những thay đổi so vói thuyết minh ban đầu (nếu có): không (về mục tiêu, nội dung, phương pháp, kết nghiên cứu tẻ chức thực hiện; Nguyên nhân; Y kiến Cơ quan quản lý) 1.7 Tổng kinh phí phê duyệt đề tài: 60 triệu đồng II Kết nghiên cứu Đặt vấn đề: Biến dạng lớn ổn định cơng trình đường vấn đề thách thức khó khăn kỹ thuật xây dựng cơng trình giao thơng (cầu, đường) Hiện tượng lún dư kéo dài theo thời gian làm ảnh hưởng đến trình khai thác, tăng chi phí tu bão dưỡng cơng trình Trong kỹ thuật xử lý đất yếu, trụ xi măng đất vải địa kỹ thuật thường kết hợp đe sử dụng gia cố đất yếu nhằm giảm độ lún tăng sức chịu tải đất tăng độ ổn định đường Đây giải pháp thường áp dụng kỹ thuật xử lý đất yếu nước Hiệu ứng vòm tượng thường xảy nên đãp nên đât yêu gia cô băng trụ xi măng đât có khác biệt độ cứng trụ lớp đất xung quanh Đó yếu tố ảnh hưởng trực tiếp đến vấn đề tối ưu thiết kế khoảng cách kích thước trụ xi mãng đất Vì vấn đề liên quan đến chi phí xây dựng cơng trình nên cần phải quan tâm nghiên cứu để áp dụng tính toán thực tế mang lại hiệu kinh tế sử dụng phưong pháp gia cố vấn đề liên quan đến lý thuyết tính tốn phân tích hiệu ứng vịm chủ đề thu hút nghiên cứu nhằm để áp dụng tính toán thiết kế vào sản xuất thực tế Nghiên cứu tiến hành đánh giá phân tích vai trò vải địa kỹ thuật đến ứng xử đường, tập trung đến chế truyền lực đất đến trụ xi măng đất Mô hình số ba chiều (3D) hai chiều (2D) xây dựng đề xuất để tiến hành phân tích ảnh hưởng vải địa kỹ thuật đến hiệu ứng vòm xảy đường Khả ứng dụng mơ hình số kiểm chứng qua trường hợp lịch sử cơng trình đường đầu cầu ngồi nước Các thơng số vải địa kỹ thuật ảnh hưởng phân bố ứng suất khảo sát đề tài Mục tiêu Mục tiêu tổng quát: Nghiên cứu vai trò vải địa kỹ thuật đến hiệu ứng vòm xảy đường, ảnh hưởng thông số vải địa kỹ thuật đến ứng xử đường biến dạng nền, phân bố ứng suất nền, từ tối ưu toán thiết kế cho gia cố trụ xi măng đất kết hợp vải địa kỹ thuật, nhằm giảm chi phí xây dựng Giới hạn phạm vi nghiên cứu: Mặc dầu tượng hiệu ứng vòm thường xảy cho cơng trình đường đất yếu gia cố vật liệu địa kỹ thuật kết hợp với trụ vật liệu rời Nghiên cứu tập trung vào trường hợp cụ thể cho gia cố trụ xi măng đất Mục tiêu cụ thễ: - Xây dựng mơ hình số 3D để phân tích ứng xử đường đất yếu gia cố trụ xi măng đất kết hợp với vải địa kỹ thuật - Thiết lập mơ hình số 2D (mơ hình biến dạng phẳng) để phân tích ứng xử đường gia cố trụ xi măng đất kết hợp với vải địa kỹ thuật Các thông số chiều dày lơp vải địa kỹ thuật, kích thước tương đương trụ xi măng đất, hệ số thấm tương đương đất thiết lập - Đánh giá ảnh hưởng vải địa kỹ thuật đến ứng xử của cơng trình đường, tập trung vào hiệu ứng vòm xảy đường Phương pháp nghiên cứu - Nghiên cứu lý thuyết tổng quan tình hình nghiên cứu đề tài, sau xác định mục tiêu cụ thê nghiên cứu Trong phân này, nghiên cứu sở lý thuyêt giải pháp gia cô đất yếu phương pháp kết hợp trụ XMĐ vải địa kỹ thuật, từ làm rõ tính ý nghĩa vân đê đặt đê tài nghiên cứu Trong đê tài này, nhóm tác giả tập trung nghiên cứu ảnh hưởng thông số vải địa kỹ thuật đến hiệu ứng vòm xảy đường - Xây dựng mơ hình số ba chiều (3D) chương trình PLAXIS: Đe tài tiến hành mơ số chiều cho cơng trình đường gia cố trụ xi măng đất kết hợp với vải địa kỹ thuật Trong đề tài này, trường hợp nghiên cứu chọn cơng trình đường đầu cầu khu vực song Sipoo, Hertsby, Phần Lan (Yapage and Liyanapathirana 2017) Hình thể mặc căt ngang cơng trình nên đường gia cô trụ xi măng đât với vải địa kỹ thuật Các thông số đầu vào số liệu quan trắc đầy đủ cơng trình nghiên cứu so sánh với kết mô số - Xây dựng mơ hình số chiều (mơ hình biến dạng phẳng chiều, 2D) chng trình PLAXIS ngun tắc, tiến hành mơ số để phân tích ứng xử cơng trình, cần thiết phải mơ ba chiều đế đánh giá tồn ứng cơng trình với yếu tố thực tế T uy nhiên mô số chiều (như nội dung 2), rat thời gian, địi hỏi máy tính phải có tính cao để phân tích chưong trình (Nguyen et al 2018) Do mơ hình số chiêu thường sử dụng thiết kế cơng trình Phần tác giả tiến hành phân tích ứng xử cơng trình với mơ hình biến dạng phang chiều để đánh giá làm việc đồng thời vải địa kỹ thuật trụ xi măng đất - Sử dụng mơ hình số chiều đề xuất Nội dung nghiên cứu 3, tiến hành khảo sát thông số ảnh hưởng đến chế truyền lực kết cấu trụ xi măng đất, vải địa kỹ thuật lóp đất đắp bên Bộ thơng số đầu vào mơ hình số số liệu thực tế từ cơng trình đường đầu cầu khu vực song Sipoo, Hertsbỵ, Phần Lan (Yapage and Liyanapathirana 2018) Sau tiến hành số phân tích sau: + Khảo sát ảnh hưởng cường độ vải địa kỹ thuật biến dạng đất, bao gôm biến dạng ngang, độ lún theo phương thẳng đứng + Khảo sát ảnh hưởng cường độ vải địa kỹ thuật ổn định đường đắp thơng qua hệ số an tồn + Khảo sát ảnh hưởng cường độ vải địa kỹ thuật tập trung ứng suất trụ xi măng đất + Khảo sát ảnh hưởng số lượng lớp vải địa kỹ thuật ổn định, biến dạng, tập trung ứng suất đường Tổng kết kết nghiên cứu Trong đề tài này, nhóm nghiên cứu xây dựng hai mơ hình so 2D 3D sau: 4.1 Phân tích mơ hình so 3D Hình 1: Một mơ hình số 3D cho đường gia cố hệ trụ xi măng đất 4.2 Phân tích mơ hình số 2D Hình 2: Một mơ hình số 2D cho đường gia cố hệ trụ xi măng đất Trong thực tế, trụ xi măng đất bố trí theo hai dạng (1) Dạng trụ xi măng đất bố trí chồng lên theo dạng tường (Overlapped columns); (2) Dạng trụ xi măng đất bố trí cách khoảng s (Isolated columns) với kiểu bố trí hình vng tam giác Khi chuyển qua mơ hình phẳng bề rộng tường xi măng đất, hệ số thấm tương đương, độ cứng trụ khác tường, Hình Trong nghiên cứu này, nhóm nghiên cứu đề xuất cơng thức tính tốn mơ hình phẳng sau: - Bề rộng tường xi măng đất mơ hình biến dạng phẳng bci sau: b = nd2 cl cl Theo công thức trên, del đường kính trụ xi măng đất; Sci khoảng cách trụ xi măng đất Từ cơng thức trên, ta thấy khoảng cách trụ gần bề rộng tường mơ hình phẳng lớn ngược lại khoảng cách trụ xa bề rộng tường nhỏ - Độ cứng (mô đun đàn hồi) tương đương tường xi măng đất mơ hình biến dạng phẳng (E^Ị) sau: Epìcỉ =E n 1- 4Sc/J + Ecl xdcl 4SC1 Theo công thức trên, Eci độ cứng (mô đun đàn hồi) trụ xi măng đất; Es mô đun đàn hồi đất xung quanh trụ Các thông số khác - Hệ số thấm tương đương trụ xi măng đất mơ hình phẳng lấy theo công thức Chen et al (2005) sau: cỉ = cl Kkpỉ ~ Kkax l ) Theo công thức trên, kC pj hệ số thấm trụ xi măng đất mơ hình phẳng; k^ hệ số thấm thực tế trụ Các thông số khác a) Mặt cho mơ hình thực tế b) Mặt hệ trụ xi măng đất mô hình phẳng Hình Mặt cho mơ hình gia cố thực tế mơ hình biến dạng phẳng 4.3 Vị trí dự án phân tích Phần trình bày phương pháp phân tích số 3D để khảo sát ứng xử vải địa kỹ thuật tải trọng đường đất yếu xử lý phương pháp trụ xi măng đất cơng trình xây dựng cầu qua sông Sipoo Hertsby, Phần Lan Mặt cắt ngang đại diện đường thể Hình 4a Đặc điểm địa chất bên cơng trình trình bày chi tiết qua nghiên cứu Forsman et al (1999) Forsman (1999) Bên đường lớp đất yếu lớp đất sét pha cát, lớp đất yếu có chiều dày 15m Trụ xi măng đất sử dụng có chiều dài 17m bố trí hai dạng xen kẽ theo phương ngang bao gồm dạng hàng dạng hình vng với đường kính trụ 0.8m, sơ đồ bố trí trụ xi măng đất Hình 2a Trụ xi măng đất thiết kế với cường độ chịu nén đơn qu=300 kPa Đe tăng khả truyền tải lên hệ thống trụ xi măng đất, lớp vải địa kỹ thuật gia cường có cường độ chịu kéo cực hạn 200 kN/m sử dụng Nen đường đắp có bề rộng 8.5m cao 1.8m thi công giai đoạn Hình 4b (Yapage and Liyanapathirana 2018) (a) Mặt cắt ngang đường gia cố trụ xi măng đất vải địa kỹ thuật (Forsman 1999) 1.8 1.6 s' -;'*^Shear planế^ Page of 12 DeeP cement mixing column Fig Soil arching in geosynthetic reinforced column-supported embankment the column head and soft soil; T is shear stress acting in embankment due to soil arching phenomenon; T is tensile forces in geosynthetic The embankment load on the DCM columns may be increased by vertical components of ten­ sile forces in geosynthetic (T) This is due to the ability of geosynthetic in interlocking with columns and the granular embankment, thereby increasing the natural arching angle of the embankment and transferring the vertical load acting on geosynthetic to the columns [35, 44] These results lead to reducing the deformation of subsoil under the embankment The shear stresses induced by the embankment soil arching are also reduced, thereby increasing the efficiency of soil arching in embankments The Width of DCM Columns in a 2-D Plane Strain Model In practical engineering, the DCM columns have been typi­ cally applied in two types of configurations, i.e., isolated and overlapped DCM columns In the plane strain model, the width of the DCM column should be converted from the actual size in in-situ conditions, as shown in Fig An equivalent width in the 2-D plane strain model was obtained by applying the equivalent area method [1, 12] The equiva­ lent width of the DCM column in the equivalent plane strain model can be deduced as follows: where hc| is the equivalent width of the DCM column in the 2-D plane strain (Fig 2); Jcl is the diameter of the isolated DCM column; Scl is spacing of adjacent the DCM columns in the direction perpendicular to the plane of the embank­ ment cross-section According to Eq (1), the equivalent width of the DCM column in the plane strain model depends on the diameter, spacing and type of configurations of DCM columns Equivalent Properties of DCM Column The equivalent stiffness of DCM walls in the plane-strain model is also converted from DCM columns in in-situ con­ ditions The stiffness of DCM walls in the 2-D model for each configuration (i.e isolated and overlapped columns) is different They depend on the diameter and spacing of DCM columns distance in the direction perpendicular to the plane of the embankment cross-section Deng [45] proposed a simplified method to obtain an equivalent stiffness of DCM walls in the plane strain model as follows: Fig Plan view of the column layout in the in-situ case and 2-D plane strain model (a) In-situ condition (b) 2-D plane strain model £) Springer 56 Page of 12 pel = F, ^pi — Ei (i _ k International Journal of Geosynthetics and Ground