Numerical modelling of compensation grouting above shallow tunnels

This paper describes the development of a numerical model for compensation grouting which is a useful technique for the protection of surface structures from the potentially damaging movements arising from tunnel construction. Pipes are inserted into the ground between the tunnel and the overlaying structure from an access shaft. Buildings on the surface are instrumented and movements are carefully monitored. Once the deformations exceed a certain Trigger Level, grout is injected into the ground to prevent damage. In the finite element model described here, compensation grouting is modelled by applying an internal pressure to zero‐thickness interface elements embedded in the mesh. An ‘observational algorithm’ is used, where the deformations of the surface are monitored and used to control the injection process. Example analyses of compensation grouting are given for three‐dimensional tunnel construction underneath a greenfield site. Different strategies are used to control the injection process and their effectiveness in preventing surface movement is assessed. The numerical model is shown to replicate general behaviour expected in the field and is capable of modelling the control of ground surface movements at a greenfield site. Copyright © 2005 John Wiley & Sons, Ltd.     

考虑蠕变性土工格栅加筋挡土墙应力与变形有限元分析

土工格栅加筋挡土墙在岩上加固工程中得到了广泛应用。采用粘弹塑性流变模型考虑地基和填士的流变性，采用作者所建议的绎验型粘弹性本构模型考虑土工格栅的蠕变性，对于土工格栅加筋挡土墒发展了非线性有限元数值分析方法，通过变动参数的对比计算与分析探讨了逐层填筑过程、加筋长度及间距布置方式等因素对土工格栅加筋挡土墙长期变形与应力特性的影响。计算与分析表明：填筑过程对面板侧向变形、格栅拉力与应变及地基中水平位移与竖向沉降具有较大的影响；加筋使墙后填土应力重新分布；面板位移、格栅拉力及应变在经历一段时间后趋于稳定状态。     

Factors affecting FFT gravimetric geoid determination precision

The Fast Fourier Transformation (FFT) has become a routine mathematical tool for the refinement of the Earth's gravity field, such as the computation of precise gravimetric geoid and terrain corrections, particularly over a large area. This paper presents ideas and methodologies to evaluate the accuracy of geoid undulation computations using FFT. A global geopotential model is used as a ‘ground truth’ gravity field model to assess the geoid determination precision by using FFT technique. It is demonstrated that special considerations must be given for a high precision FFT gravimetric geoid determination. A maximum of a few decimetres error could be introduced by the FFT algorithm if the gravity anomalies are not long wavelength filtered and/or no zero padding is applied.     

Photogrammetric techniques for monitoring tunnel deformation

This paper presents two innovative methods for tunnel monitoring that are based on digital photogrammetry. Both have been conceived to speed up operations that are currently accomplished by using engineering geodesy techniques and instruments. On the same time, proposed solutions are cheap and affordable. The first one is aimed at measuring relative deformations of transversal cross-section of tunnels. Some special targets are placed on the tunnel vault and their coordinates are measured by means of a small photogrammetric block made up of four images. A wire is used to setup the scale and to make all measurements comparable overtime. The second method can be applied for the measurement of vertical deformations along the longitudinal profile of tunnels. A new image-based approach called ‘photogrammetric levelling’ is discussed here, which is based on the metric rectification of each single image depicting a couple of special rods to be hung on levelling benchmarks. This technique can be used to replace traditional optical and digital level instruments. Both applications can be carried out by using a calibrated amateur camera. Some experiments in controlled and real environments allowed assessing performances and limitations of these techniques for operational surveys in tunnel monitoring.     

Probabilistic analysis of underground pillar stability

The majority of geotechnical analyses are deterministic, in that the inherent variability of the materials is not modelled directly, rather some ‘factor of safety’ is applied to results computed using ‘average’ properties. In the present study, the influence of spatially varying strength is assessed via numerical experiments involving the compressive strength and stability of pillars typically used in underground construction and mining operations. The model combines random field theory with an elasto‐plastic finite element algorithm in a Monte‐Carlo framework. It is found that the average strength of the rock is not a good indicator of the overall strength of the pillar. The results of this study enable traditional approaches involving factors of safety to be re‐interpreted as a ‘probability of failure’ in the context of reliability based design. Copyright © 2002 John Wiley & Sons, Ltd.     

