Consolidation behavior of soil–cement column improved ground

Columnar inclusion is one of the effective and widely used methods for improving the engineering properties of soft clay ground. This article investigates the consolidation behavior of composite soft clay ground using both physical model tests under an axial-symmetry condition and finite element simulations using the PLAXIS 2D program. It was determined that the final settlement and the rate of consolidation of the composite ground depended on the stress state. For an applied stress that is much lower than the failure stress, the final settlement of the composite ground was lower, and the consolidation was rapid. When the soil–cement column failed, the stress on the column suddenly decreased (due to strain-softening); meanwhile, the stress on the soil increased to maintain the force equilibrium. Consequently, the excess pore pressure in the surrounding clay increased immediately. The cracked soil–cement column acted as a drain, which accelerated the dissipation of the excess pore pressure. The consolidation of the composite ground was mainly observed in the vertical direction and was controlled by the area ratio, which is the ratio of the diameter of the soil–cement column to the diameter of the composite ground, a. The stress on the column was shown to be low for a composite ground with a high value of a, which resulted in less settlement and fast consolidation. For a long soil–cement column, the excess pore pressures in the surrounding clay and the column were essentially the same at a given consolidation time throughout the improvement depth. It is proposed that the soil–cement column and surrounding clay form a compressible ground, and the consolidation occurs in the vertical direction. The composite coefficient of consolidation (c_v(com₎) that was obtained from the physical model test on the composite ground can be used to approximate the rate of consolidation. This approximation was validated via a finite element simulation. The proposed method is highly useful to geotechnical engineers because of its simplicity and reliable prediction.     

A practical evaluation of the surcharge preload period in staged construction subject to creep

Soft clay exhibits creep behavior, but simple methods of surcharge preload assessment generally do not take into account creep during primary consolidation. Because Yin–Graham’s model can predict both primary and secondary settlement, it is employed in this paper to obtain the formulae for critical settlement at the unloading time during surcharge preload and for final settlement at the end of the service life. Because “aged” soft natural clay exhibits obvious apparent preconsolidation pressure during a long-term sedimentary history as a result of creep effects and because the field permeability coefficient is considerably larger than the laboratory permeability coefficient, most field measurements indicate that the theoretical excess pore pressure based on Terzaghi’s theory is greater than the measured excess pore pressure even in soft natural clay with obvious viscous behavior. Because of the widespread application of the degree of consolidation in terms of effective stress based on Terzaghi’s theory in real preload projects, the analytical solution for the surcharge preload period subject to creep is derived through the combination of Yin–Graham’s model and Terzaghi’s theory for consolidation. Compared with the existing solution considering secondary settlement, the formula for the preload period presented in this paper is easily applied to assess the preload period using a chart. The case study described indicates that when the consolidation parameters of Terzaghi’s theory are calculated from field-measured excess pore pressure in preload tests, the surcharge preload period determined as described in this paper is suitable for preload design and performance.     

弹黏塑性模型及其在预压处理软基沉降计算中的应用

以准确计算预压荷载作用下软土路基的工后沉降为目的,分析了不同预压法加固软土地基时土体的应力变化。提出了用弱化应力路径变化过程的弹黏塑性模型表示软黏土的应力-应变关系。结合经典比奥固结理论,推导了预压荷载作用下土体沉降计算的有限单元法。通过具体算例,验证了所提方法。结果表明：（1）不同预压方法的加固机制和应力路径均不相同。堆载预压法加固软基是一不等向的正压固结过程,真空预压法则是在负压作用下的等向固结过程;（2）弹黏塑性模型是不受瞬时施加应力的大小及具体应力路径变化过程影响的软土流变模型,运用于预压荷载作用下的软基时具有不考虑应力路径和不划分主次固结的优越性;（3）在比奥固结理论中,用弹黏塑性模型反映软土的物理方程时,可计算软基考虑了弹黏塑变形性质的固结沉降和工后沉降;（4）弹黏塑性模型的软土体黏性参数? /V和塑性参数? /V对竖向位移都有比较明显的影响。     