Engineering xdrl ^0 +E“Ỉ 4-W (2) where is the equivalent modulus of the DCM wall; Es and Ecl are the moduli of the soil and the DCM columns, respec­ tively Under embankment load, the vertical stress acting on the head of DCM columns depends on the stiffness of col­ umns However, the strength of DCM columns is not con­ stant and develops according to time, especially during the early stage of construction This can affect the predicted results of numerical approaches The consideration of the strength development of DCM columns is still challenging in the current numerical models [25] Therefore, the effects of the strength development of DCM columns are assumed to be ignored in this paper Chen et al [46] proposed a simplified method to obtain the equivalent vertical permeability of DCM walls in the plane strain as follows: cL pl = kax _ ndcl\ (3) where k^x is the permeability of DCM columns in the in-situ case Equations (2) and (3) show that the equivalent proper­ ties of the DCM wall in the plane strain model can differ­ ent with differential configurations of row (i.e isolated and overlapped columns) Application of 2-D Numerical Analysis to the Test Embankment The Field Description This paper presents a two-dimensional numerical imple­ mentation of the performance of the geosynthetic reinforced column-supported embankment over the soft soil deposit to approach a new bridge over the Sipoo River at Hertsby, Finland The soil profiles at the site were detailed in the previous studies [47,48] The soil characteristics of this case study can be summarized as follow: the subsoil includes the soft soil layer of 15 m deposited on the silt layer of m To improve the soft soil deposit, DCM columns with diameters of 0.8 m and 17 m length were installed into the subsoil The soil-cement samples were taken to test the strength DCM column The unconfined compressive strength (qu) of DCM columns was 300 kPa The DCM columns were used with two types of configurations including the isolated and over­ lapped DCM columns, in which the rows of isolated and overlapped DCM columns were installed alternatively paral­ lel to the center line of the embankment in the longitudinal direction The cross-section of the embankment and column layout is shown in Fig Springer (2023) 9:56 Fig Cross section of the embankment and plan view of the DCM columns layout To increase the effectiveness of the ground improvement method by DCM columns, the embankment was stabilized with the geosynthetic basal reinforcement layer The ulti­ mate tensile strength of the geosynthetic layer was 200 kN/m in both longitudinal and transverse directions As previously presented, the role of geosynthetic in embankment is to increase the loads transferred to the columns and reduce the loads transferred to the surrounding soil The geosynthetic was placed 300 mm above the column head and sandwiched in the filling material The unit weight of embankment mate­ rial is 20 kN/m3 After Yapage and Liyanapathirana [27], the construction schedule of the embankment comprised three stages The first 0.6 m of embankment including the installa­ tion of a geosynthetic reinforcement layer was constructed in 30 days, followed by 30 days for consolidation The second stage of 0.9 m embankment loading was applied in 90 days, followed by 150 days for consolidation The third stage was carried out with 0.3 m in 120 days Figure presents the construction schedule of the embankment fill The 2-D Numerical Model of Field Test To evaluate the applicability of the developed equivalent plane strain model, the 2-D model was applied to the above case history In this study, the numeral program Plaxis [49] was used to simulate the staged construction process of the geo­ synthetic reinforced column-supported embankment Because of the symmetry of the problem, only half of the geometry was considered for the numerical model The width of the finite element model is extended by 30 m in the horizontal direction (x direction), which is four times the base width of the embankment to minimize the boundary effects [37] The boundary condition is as follows: the vertical and horizontal International Journal of Geosyntheticsand Ground Engineering Page of 12 (2023) 9:56 56 Fig Construction schedule of the embankment fill Time (days) method was implemented based on the concept that the mesh was made finer at where stress and deformation are signifi­ cant to ensure accurate computations, specifically, the mesh between columns was very fine due to large relative displace­ ment between columns and soils whereas the layer beneath the columns and the right side of embankment toe were treated with coarser mesh because of lower stress concentration and deformation The standard 15-node triangular elements which are commonly used in Plaxis for soft soil embankment were adopted in this current analysis Because the DCM columns in the field were installed in two types of configurations (i.e., isolated and overlapped DCM columns), therefore the