混凝土面板堆石坝应力变形长期性状有限元模拟

为了获得混凝土面板堆石坝长期力学行为（尤其流变变形对混凝土面板堆石坝工作性状的影响）定量分析成果,运用ABAQUS有限元对国内某抽水蓄能电站混凝土面板堆石坝进行了数值模拟。采用考虑非线性强度的改进双屈服面流变模型描述堆石料长期力学性能,其中瞬时塑性变形采用改进双屈服面模型确定,而黏塑性流变变形采用指数衰减函数定义。有限元分析获得坝体、单元和面板在填筑期、蓄水期与运行期的应力与变形一般规律。结果表明：运行阶段堆石流变变形对混凝土面板堆石坝应力、变形性状产生显著影响。研究结论有益于进一步了解和合理预测混凝土面板的长期性能。     

Pile group settlement: A probabilistic approach

The uncertain settlement response of pile groups is determined using a ‘hybrid’ formulation and a first-order perturbation technique. The spatially varying soil modulus, which gives rise to the uncertainties in the pile group settlement, is modeled as a homogeneous random field. The random field is assumed to be one-dimensional since the ‘hybrid’ formulation does not account for horizontal variation in the soil properties. Using the proposed method, the coefficient of variation of the pile group settlement is computed. The single-pile solutions obtained compare favorably with the solutions from a conventional stochastic finite element analysis. Pile groups of sizes ranging from two to twenty-five piles are studied. It is observed that the coefficient of variation is not significantly affected by the pile spacing as well as the group size. By defining an appropriate performance function, the reliability index of a pile group system is also found to be approximately the same as that of a single-pile system. These observations suggest that the solutions for a single pile may be used to estimate the uncertainties in the settlement response of pile groups.     

Performance of reinforced,DMM column-supported embankment considering reinforcement viscosity and subsoil’s decreasing hydraulic conductivity

It has been widely accepted that reinforcement made of polyethylene and polypropylene is susceptible to creep and soil’s hydraulic conductivity varies with its void ratio. However, unfortunately there is no available sensitivity analysis on time-dependent embankment behaviour taking either reinforcement viscosity or time varying hydraulic conductivity of subsoil into consideration. The influence of geosynthetic reinforcement viscosity and decreasing hydraulic conductivity with consolidation on the time-dependent performance of embankments with floating columns is investigated using a fully 3D coupled model. For an embankment at the working height corresponding to a post-consolidation polypropylene geotextile strain of about 5%, it is shown that the assumption of constant hydraulic conductivity and the failure to consider the viscous behaviour of geosynthetic reinforcement can underestimate time-dependent embankment deformations (including differential crest settlement and horizontal toe movement). The effects of factors including the foundation soil, reinforcement stiffness, column stiffness, column spacing, column type (floating and fully penetrating), and construction rate, on the time-dependent behaviour of column supported embankments are explored.     

Analytical‐numerical solution for stress distribution around tunnel reinforced by radial fully grouted rockbolts

This paper presents an analytical‐numerical approach to obtain the distribution of stresses and deformations around a reinforced tunnel. The increase in the radial stress of the reinforced tunnel, based on the performance of a bolt, is modeled by a function, which its maximum value is in the vicinity of the bolt periphery and it exponentially decreases in the far distance from the bolt. On the basis of this approach, the shear stiffness between the bolt and the rock mass and the shear stress distribution around the bolt within the rock mass are also analytically obtained. The results are compared with those obtained by the assumption of ‘uniform increase of radial stress’ method, which is made by the previous studies. The analyses show when the bolts' spacing is large, the safety factor must be increased if the ‘uniform increase of radial stress’ method is used for the design. Finally, a procedure is introduced to calculate the non‐equal deformation of the rock mass between the bolts at any radius that can be useful to compute the bending moment in shotcrete layer in New Austrian Tunnelling Method (NATM) approach. Copyright © 2016 John Wiley & Sons, Ltd.     

软岩矿区地面下沉及其对工业建筑物影响分析

根据鲁中软岩矿区开采引起地面下沉及地面井塔楼等建筑物倾斜变形的工程实际,采用非确定性研究方法,将深埋破碎金属矿体开采引起地面沉陷或岩体移动变形这一客观现象视为一随机事件,建立了开采引起地面沉陷或岩体移动变形分析的数学模型。利用该模型可对开采引起地面沉陷及其对地表工业建筑物影响进行具体分析评价。通过具体计算分析结果表明,在软岩地层条件下矿体开采地表移动变形的影响范围有随着采深的增加而逐渐增大的趋势。     

Homogenization framework for three‐dimensional elastoplastic finite element analysis of a grouted pipe‐roofing reinforcement method for tunnelling