沉积泥砂非线性大变形固结沉降计算模型

沉积形成的水底黏性泥砂自重固结过程表现出显著非线性大变形固结特征,应采用大变形固结理论进行泥砂沉积固结计算。基于软黏土一维非线性大应变固结理论,应用有效应力、渗透系数与孔隙比间扩展幂次函数固结本构关系,由达西定律、有效应力原理、连续介质方程等建立大变形固结控制方程,根据固结单元孔隙水渗流、单元变形与泥砂沉积层固结沉降耦合关系形成黏性泥砂大变形自重固结数值模型。泥砂自重作为固结荷载,数值模型假定沉积泥砂各向同性且固结沉降应变、孔隙水渗流仅发生于竖直方向,为一维单向沉积固结过程;采用泥砂沉降柱试验确定泥砂非线性扩展幂次函数关系参数。模型应用中,划分竖向固结单元,由沉积泥砂固结本构关系确定各固结单元有效应力及超孔隙水应力,通过超孔隙水应力时间维度上的消散过程及各固结参数间的耦合关系计算泥砂固结沉降。数值模型计算结果表明,沉积黏性泥砂自重固结初期表现为有效应力调整过程,初始有效应力与孔隙比根据固结本构关系匹配调整为扩展幂次函数关系;沉积泥砂应变与应力固结度存在20%左右误差,泥砂固结沉降发展快于超孔隙水应力消散过程,证明沉积泥砂固结沉降变形的发展与超孔隙水应力消散并非同步耦合。计算模型应用于室内沉降柱试验模拟淤积黏性泥砂自重固结沉降预测中,模型输出与试验结果符合良好。     

软黏土层一维有限应变固结的超静孔压消散研究

根据土力学固结理论计算分析软黏土层固结过程的超静孔隙水压力值,确定软黏土体固结过程的强度增长,对排水固结法处理软土地基至关重要。软黏土层固结过程中土体变形较大时,有限应变固结理论和小应变固结理论计算分析软黏土固结所得结果差异较大。利用非线性有限元法及程序,通过对软黏土层固结工程算例的计算结果分析,研究了有限应变固结理论和小应变固结理论计算分析软黏土层一维固结超静孔压值消散的差异;探讨了软黏土体一维固结过程中,几何非线性、土体渗透性变化和压缩性变化对超静孔隙水压力消散的影响。研究结果表明,当土体的变形较大时,有限应变固结理论计算出的超静孔压要比小应变固结理论得到的值消散的更快。考虑土体固结过程中渗透性的变化时,超静孔压消散变慢;可用软黏土渗透性变化指数ck 反映渗透性变化对超静孔压消散的影响,渗透性变化指数ck值越小、超静孔压消散越慢。固结过程中软黏土压缩性的大小及变化也影响超静孔压的消散,可用软黏土的压缩指数cc反映固结过程中压缩性的大小及变化对超静孔压消散的影响,软黏土的压缩指数cc越小,固结过程软黏土层中的超静孔压消散越快。     

考虑应力水平的软土固结系数计算与试验研究

在固结度计算中通常将固结系数视为常数,实际上并非如此.通过研究软土固结系数在压缩过程中随应力水平变化的规律,推导出正常固结和超固结状态下固结系数与有效应力之间的表达式.在正常固结状态下,当应力水平小于在前期固结压力时,固结系数随应力水平的增加而增加;当超过前期固结压力后,固结系数随应力水平的增加而减小;在超固结状态下,固结系数随应力水平的增加而增加,在一定程度后趋于平稳.室内试验结果进一步说明了和验证固结系数这一特点.推导的固结系数与固结应力水平关系表达式是可行的,其计算值与试验结果的变化趋势一致,大小基本吻合,将其用于计算变形速率和固结度中,可提高准确性.     