equivalent width and modu­ lus of the walls of the columns in the plane strain model (transverse direction) are different and calculated from Eqs (1-2) The hydraulic conductivity of DCM columns can be assumed to be the same as surrounding soil [47], The constitutive behavior of subsoil layers and embankment was modeled by the Mohr-Coulomb model Softening behavior of DCM columns is not included in this analysis because the applied loads are not sufficient to show the strain-softening behavior of DCM columns [27] The geotechnical parame­ ters in the 2-D numerical analysis were presented in Table 1, where E is the elastic modulus of materials; V is the Pois­ son’s ratio; Y is the unit weight; c is the effective cohesion; (p is the effective friction angle; ky is the vertical hydraulic conductivity; and kx is the horizontal hydraulic conductivity, in which kx = Iky The subsoil layers are normally consoli­ dated soils Note that the properties of subsoil are collected from previous studies [27, 47, 48] Fig Mesh properties in the plane strain model of the test embank­ ment displacements were fixed at the bottom boundary, the horizon­ tal displacements were fixed at the left and right boundaries, the pervious boundaries were applied in the ground surface and bottom boundary of the model, and the impervious bound­ aries were applied of the left and right sides of the model The geometry and mesh properties of the plane strain model used for test embankment are shown in Fig In this study, the standard 15-node triangular elements are used in finite element analysis The mesh for this analysis consists of 1593 elements and 12,975 nodes In this study, the mesh in the finite element Table Geotechnical parameters of subsoils in numerical analysis Materials y(kN/m3) E (MPa) V c(kPa) H°) ky (m/s) k-Á (= 2ky) (m/s) Soft clay 16 0.3 0.3 10 6.3xl0“u 1.26X1O-10 Silt 17 1.6 0.3 13 6.3x10“10 1.26X10-9 Embankment 20 15 0.3 30 6.3xl0“6 1.26X10-5 ểỊỊ Springer 56 International Journal of Geosynthetics and Ground Engineering Page of 12 In this study, the effective cohesion of DCM columns is chosen as 0.3gK, which is based on the previous studies [50, 51] The elastic modulus of DCM columns can be used with 100ậK [52] The geosynthetic reinforcement is modeled as an elastic and isotropic material using the geogrid element The properties of the DCM wall and geosynthetic in the numeri­ cal plane strain analysis are presented in Table where EA is the axial stiffness of the geosynthetic at the column head (S1) is always larger than that at the sur­ rounding soil (S2) due to the stiffness difference between the surrounding soil and DCM columns This confirms that the 2-D numerical model developed in this study can apply to analyze the load transfer mechanism between geosynthetic reinforcement, DCM columns and subsoils Forsman [47] reported the results of strain in geosynthetic versus time at Al and AỐ The location of Al and A6 points is shown in Fig 5, in which the strain gauge Al was placed on the column head in an isolated row and the strain gauge A6 was placed at the geosynthetic on the surrounding soil Figure shows the strain variation in the geosynthetic layer with time The strain results from the numerical model at Al and A6 are in good agreement with the measured data The measured strain at Al shows extremely high strain between 1000 and 1600 days This may due to an error in measuring the strain in the field at strain gauges Both observed and predicted results show that the strain in the geosynthetic over the column head is much higher than the strain in the geosynthetic over the subsoil Figure shows the variation of tension in the geosyn­ thetic layer along the width of the embankment during the Analysis Results Figure shows the settlements with time from the field data and numerical analysis The settlements were observed at the column head and surrounding soil, which were signed at s and S2, respectively The location of SI and S2 was shown in Fig The settlement results from three-dimensional numerical analysis by Yapage and Liyanapathirana [27] were also compared in this study The results show that the settle­ ments obtained from the equivalent plane strain model agree well with the measured settlement and are better than the predicted settlements by Yapage and Liyanapathirana [27] The measured and predicted results agree that the settlement Table Geotechnical parameters of DCM walls and geosynthetic in numerical analysis Materials Al (m) /(kN/m3) E(MPa) zz Overlapped wall in soft soil 0.72 20 26.9 H°) ky (m/s) kx (= 2ky) (m/s) 0.3 90 30 6.3 xio-11 1.26 X1O“10 c (kPa) Overlapped wall in silt 0.72 20 27.1 0.3 90 30 6.3x10“10 1.26xl(T9 Isolated wall in soft soil 0.36 20 13.63 0.3 90 30 6.3xl0“u 1.26x10“10 Isolated wall in silt 0.36 20 14.35 0.3 90 30 6.3xlO“10 1.26xl(T9 Geosynthetic EA = 1700 kN/m Fig Measured and numerical results of settlement versus time Time (days) 1000 100 Springer (2023) 9:56 International Journal of Geosyntheticsand