道路毕业设计 中英文翻译

P J Gräbe1∗and F J Shaw2

1Department of Civil Engineering,University of Pretoria,Pretoria, South Africa

2Transnet Freight Rail(Track Technology),Track Testing Centre, Jeppestown,South Africa

手稿是在2009年12月9日收到并被录取修订后的2010年3月17日出版。

DOI:10.1243/09544097JRRT371

文摘：南非国有铁路货运物流公用事业公司监视一条2004建造的在南非煤线上的新的轨道地基，这个网站的一个主要组成部分康复工程，旨在增加的容量线来维持未来增长的年度吨位。复杂的仪表用于测量弹性和永久变形道基础。初步研究结果在建设新轨道的基础不久后。收集的5年时间的永久变形结果,现在发表给长期行为的轨道基础提供新的了解。永久变形的测量用来计算轨道基础的预期设计寿命。结果是用来预测永久变形,并最终设计轨道的基础在载重加载条件的寿命。这项研究为鉴于持续的资本扩张计划康复工程和其他载重线提供了科学依据。

关键词：永久变形、弹性变形、跟踪基础,基础设计,设计寿命预测

1说明

1.1背景

南非的煤炭线是一个煤炭出口线连接有大约40个矿山从普马兰加煤田煤码头到理查德湾(RBCT)。这个Ogies/Blackhill-RBCT线路在1976年开通作为一个单一的线路,随后在1983–19年翻了一番。这条线路最初是设计来处理76组18.5吨/车轴重年产2100万吨的马车队。这条线路改造多年来荷载200马车队(26吨/轴),总长2.5公里长,总共20800吨。装载列车的坡度是1:160(0.6)和空火车是1:66(1.5%),最小曲线半径500米，轨距1065毫米。轨道从Ogies到RBCT的距离分别是565公里(线路1)和560公里(线路2)。装载货运大多数情况下由1号线运输,这也是两条线路中最新的。当前线路的运输吨位是在7000万到8000万吨之间的煤炭(分析),但它也运输了一个大部分的普通货物。当前这一个预测设计寿命为40年26吨/轴的基础设计细节,交由Hall公司,并且用S410土木工事规范充分描述。这900毫米深设计sub-ballast路基、实行了严格的标准,但也包括稳定化处理sub-ballast层(厚度的300毫米)与水泥或石灰的可能性。一套详尽的排水条件评估也包括一部分的基础设计和改造测试。设计忠最重要的特性摘要由表1所示。

1.2地基失效

运煤专线上地基失效的最初迹象于1994-1995年期间在弗雷海德到理查德湾部分被观察到,在它初步建成大约20年后。根据文献,轨道基础包括自然地质(形成),放置土壤(填和底层道渣。在南非,这个术语形成通常是用来表示地基。这些迹象包括损失的轨道几何,白石渣,和液压泵通过分压路基稳定层和碎石渣。大量的地基调查后开始确定失败的原因，以及问题的严重程度。

调查确定了地基失效败主要原因有以下几点：

（一）由于缺乏基本层路基支持开裂的稳定化处理的分压层（即不平衡设计方面的层刚度）；

（二）由于温度，湿度变化而风化分解构造层所造成的循环荷载，从而减少了功能材料的性能；

（三）遗漏一些所需的土方层（在大多数情况下，一、二层）特别是在削减的特定地点；

（四）排水不足和由此产生的饱和的基础，从而减少刚度和抗压强度。

在地基的调查和试验结果的基础上，一个状态测试系统被开发出来，即基础条件指数（指数）用来计算每个调查轨道区段。基础条件指数是一个加权因素，考虑到材料的性能，地层刚度值，水分条件，和考虑中的地质学的特定轨道。然后这些值用于区分恢复次序和显示每个轨道段的剩余使用寿命期望值。恢复开始于1995和持续至今。其目的是恢复所有轨道段使其基础条件指数值低于50%（两条线路）。到目前为止，大约200公里或1125km的轨道的18%已经重建。