考虑变渗透系数的饱和黏土一维流变固结分析

为进一步探讨饱和黏性土的弹黏塑性和变渗透性对一维固结进程的影响,引入考虑时间效应的统一硬化（UH）本构模型描述饱和黏土的弹黏塑性,并用Taylor的经验关系式表示其渗透系数与孔隙比的关系,修正了太沙基一维固结理论,并利用有限差分法对方程进行求解。通过与一维流变固结试验结果对比,验证本文计算方法的有效性以及UH模型的适用性。在此基础上,讨论了UH模型参数、压缩指数与渗透指数的比值以及荷载强度等对固结过程的影响。计算结果表明:饱和黏土的黏滞性使得在固结初期地基内部出现了孔压升高现象,并减缓了固结中后期地基孔压的整体消散,增大了地基的沉降量,并且这种现象随着初始超固结参数的增大而更明显;另外,随着压缩指数与渗透指数比值的减小,地基固结进程会加快,但地基最终沉降量不受影响;同时,在固结后期,当压缩指数不大于渗透指数时,较小荷载强度对应的地基内孔压消散较慢,然而,当压缩指数大于渗透指数时,荷载强度对孔压消散的影响则相对很小。     

Effect of overburden pressure and degree of saturation on compressibility characteristics

The settlement of a structure founded on clay comprises of immediate and consolidation settlements. In the case of clays, consolidation settlement is more than immediate settlement. The parameters influencing consolidation settlement of a normally loaded clay layer are degree of saturation (S%), void ratio (e) of soil prior to excavation, amount of overburden (σ_o) removed, amount of rebound and intensity of loading (σ) upon building superstructure. This paper presents the effect of the above parameters on compressibility characteristics of a clay. The different steps undertaken for footing construction were simulated in the laboratory. Remoulded clay samples were prepared from oven-dry fraction passing 425 μm sieve. The density of the samples was kept constant at 13 kN/m³. Degree of saturation was varied at 25%, 50%, 75% and 100%. The surcharge on the samples (overburden in the case of field clay layer) was varied as 25 kPa, 50 kPa and 100 kPa. Compressibility characteristics such as initial compression under the applied surcharge (overburden), rebound upon removal of surcharge and recompression were studied through one-dimensional consolidation tests. The rate and amount of initial compression, rebound, e-σ and e-log σ curves, compression index (C_c), coefficient of compressibility (a_v) and coefficient of volume compressibility (m_v) were studied.     

吹填场区软黏土地基的次固结特性研究

针对天津中心渔港吹填场区软黏土地基进行了一系列的固结压缩试验,获得应力、应变与时间的关系,对比分析了吹填土层和天然沉积土层的固结和次固结特性,为吹填场区软黏土地基变形模型建立及长期工后沉降预测提供理论依据。研究表明,吹填土和天然沉积土的应变速率与时间双对数曲线具有很好的线性相关性;处理后吹填土含水率和压缩性较低,天然沉积土含水率和压缩性高;随荷载P增大,吹填土的次固结系数Ca?变化不大,天然沉积土的次固结系数Ca先增大后减小,最终趋于稳定;次固结系数Ca与压缩指数Cc具有良好的线性相关性,其随时间的增加均呈对数下降趋势。     

基于一维和三维固结挤土桩沉降时效计算分析

饱和软黏土地基中的挤土桩,施工引起的桩侧土体超孔隙水压力消散和竖向荷载引起的桩底土体固结是导致其沉降的主要因素。基于三维固结理论,研究了桩侧地基土再固结沉降的变化规律,并从桩-土相互作用的原理出发,结合边界条件,推导出了在桩侧地基土再固结沉降的作用下挤土桩沉降的计算公式。运用太沙基一维固结理论并采用分层总和法计算竖向荷载作用下桩底土体的沉降。提出了饱和软土中挤土桩沉降时效的计算方法。并对工程实例进行了计算分析,其结果符合工程实际沉降规律。     