Ground Engineering Page of 12 (2023) 9:56 Fig Strain variation in the geosynthetic layer with time 56 Time (day) Fig Variation of tension in the geosynthetic layer along the width of the embankment construction and operation period It is shown that the ten­ sion is mainly concentrated over the isolated and overlapped columns These results could be explained that the DCM columns have higher stiffness compared to the surround­ ing soft subsoil Therefore, DCM columns attract more load increasing the vertical stress acting on the geosynthetic laid over DCM columns The results also show that the tension in geosynthetic over the overlapped columns is higher than that of the isolated columns These results could be explained that the higher loads are transferred to overlapped columns because of the higher area replacement ratio and stiffness (as calculated in Eq and shown in Table 2) of the overlapped columns than that of the isolated columns The obtained results in this section confirm the accuracy of the developed model in this study and its ability to study the load transfer mechanism of geosynthetic reinforced column-supported embankment Effects of Geosynthetic on Embankment Behavior In this section, the effects of geosynthetic on embankment performance are investigated, in which the behavior of the load transfer mechanism is focused The above numerical analysis for test embankment is also used in this section To investigate the effects of geosynthetic on the load transfer mechanism, five of the axial stiffness of geosynthetic con­ ducted in numerical analysis are 50 kN/m, 100 kN/m, 200 kN/m, 500 kN/m, 1000 kN/m, and the case without using the geosynthetic for embankment improvement The effects of geosynthetics were investigated through factors such as differential settlement, lateral displacement, stress concen­ tration ratio and stability of the embankment £1 Springer 56 Page of 12 International Journal of Geosynthetics and Ground Engineering Effect of Geosynthetic on Differential Settlement In this study, differential settlement is defined as the differ­ ence in the settlement at the ground surface level between that at the head of the column (SI) and surrounding soil (S2) Figure shows the variation in ground surface dif­ ferential settlement with various stiffness of geosynthetic The results show that when the stiffness of geosynthetic increases, the differential settlement reduces For the case without using geosynthetics, the differential settlement occurs with the largest value This is because the stress part from the embankment load on subsoil is larger than the cases with the geosynthetic It can imagine that the geo­ synthetic plays a role to reduce the external stress acting on the surrounding soil between the adjacent columns under the embankment load The results show that the differential settlement reduces significantly as the stiffness geosynthetic ranges from (without geosynthetic inclusion) to 200 kN/m When the geosynthetic stiffness is larger than 200 kN/m, there is little change in differential settlement Fig Variation of differential settlement of ground surface (between Point SI and S2) with various stiffness of geosynthetic Fig 10 Variation of stress concentration ratio with geosyn­ thetic stiffness Springer (2023) 9:56 Effect of Geosynthetic on the Stress Concentration Ratio The load transfer mechanism of geosynthetic reinforced column-supported embankment was typically evaluated by the stress concentration ratio [53] The stress concentration ratio is defined as the ratio of the vertical stress acting on the DCM column head and the vertical stress acting on the surrounding soil at the same level The stress concentration ratio (n) can be expressed as follows: n = —— (4) where ơcl and ơs are vertical stress acting on the DCM col­ umn head and the surrounding soil, respectively Figure 10 shows the variation of stress concentration ratio with the geosynthetic stiffness The results indicated that when the geosynthetic stiffness increases, the stress concentration ratio increases This means that the stress transferred onto the DCM column head from the surround­ ing soil increase as increasing the geosynthetic stiffness International Journal of Geosyntheticsand Ground Engineering Page of 12 (2023) 9:56 When the geosynthetic layer is used in the embankment, the stress concentration ratio increase significantly These results show obviously when the geosynthetic stiffness ranges from (without the geosynthetic) to 200 kN/m The variation of stress concentration little changes as the geosynthetic stiffness is larger than 200 kN/m Generally, geosynthetics play a role in the improvement of the soil arching development in embankments Effect of Geosynthetic on the Lateral Displacement of Subsoil The effects of geosynthetic on the lateral displacement distribution of subsoil at the toe of the embankment are shown in Fig 11 The results indicated that the lateral displacement of subsoil with depth in the cases with the