This paper deals with the grouted pipe‐roofing reinforcement method that is used in the construction of tunnels through weak grounds. This system consists on installing, prior to the excavation of a length of tunnel, an array of pipes forming a kind of ‘umbrella’ above the area to be excavated. In some cases, these pipes are later used to inject grout to strengthen the ground and ‘connect’ the pipes. This system has proven to be very efficient in reducing tunnel convergence and water inflow when tunnelling through weak grounds. However, due to the geometrical and mechanical complexity of the problem, existing finite element frameworks are inappropriate to simulate tunnelling using this method. In this paper, a mathematical framework based on a homogenization technique to simulate ‘grouted pipe‐roofing reinforced ground’ and its implementation into a 3‐D finite element programme that can consider stage construction situations are presented. The constitutive model developed allows considering the main design parameters of the problem and only requires geometrical and mechanical properties of the constituents. Additionally, the use of a homogenization approach implies that the generation of the finite element mesh can be easily produced and that re‐meshing is not required as basic geometrical parameters such as the orientation of the pipes are changed. The model developed is used to simulate tunnelling with the grouted pipe‐roofing reinforcement method. From the analyses, the effects of the main design parameters on the elastic and the elastoplastic analyses are considered. Copyright © 2004 John Wiley & Sons, Ltd.     

Relationship between small and large strain solutions for general cavity expansion problems in elasto-plastic soils

This paper presents a closed-form relationship between small and finite strain cavity expansion solutions. Its derivation is based on the non-linearly elastic–perfectly plastic cylindrical (or spherical) problem considering a general Mohr’s criterion and constant plastic dilatancy. It is shown, however, that it is sufficiently accurate for general expansion problems not obeying plane-strain rotationally (or spherically) symmetric conditions and involving strain-hardening/softening constitutive behaviour. Therefore, this relationship quantifies the error stemming from the computational assumption of small deformations and provides a simple and efficient way of accounting for geometric non-linearity based entirely on conventional computational methods: ‘self-correction’ of small strain analyses results.     

The Impact of Grain Crushing on Road Performance

This paper presents the results of a study of grain crushing in road construction and its effect on road behaviour. Sieve analyses of field samples confirmed that grain crushing occurs during compaction of the base layer despite the good quality of aggregates used. Laboratory testing indicated that grain crushing reduces the resilient modulus of the aggregate material by half and increases the permanent deformations by onefold to threefold depending on the state of density and stresses considered. Road design and analyses undertaken to delineate the effect of grain crushing on performance showed that particle breakage yields a significant increase in rutting and longitudinal and alligator cracking of roads.     

Simplified numerical modelling of pile penetration – the press‐replace technique

This paper presents a simplified finite element analysis technique, the ‘Press‐Replace’ technique, to model pile penetration problems in geotechnical engineering, particularly, pile jacking. The method is employed in standard finite element analysis software. The method involves a straining and a consequent geometry update phase. First, a cone penetration test in (undrained) clay is modelled and compared with the results of analytical, semi‐analytical and more advanced finite element techniques. The model sensitivity for the step size and mesh is investigated using a hypoplastic constitutive model. An optimum way of modelling based on the numerical performance is shown. Copyright © 2015 John Wiley & Sons, Ltd.     

Radial Deformations Induced by Groundwater Flow on Deep Circular Tunnels

Summary. The magnitude and distribution of ground deformations around a tunnel are often monitored during construction and provide key information about ground-support interaction and ground behavior. Thus it is important to determine the effects of different parameters on ground deformations to accurately and effectively evaluate what contributes to ground and support behavior observed during excavation. This paper investigates one such relation: the effects of seepage on radial deformations. A number of numerical analyses have been conducted with the following assumptions: deep circular unsupported tunnel, elastic ground, isotropic far field stresses, dry ground or saturated ground with steady-state water seepage. The analyses cover a wide range of tunnel sizes, effective stresses, and pore pressures. Results from the numerical simulations confirm previous analytical solutions for normalized radial deformations behind the face (i.e. on the tunnel side of the face) of a tunnel excavated in dry ground, and have been used to propose a new analytical formulation for normalized radial displacements ahead and behind the tunnel face for both dry and saturated ground with water flow. Water seepage substantially increases the magnitude and distribution of the normalized radial deformations ahead of the face and at the tunnel face, but does not change much the displacement distribution behind the tunnel face.     

Determining basic characteristics of stars from evolutionary computations

A technique for determining a star’s radius from its atmospheric characteristics (effective temperature, surface gravity, and metallicity) is realized based on modernmodel computations of the stellar internal structure and evolution. The atmospheric characteristics can also be used to find the mass and luminosity of the star. The star’s rate of evolution and the initial mass function are taken into account when determining the stellar characteristics, increasing the correctness of the results. Computations of stellar evolution of with and without the stellar rotation taken into account make it possible to remove ambiguity due to missing data on the star’s rotational velocity. The results are checked and uncertainties estimated using stars occupying two heavily populated regions in the Hertzsprung–Russell diagram that have been well studied using various methods: the main sequence and red giant branch. Good agreement with the observations is achieved; there are almost no systematic deviations of the derived point estimates of the fundamental characteristics. The metallicities of the individual components of eclipsing variable stars are estimated using observational data on for such stars displaying lines of both components in their spectra. These metallicities were determined as a function of the stellar masses in a way that eliminates systematic deviations in the derived fundamental characteristics.     