Analytical solution for 1D consolidation under haversine cyclic loading

Presented and discussed in this paper is an exact analytical solution of the nonhomogeneous partial differential equation governing the conventional one‐dimensional consolidation under haversine repeated loading. The derived analytical solution to the 1D consolidation equation is compared with the numerical solution of the same consolidation problem via FEM. The series solution takes into account the frequency of repeated loading through a dimensionless time factor T₀. The paper reveals that an increase in the frequency of imposed repeated haversine loading (a decrease in period of repeated loading) causes an increase in the number of cycles required to achieve the steady state, whereas the effect of frequency on the maximum excess pore water pressure at the bottom of a clay layer with permeable top and impermeable bottom for the range of frequencies studied is generally insignificant. The effective stress at the bottom of the clay deposit with permeable top and impermeable bottom increases with time but with some fluctuations without changing the sign. These fluctuations become more pronounced for increasing values of T₀. An increase in T₀ also causes an increase in maximum effective stress. Copyright © 2013 John Wiley & Sons, Ltd.     

Criteria of Acceptance for Constant Rate of Strain Consolidation Test for Tropical Cohesive Soil

In this study, the rapid consolidation equipment (RACE) was developed as an alternative device to the conventional consolidation test using Oedometer, consuming merely a few hours for the whole precedure to determine the consolidation characteristics of cohesive soil. RACE operates based on the constant rate of strain (CRS) consolidation theory, which is a continuous loading method of testing, requiring a good estimation of the loading rate such that it is ideal for the achievement of steady state condition during testing. The steady state condition is achieved when the c _v values from drained and undrained face of CRS converged with the c_v from Oedometer test. A slightly modification has been made on the normal constant rate of strain (CRS) test by proposing a direct back pressure system to the specimen using a tube to saturate the soil sample. This research has produced a set of criteria for determining the suitable rate for the rapid consolidation test based on the ratio of normalized strain rate, β, and proposed a new coefficient in terms of a ratio of β to clay fraction (CF), as a part of new criteria for testing a fine soil. Four types of sample were tested with different rates of strain using the RACE and their results were compared with those conducted using the Oedometer on the same soil type, from which fairly good agreements were evident in many specimens. It was found from the study that the minimum value of normalized strain rate, β, for the CRS test is 0.005 and for the u _a /σ _v ratio is suggested as 0.01. Also, the maximum β/CF for soils with clay friction lower and higher than 50 % are 0.008 and 0.001, respectively. The minimum β/CF value for both conditions is 0.0001.     

Effect of Stern-layer on the compressibility behaviour of bentonites

The Stern theory as applicable to interacting parallel clay platelet systems was used to study the compressibility behaviour of bentonites. For a constant surface electrical potential, the distribution of the total electrical charge among the Stern-layer and the Gouy-layer was found to have significant influence on the electrical potential at the midplane between clay platelets. Consideration of the Stern-layer was found to reduce the repulsive pressure or the swelling pressure between clay platelets at large platelet spacing, whereas the repulsive pressure increased significantly when the interacting Gouy-layers were pushed aside. A far greater repulsive pressure was noted for Ca-bentonite than that occurred for Na-bentonite at a platelet distance close to 1.0 nm. Similarly, strong interaction between clay platelets was noted due to suppressed Gouy-layers when the bulk fluid concentration was increased. The repulsive pressure generated due to the overlapping of the Stern-layers was found to be sensitive to changes in the specific adsorption potential, the dielectric constant of the pore fluid in the Stern-layer, and the surface electrical potential. Comparisons of the calculated pressure–void ratio relationships from the Stern theory and the Gouy-Chapman diffuse double layer theory with the experimental consolidation test results of Na- and divalent-rich bentonites showed that, in general, the Stern theory improved the predictions of pressure–void ratio relationships, particularly for pressures greater than 100 kPa; however, strong agreements were lacking in all the cases studied.     