geosynthetic is less than that in the case without the geo­ synthetic installation The lateral displacement of subsoil decreases as the geosynthetic stiffness increases These results confirmed that the geosynthetic can restrict the outward thrusts to adjacent elements [35] Therefore, the 56 general stability of the embankment can increase The presence of geosynthetic in embankment contributes to concentrating the stress on the DCM column heads and decreasing stress on surrounding subsoils Therefore, the lateral displacement of subsoil can reduce and increase the stability of the embankment Effect of Geosynthetic on the Stability of Embankment Fill (Fs) The stability of embankment on subsoil was evaluated by the factor of safety (Fs), which was typically analyzed from the limit equilibrium method or finite element method [54] In numerical analysis, the factor of safety can be calculated from the Phi-C reduction method [49] The strength param­ eter tanệ and c of subsoil are successively reduced auto­ matically by the same factor in accordance with additional steps until failure of the structure occurs in which non-convergence of algorithm and elastic equilibrium is achieved [35,40, 54] This is also accompanied by a rapid increase in the maximum deformation After Brinkgreve et al [49], the factor of safety is calculated as follows: _ Input strength _ Strength at failure tan input _ cinput ^reduced where cinput and tan Ộinput are strength values of soil which are inputted in the numerical analysis Creduced and tan reduCed are strength values of soil at the failure state Figure 12 shows the variation of Fs of the embankment with the various value of geosynthetic stiffness at the end of the construction of the embankment The results indi­ cated that the geosynthetic can improve the stability of the embankment by increasing Fs with the geosynthetic stiff­ ness The Fs increase rapidly as the geosynthetic stiffness increases from kN/m (for the case without the geosynthetic improvement) to 200 kN/m The stability of the embankment then insignificantly increases when the geosynthetic stiffness is larger than 200 kN/m Summary and Conclusions This paper developed an equivalent plane strain model to analyze the performance of geosynthetic reinforced columnsupported embankment, in which the DCM columns are installed simultaneously with the isolated and overlapped configurations The numerical analysis was then applied to the test embankment on soft soil in Hertsby, Finland Sub­ sequently, the role of the geosynthetic on the soil arching behavior was investigated through the developed model Fig 11 The horizontal displacements at the toe of the embankment with various stiffness of geosynthetic AJ Springer 56 Page 10 of 12 International Journal of Geosynthetics and Ground Engineering (2023) 9:56 Fig 12 Variation of stability of embankment with geosynthetic stiffness Based on the analysis results, the following conclusions are given: • The results of settlement and strain in geosynthetic obtained from the developed equivalent plan strain model are in good agreement with the measured settlement of case history and the previous study It is recommended that the developed model can be used to analyze the per­ formance of geosynthetic reinforced column-supported embankment; • The geosynthetic layer in embankment plays an impor­ tant role in the improvement of the performance of geo­ synthetic reinforced column-supported embankment such as: (1) increasing the soil arching efficiency and the stability of embankment, (2) reducing the differential settlement and lateral displacement; • The significant influence of the geosynthetic layer is obvious when the geosynthetic stiffness ranges from kN/m (without geosynthetic inclusion) to 200 kN/m The stability of the embankment is mostly constant when the geosynthetic stiffness is larger than 200 kN/m; • The tension in geosynthetic over the overlapped columns is higher than that of the isolated columns The higher loads are transferred to overlapped columns because of the higher area replacement ratio and stiffness of the overlapped columns than that of the isolated columns Acknowledgements The support of this research by the Indus­ trial University of Ho Chi Minh City (No 22/1XD01) is gratefully acknowledged Data availability The data presented in the paper are presented in the main text The results were understood from figures, tables which men­ tioned in this article Declarations Conflict of interest The authors declare no conflict of interest Springer References Yapage NNS, LiyanapathiranaDS, Poulos HG, Kelly RB (2015) Numerical modeling of geotextile-reinforced embankments over deep cement mixed columns incorporating strain-softening behav­ ior of columns Int J Geomech https://doi.org/10.1061/(ASCE) GM 1943-5622.0000341 Lei H, Fang Q, Liu J et al (2021) Ultra-soft ground improvement using air-booster vacuum preloading method: laboratory model test study Int J Geosynth Ground Eng 7:87 https://doi.org/10 