Application of remote sensing and GIS for delineating groundwater recharge potential zones of Kovilpatti Municipality,Tamil Nadu using IF technique

During the last three decades, remotely sensed data (both satellite images and aerial photographs) have been increasingly used in groundwater exploration and management exercises. An integrated approach has been adopted in the present study to delineate groundwater recharge potential zones using RS and GIS techniques. IRS-1C satellite imageries and Survey of India toposheets are used to prepare various thematic layers viz. geology, soil, land-use, slope, lineament and drainage. These layers were then transformed in to raster data using feature to raster converter tool in ArcGIS 9.3 software. The raster maps of these factors are allocated a fixed score and weight computed from Influencing Factor (IF) technique. The weights of factors contributing to the groundwater recharge are derived using aerial photos, geology maps, a land use database, and field verification. Subjective weights are assigned to the respective thematic layers and overlaid in GIS platform for the identification of potential groundwater recharge zones within the study area. Then these potential zones were categories as ‘high’, ‘moderate’, ‘low’, ‘poor’. The resulted map shows that 19 % of the area has highest recharge potential, mainly confined to buried pediplain, agriculture land-use and river terraces (considerable amount of precipitated water percolates into subsurface), 28 % of the area has moderate groundwater recharge potentiality and rest of the area has low to poor recharge potentiality. The residual hills and linear ridges with steep slopes are not suitable for artificial recharge sites. Finally, 13 % of total average annual precipitated water (840 mm) percolates downward and ultimately contributes to recharge the aquifers in the Kovilpatti Municipality area. The paper is an attempt to suggest for maintaining the proper balance between the groundwater quantity and its exploitation.     

Lower bound limit analysis using finite elements and linear programming

This paper describes a technique for computing lower bound limit loads in soil mechanics under conditions of plane strain. In order to invoke the lower bound theorem of classical plasticity theory, a perfectly plastic soil model is assumed, which may be either purely cohesive or cohesive-frictional, together with an associated flow rule. Using a suitable linear approximation of the yield surface, the procedure computes a statically admissible stress field via finite elements and linear programming. The stress field is modelled using linear 3-noded traingles and statically admissible stress discontinuities may occur at the edges of each triangle. Imposition of the stress-boundary, equilibrium and yield conditions leads to an expression for the collapse load which is maximized subject to a set of linear constraints on the nodal stresses. Since all of the requirements for a statically admissible solution are satisfied exactly (except for small round-off errors in the optimization computations), the solution obtained is a strict lower bound on the true collapse load and is therefore ‘safe’. A major drawback of the technique, as first described by Lysmer,¹ is the large amount of computer time required to solve the linear programming problem. This paper shows that this limitation may be avoided by using an active set algorithm, rather than the traditional simplex or revised simplex strategies, to solve the resulting optimization problem. This is due to the nature of the constraint matrix, which is always very sparse and typically has many more rows that columns. It also proved that the procedure can, without modification, be used to derive strict lower bounds for a purely cohesive soil which has increasing strength with depth. This important class of problem is difficult to tackle using conventional methods. A number of examples are given to illustrate the effectiveness of the procedure.     

Influential factors in evaluating the construction pore pressure in earth dams by using UDAM program

The aim of this article is to discuss about the influential parameters affecting the state of the pore pressure within the low permeability section of an earth dam body during the periods of construction, immediately after construction, and also during some times elapsing after construction. Because the condition of soil in constructing earth dams is usually unsaturated, so the matter of unsaturated soils should be considered here and a special finite element program suitable to this topic needs to be applied. The finite element program used in this study is the UDAM finite element program which has been compiled specifically for illustrating the behavior of unsaturated soils. The results of the UDAM computations are discussed in view of the pore water pressure developed within the body of dam slope during the stages of construction, and its maximum positive values immediately after the construction and its variations in the post-construction times are shown. Because the positive pore pressure decreases the shear strength of soil and the negative pressure (i.e. suction) increases the strength, the state of slope stability is correlated with the influential factors which can affect the situation of pore pressure distribution within a given section. Therefore, based on the present computations, the effect of height of embankment, initial degree of saturation, coefficient of permeability, degree of compaction and finally the effect of elapsing time are illustrated.     

Ability and limits of numerical methods for the design of deep construction pits

The evaluation and prediction of deformations is becoming a main accent for the work of geotechnical engineers. Numerical methods are a powerful instrument to solve this task. Hence, in order to get reliable results, some requirements on the use of finite elements has to be considered. The calculation is limited by the quality of the models and procedures used in practice. The limits are discussed in this paper. It also deals with the results of back-analysis of deformations of construction pits. The numerical results are compared with conventional calculations.