A Critical Reappraisal of the Average Degree of Consolidation

Since its development in 1925, Terzaghi’s expression for the average degree of consolidation has been extensively used in teaching, research and consulting to determine the consolidation settlement that has taken place at a specific time in a geotechnical problem. Recent research by the authors has revealed that the term degree of consolidation is not very meaningful when the initial pore pressure distribution is highly skewed. In view of these findings, a review of all aspects of Terzaghi’s consolidation theory is required, particularly when considering asymmetric initial pore pressure distributions. An exact method for estimating the consolidation settlement of a clay stratum using the mass flux per unit area out of the drainage boundaries is proposed. Graphical representations of both exact and traditional methods reveal identical average degree of consolidation curves. In light of this, Terzaghi’s expression for the average degree of consolidation was re-examined. Upon application of the original governing one-dimensional consolidation equation, it was found that the traditional and exact methods for calculating the average degree of consolidation are identical. Thus, the widespread proclivity for geotechnical engineers to use Terzaghi’s average degree of consolidation equation to estimate the consolidation settlement of a clay stratum has been validated.     

结构性土一维非线性大应变固结半解析解

以结构性较强的天然饱和软黏土为研究对象,考虑了沉积作用对其自重应力的影响,以及压缩性和渗透性的非线性变化,推导了任意加载条件下结构性土一维大应变固结控制方程,并采用半解析的方法对方程进行求解计算。再将其退化为无结构性的饱和软黏土固结解,与已有的大应变固结解进行了对比,验证了该解的正确性。最后将该半解析解计算结果与小应变固结理论解、不考虑结构性的固结理论解计算结果进行对比分析。结果表明：大应变固结理论的沉降计算值大于小应变固结理论的计算值,且二者的差值随着荷载的增加而增加;当考虑土体的结构性时,地表沉降计算值小于不考虑土体结构性的沉降计算值。     

Interaction of longitudinal surface settlements for twin tunnels in shallow and soft soils: the case of Istanbul Metro

Increasing demands on infrastructures increases the attention on shallow soft ground tunneling methods in urbanized areas. Especially, in metro tunnel excavations, it is important to control the surface settlements observed before and after excavation, which may cause damage to surface structures. To solve this problem, earth pressure balance machines (EPBMs) have widely been used throughout the world. This study focuses on surface settlement measurements, the interaction of twin tunnel surface settlement, and the relationship between shield parameters and surface settlement for parallel tunnels using EPBM shields in clay and sand soils. In this study, the tunnels were excavated using two EPBMs. The tunnels were 6.5 m in diameter, as twin tubes with a 14 m distance from center to center. The EPBM in the first tube followed about 100 m behind the other tube. Segmental lining with 1.4 m of length was employed as a final support. The results from this study showed that (1) the most important parameters for the maximum surface settlements are the face pressure and backfill; (2) in twin tunnel excavation with EPBM for longitudinal profile, the settlement rate reached its peak value when the shield came to the monitoring section and this peak value continued until the shield passed the monitoring section; (3) every shield affected the other tunnel’s longitudinal surface settlement profile by approximately 35–36.8 %; (4) S _A, S _B and S _C values were found to be 38.0, 35.8 and 26.2 %, respectively for an EPBM, and (5) ensuring good construction quality is a very effective way to control face stability and minimize surface settlement.     