1007/s40891-021-00332-4 Indraratna B, Zhong R, Fox p, Rujikiatkamjorn c (2017) Large strain vacuum-assisted consolidation with non-Darcian radial flow incorporating varying permeability and compressibility J Geotech Geoenviron Eng ASCE 143(l):04016088 Nguyen B-P, Kim Y-T (2019) Radial consolidation of PVDinstalled normally consolidated soil with discharge capac­ ity reduction using large-strain theory Geotext Geomembr 47(2):243-254 Pandey BK, Rajesh s, Chandra s (2022) Performance of soft clay reinforced with encased stone column: a systematic review Int J Geosynth Ground Eng 8:40 https://doi.org/10.1007/ S40891-022-00387-X Chai J-C, Miura N (1999) Investigation of factors affecting vertical drain behavior J Geotech Geoenvironm Eng ASCE 125 (3) :216-226 Chu J, Bo M, Choa V (2006) Improvement of ultra-soft soil using prefabricated vertical drains Geotext Geomembr 24:339-348 Bergado DT, Balasubramaniam AS, Fannin RJ, Holtz RD (2002) Prefabricated vertical drains (PVDs) in soft Bangkok clay: a case study of the new Bangkok international airport project Can Geo­ tech J 39:304-315 Rowe RK, Taechakumthorn c (2008) Combined effect of PVDs and reinforcement on embankments over rate-sensitive soils Geo­ text Geomembr 26(3):239-249 10 Mesri G, Khan QQ (2012) Ground improvement using vacuum loading together with vertical drains J Geotech Geoenvừon Eng 138(6):680-689 11 Ghandeharioon A, Indraratna B, Rujikiatkamjorn c (2012) Labo­ ratory and finite-element investigation of soil disturbance associ­ ated with the installation of mandrel-driven prefabricated vertical drains J Geotech Geoenvữon Eng ASCE 138(3):295-308 12 Ariyarathne p, Liyanapathirana D, Leo c (2013) A com­ parison of different two dimensional idealizations for a International Journal of Geosyntheticsand Ground Engineering 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 (2023) 9:56 geosynthetic reinforced pile-supported embankment Int J Geomech 13(6)1754-768 Kim Y-T, Nguyen B-P, Yun D-H (2018) Effect of artesian pres­ sure on consolidation behavior of drainage-installed marine clay deposit J Mater Civ Eng 30(8)104018156 Lorenzo GA, Bergado DT (2003) New consolidation equation for soil-cement pile improved ground Can Geotech J 40(2)1265-275 Chai J, Khan s, Shrestha s (2021) Behavior of an embank­ ment with a reinforced slope on column improved clay depos­ its Int J Geosynth Ground Eng 7:88 https://doi.org/10.1007/ s40891-021-00331-5 Nguyen B-P, Doan N-P, Daeho-Yun, Kim Y-T (2021) Verti­ cal stress distribution on stiffened deep cement mixing column under embankment load In Vol 126 of Challenges and Innova­ tions in Geomechanics IACMAG 2021, edited by M Baria, A Di Donna, and D Sterpi Cham, Switzerland: Springer Lecture Notes in Civil Engineering Fulambarkar s, Bangari G, Manna B et al (2021) Numerical analysis of embankment built on Indian marine clay improved with DM column Int J Geosynth Ground Eng 7:95 https://doi org/10.1007/S40891-021-003 42-2 Bergado DT, Anderson LR, Miura N, Balasubramaniam AS (1996) Soft ground improvement, in lowland and other envi­ ronments ASCE Press, New York Indraratna B, Redanaiw (1997) Plane train modeling of smear effects associated with vertical drains J Geotech Geoenviron Eng ASCE 123(5):474-478 Chai J, Saito A, Hino T et al (2022) Behaviour of winged PVD and the method for calculating its induced degree of consolida­ tion Int J Geosynth Ground Eng 8:50 https://doi.org/10.1007/ S40891-022-00394-y Prabavathy s, Rajagopal K, Pitchumani NK (2021) Investiga­ tion of smear zone around PVD mandrel using image-based analysis Int J Geosynth Ground Eng 7:94 https://doi.org/10 1007/S40891-021-00337-Z Chew SH, Kamruzzaman AHM, Lee FH (2004) Physicochemi­ cal and engineering behavior of cement treated clays J Geotech Geoenviron Eng ASCE 130(7):696-706 Chai JC, Carter JP (2011) Deformation analysis in soft ground improvement Springer, Dordrecht Demiroz A, Battal H (2023) Investigation of the effects of mixtures of fly ash and cement types on jet-grout columns Int J Geosynth Ground Eng 9:16 https://doi.org/10.1007/ S40891-023-00435-0 Nguyen B-P, Nguyen TT, Nguyen THY, Tran T-D (2022) Perfor­ mance of composite PVD-soil cement column foundation under embankment through plane-strain numerical analysis ASCE’s Int J Geomech https://doi.Org/l0.1061/(ASCE)GM 1943-5622.00024 94 Yapage NNS, Liyanapathừana DS, Poulos HG, Kelly RB, Leo CJ (2014) Modelling of an embankment over soft ground improved with deep cement mixed columns: a case history J Geotech Geoenviron Eng 140(11):10 Yapage NNS, Liyanapathirana DS (2018) Behaviour of geosyn­ thetic reinforced column supported embankments J Eng Design Technol 16(1):44-62 Zhang L, Zhou s, Zhao H, Deng Y (2018) Performance of geosynthetic-reinforced and pile-supported embankment with considera­ tion of soil arching J Eng Meeh 144(12):06018005 Meena NK, Nimbalkar s, Fatahi B, Yang G (2020) Effects of soil arching on behavior of pile-supported railway embankment: 2D FEM approach Comput Geotech 