1.3地基的设计理念

新线路基础设计所采用的理念包括以下几个方面：（一）采用优质进口砾石和碎石；

（二）高密度压实；

（三）大量的排水系统设计以应对高降雨模式；

（四）特定场地的设计代替一般的设计；

（五）指定全面品质监控作为设计的一部分。

初始S41026吨/轴基础设计和新的设计的区别如下：

（一）轨道基础两侧的地下鳍排水系统。鳍排水是一个复合排水使用流网或土工格栅层之间的土工织物并且指引地下水和/或表面水到管道排水系统（图1）；

图1

（二）一个多方位的排水土工布和分离层防止污染的结构层的原位材料；（三）碎石底层道渣层代替稳定层防止过早开裂和由于设计方面的层刚度不平衡产生的地基失效；

（四）为更好的地表水径流，斜坡上的基础从1；5050（2%）增加到1:25（4%）。

为了验证和测试性能的新的基础设计，南非国有铁路货运物流公司（轨道技术）在煤炭生产线上一个合适的地点发起了一个全面的现场仪表项目，命名为Bloubank。

2位置说明

位置描述在以往的出版物，但为明确起见，位置最重要的特色的总结列在这里。

2.1综述

该bloubank试验场是位于南部60公里的弗雷海德，弗雷海德–乌伦迪轨道区段。该地区的地质条件包括冰碛岩风化形成部份的弗雷海德地质构造。冰碛岩是过程中颗粒，沉积岩由冰川和冰盖组成。该试验场是在削减在双小节线轨道。只有新建成的1号线用仪器装备，进行列车装载。这个的别的地基将专用于完成恢复并为全面实施基础研究提供理想的机会。

期间和之后的建设新的基础，大量的仪器建立在基础层上。第一次测量在试验现场，当轨道通车于2004年四月二日，而这一新建成的轨道基础的弹性变形和长期永久变形将进行定期监测，以便2009年三月最后读数。

2.2地基设计

图1显示了Bloubank试验场基础设计的概略介绍。

设计需要开挖800mm旧的物质基础，重建4×200毫米高品质的结构层，以及大量的排水设计纳入鳍水渠和土工合成材料产品地下水切断和分离。轨道结构包括60公斤/米接力的支持轨道风云–这一词是用于混凝土轨枕用拳头紧固件和最大设计轴重30吨–具体联系（轨枕）与但中心间距270系外型–300镇流器之间的纽带和基础。

选定材料的性能，如图1所示表2总结。如适用，所需的最低标准是在方括号后的实际价值的土壤性质。

2.3使用仪器

三个测量站（1，2，3），线路被选为试验段。一些仪器在试验现场已经安装在建设基础层。其余的仪器被安装在轨道通车。图2显示了一个计划的网站，包括所有的应变和多深弯（MDD）仪器仪表。钻外的左、右轨三MDDs，在该中心的铁路轨道。对每一个MDDS洞口安装一串6MDDs模块相关层接口仪表。

在车站2，压力盘也安装在该中心的轨道基础不同层之间的交通压力测量轨道基础在不同深度。线性运动测量线性可变差动变压器（LVD T）。该仪器在Bloubank网站包括以下（图2和3）：