Consolidation of sensitive clay with vertical drain

The coefficient of consolidation is one of the most important parameters that control the rate of consolidation. Conventional consolidation theories assume that the coefficient of consolidation is constant during the whole consolidation process. In the case of sensitive clay, the coefficient of consolidation is strongly dependent on the level of effective stress of clay. With the dissipation of pore water pressure and the increase of effective stress, the soil structure of the upper subsoil is gradually destroyed downwards and its coefficient of consolidation becomes smaller. At the same time, the coefficient of permeability of the vertical drains drops down because of the kinking or bending effect. The destructured upper subsoil and the kinking of the vertical drain hinder the dissipation of the pore pressure in the lower subsoil. This paper presents a model to describe the above important phenomena during the consolidation of sensitive clay with vertical drain. The solution for proposed model can be obtained by extending the closed‐form solution of the consolidation of double‐layered ground with vertical drain by the interactive method introducing the concept of the moving boundary and the reduction of discharge capacity of vertical drain. The numerical results obtained from the finite element method package PLAXIS (Ver. 7.2) are adopted to compare those obtained from the present algorithm. Moreover, the rationality of the moving boundary is explained by the distributions of the excess pore water pressure in natural soil zone along the radial direction. Wenzhou airport project is taken as a case study in this paper. The results for the sensitive soil with decaying sand drain agree very well with the in situ measured data. The calculated results can properly explain two general phenomena observed in the consolidation of soft sensitive soil ground with vertical drains: one is that the time to achieve the same consolidation degree is much longer under heavy loading than that under light loading; the other is that the consolidation speed is much slower in the lower subsoil than in the upper subsoil. Finally, it is indicated that the vertical drains can decrease the hindrance effect of the destructured subsoil. Copyright © 2007 John Wiley & Sons, Ltd.     

A general semi-analytical solution for consolidation around an expanded cylindrical and spherical cavity in modified Cam Clay

This paper presents a general semi-analytical solution for undrained cylindrical and spherical cavity expansion in Modified Cam Clay (MCC) and subsequent consolidation. The undrained cylindrical and spherical cavity expansion response in MCC model is obtained through the similarity solution technique. Then, the subsequent consolidation process around the cavity is governed by the classical partial differential equation for consolidation. Finite Difference Method (FDM) is selected for solving the consolidation equation numerically. The proposed semi-analytical solution is validated by comparing the prediction of the dissipations of the pore pressure with Randolph’s closed-form solution for elastic-perfectly plastic soil. Parametric study shows that G₀/p₀′, R and M have significant influence on the cavity wall excess pore pressure dissipation curve, while it is not sensitive to the value of ν′. It is also found that the negative pore pressure generates around the expanded cylindrical and spherical cavity wall during the consolidation process when R > 5 for typical Boston blue clay. The developed solution has potential applications in geotechnical problems, such as the pile foundation, in-situ test, tunnel construction, compaction grouting, and so forth.     

Finite element analysis of consolidation of layered clay soils using an elastic visco-plastic model

This paper presents a general one-dimensional (1-D) finite element (FE) procedure for a highly non-linear 1-D elastic visco-plastic (1-D EVP) model proposed by Yin and Graham for consolidation analysis of layered clay soils. In formulating the 1-D FE procedure, a trapezoidal formula is used to avoid the unsymmetry of the stiffness matrix for a Newton (modified Newton) iteration scheme. Unlike many other 1-D FE approaches in which the initial in situ stresses (or stress/strain states) are considered indirectly or even not considered, the initial in situ stress/strain states are taken into account directly in this paper. The proposed FE procedure is used for analysis of 1-D consolidation of a clay with published test results in the literature. The FE modelling results are in good agreement with the measured results. The FE model and procedure is then used to analyse the consolidation of a multi-layered clay soils with a parametric study on the effects of the variations of creep parameters in Yin and Graham's 1-D EVP model. It is found that the creep parameters ψ/V and t₀ have significant influence on the compression and porewater pressure dissipation. For some boundary conditions, changes of parameters in one layer will have some effects on the consolidation behaviour of another layer due to the different consolidation rates. Finally, the importance of initial stress/strain states is illustrated and discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

饱和土体小孔扩张问题的弹塑性解析解

将土体在圆孔扩张过程中的应力分布分为三个区域，基于修正剑桥模型，推导了圆孔扩张过程中土体在三个区域的超孔隙水压力的解析表达式，对比分析了固结比对土体中应力分布的影响。分析推导可为沉桩、旁压试验、静力触探等岩土工程问题提供理论依据。