123:103601 Pham TA, Tran QA, Villard p, Dias D (2021) Geosyntheticreinforced pile-supported embankments—3D discrete numerical analyses of the interaction and mobilization mechanisms Eng Struct 242:112337 Page 11 of 12 56 31 Zhao L, Chen Y, Chen w, Wang J, Ren c (2023) The performance of T-shaped deep mixed soil cement column-supported embank­ ments on soft ground Constr Build Mater 369:130578 32 Van Eekelen SJM, Bezuijen A, van Tol AF (2013) An analyti­ cal model for arching in piled embankments Geotext Geomembr 39(7):78-102 https://doi.Org/10.1016/j.geotexmem.2013.07.005 33 King L, BouazzaA, Dubsky s, RoweRK, Gniel J,BuiHH (2019) Kinematics of soil arching in piled embankments Geotechnique 2019:1-18 https://doi.oig/10.1680/jgeotl8.P104 34 Nguyen B-P, Nguyen TT, Nguyen T, Guo w (2023) Analytical model for consolidation and bearing capacity of soft soil stabilized by combined PVD-deep cement mixing columns Bull Eng Geol Environ 82:286 https://doi.oig/10.1007/sl0064-023-03287-0 35 Nguyen MT (2006) The behavior of DCM (Deep cement mixing) columns under highway embankments by finite element analysis PhD Dissertation Pukyong National University Busan, Korea 36 Chai JC, Miura N, Sakajo s, Bergado DT (1995) Behavior of vertical drain improved subsoil under embankment loading Soils Found 35(4):49-61 37 Chai J-C, Shen S-L, Miura N, Bergado D-T (2001) Simple method of modeling PVD improved subsoil J Geotech Geoenviron Eng ASCE 127(11):965-972 38 Tran TA, Mitachi T (2008) Equivalent plane-strain modeling of vertical drains in soft ground under embankment combined with vacuum preloading Comput Geotech 35:655-672 39 Nguyen B-P, Yun D-H, Kim Y-T (2018) An equivalent plane strain model of PVD-improved soft deposit Comput Geotech 103:32-42 40 Navin MP, Filz GM (2005) Statistical analysis of strength data from ground improved with DMM columns Deep Mixing '05: International Conference on deep mixing best practice and recent advances, 145-154 41 Huang J, Han J (2009) 3D coupled mechanical and hydraulic mod­ eling of a geosyntheticreinforced deep mixed column-supported embankment Geotext Geomembr 27(4):272-280 42 Madhyannapu RS, Puppala AJ, Hossain s, Han J, Porbaha A (2006) Analysis of geotextile reinforced embankment over deep mixed soil columns: using numerical and analytical tools Geo­ Congress 2006: Modelling and Characterization of Deep Soil Cement, Atlanta 43 Yapage NNS, Liyanapathirana DS (2014) Two-dimensional par­ ametric study of geosynthetic column supported embankments Geosynth Int 21(3):213-232 44 Pham TA, Dias D (2021) Comparison and evaluation of analyti­ cal models for the design of geosynthetic-reinforced and pilesupported embankments Geotext Geomembr 49(3):528-549 45 Deng YF (2005) Interaction principle between deep mixing col­ umns and surrounding soils and determination method of column spacing Ph.D Dissertation, Southeast University, Nanjing, China, in Chinese 46 Chen L, Liu s, Han J, Zhang D (2009) Numerical analysis of consolidation of soft ground improved by the DJM-PVD com­ bined method In: Iskander M, Laefer DF, Hussein MH (eds) Contemporary topics in ground modification, problem soils, and geo-support, geotechnical special publication 187 ASCE, Reston, pp 321-e328 47 Forsman J (2001) Geovahvistetutkimus, Helsinki 48 Forsman J, Honkala A, Smura M (1999) Hertsby case: a col­ umn stabilised and geotextile reinforced road embankment on soft subsoil In: Brendenberg H, Holm G, Broms BB (eds) Dry mix method for deep soil stabilization Balkema, Rotterdam, pp 263-368 49 Brinkgreve RBJ, Zampich LM, Ragi Manoj N (2017) Plaxis: Finite element code for soil and rock analyses: Version 17 Balkema, Rotterdam 50 Broms BB (1999) Keynote lecture: Design of lime, lime/cement and cement columns In Int Conf., on Dry Mix Methods: Dry Mix rfi Springer 56 51 52 53 54 Page 12 of 12 International Journal of Geosynthetics and Ground Engineering Methods for Deep Soil Stabilization 1st ed., edited by H Bredenbeig, G Holm, B B Broms, 125-153 Rotterdam, Netherlands: Balkema Kivelo M (1998) Stabilization of embankments on soft soil with lime/cement columns PhD Thesis, Royal Institute of Technology Bruce DA (2002) An introduction to the deep mixing methods as used in geotechnical applications—VolumeHI: the verification and properties of treated ground”, FHWA-RD-99-167, Final Report, p 455 Nguyen B-P, Nguyen TT, Le TT et al (2023) Consolidation and load transfer characteristics of soft ground improved by combined PVD-SC column method considering finite discharge capacity of PVDs Indian Geotech J 53:127-138 Do T-N, Ou C-Y, Lim A (2013) Evaluation of factors of safety against basal heave for deep excavations in soft clay using the Springer (2023) 9:56 finite-element method J Geotech Geoenviron Eng ASCE 139(12):2125-2135 Publisher's Note springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations Springer Nature or its licensor (e.g a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is 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