图2

图3

（一MDDs为测量层挠度（每个地点6MDDs，每站三个地点，总数=54）；（二）轮负荷测量应变计（每一个轨道在三站，总数=6）；

（三）侧向力测量应变计（每一个轨道在三站，总数=6）；

（四）配合反应测量应变计（每一个轨道在三站，总数=6）；

（五）基础压力测量压力板（五的压力板2站）；

（六）水平和垂直运动的测量与LVD T（只在车站2，总数=4）；

（七）轨道运动相对于领带（站2，总数=2）；（八）铁路，领带，和压载加速度加速度（只在车站2，总数=3）。

本文侧重于测量永久变形，因为它影响轨道基础设计。弹性变形和地基压力测量被描述以前的文件。

2.4列车荷载

大多数的交通，这是衡量在试验现场，包括20和26吨/轴煤和一般的货运车辆。通常，煤炭列车由100或200辆车与短火车的情况一般货运交通，所有与电力机车牵引。

3轨道基础设计参数

大多数铁路的轨道基础设计经验和/或经验或半经验方法。但轴重轻，速度和频率很低时，这些方法一般产生现实的和适当的设计值。

它不过是表明，重轴荷载，经验设计方法可导致不适当的轨道结构需要昂贵的维修或故障导致过早。这是因为影响的主应力轴旋转（1），造成非常大的增加，永久应变和减少弹性模量。系统建模不能进行常规三轴试验，和更复杂的测试，如环状空心圆柱试验或循环单剪试验，需要估计的永久变形下轨道。

轨道基础设计方法的李和塞利格是基于双参数，其目的是防止最常见的轨道路基破坏造成的重复加载轨道基础。测量Bloubank将被用来评价这些准则在以下段落。

3.1地基塑性应变

路基破坏可以先与路基累积塑性应变（ε磷）由以下方程开发锂和锂和塞利格在ε磷是土壤累积塑性应变，在一些重复应力中的应用，σ=（σ1−σ3）偏应力造成的列车轴荷载，σ的土壤抗压强度，和，男，乙的参数依赖于土壤类型。随行的设计准则，防止路基渐进破坏是提出了在ε是允许塑性应变在路基表面和2%，根据设计推荐李和塞利格。

3.2路基塑性变形

路基破坏可其次与路基累积塑性变形（ρ）由以下方程开发锂和锂和塞利格，是路基深度。

随行的设计准则预防路基过大的塑性变形是在ρ是允许塑性变形的路基层的设计周期，是25毫米根据设计推荐李和塞利格。

在确定的主要轨道基础设计参数，现场实际数据从煤炭重载基金会将介绍和讨论。

4实地测量

如前所述，该Bloubank现场仪器与一系列的mdds变形测量在三个试验站和在不同深度。四月至2004andmarch2009，该Bloubank试验场进行大约363mgt。总永久变形数据为每个测量站，在左，中心，和正确的地点，绘制在图4。回归分析是用来适应曲线通过所有九套数据。结果发现，对数函数形式=y0+蛋白（×−讨论），在节奏，讨论，和一个变量的累积，永久变形，和吨位，提供了足够的准确和精确的估计的永久变形的发展。回归分析的决定系数（R2）产生的价值观，从0.979到0.995，平均0.986。表3总结得出的结果的回归分析的累积塑性变形数据。

图4显示了一个典型的沉降趋势较高的初始利率的永久变形，大大减少由于吨位的增加和几乎成为不断接近年底的图。在测量期间，不同的利率的永久变形，可以观察到，主要是因季节温度的变化和由此产生的路基条件。减少永久变形站1是指出，和原因出人意料的变化将是调查时，更多的数据是可用的。

图4测量在图4被用来计算路基累积塑性应变（ε磷）在三个试验站和各自的位置（左，中，右）。为目的的下列计算，累积应变得到总结的应变发生在整个轨道基础，即在路基以及在特殊的分压、分压层。表4显示了地雷探测犬孔深度测量在安装的时候，这是至关重要的计算个别基础系。图5显示了最大塑性应变的基础上大约5年后（即363mgt）。

测量证实，最大总应变（总挠度）在一个轨道结构发生在轨道中心线并没有直接下方的导轨。为深度变浅，这可能并非如此，但从累积塑性应变，证据是明确的。这种现象也被观察到挖掘失败的基础上。还应该指出，关于土壤条件，站1站3干燥和潮湿的。这是根据视觉观察期间的钻探孔的地雷探测犬。1站可以，因此，被称为'好'和'坏'站3站。越来越多的塑性应变作为观察时，移动的方向，从站1站3支持这一事实。

累积塑性应变在各测量站是在破坏极限2%的前5年，这一相对较新的基础。测量将用于以后预测累积塑性应变的设计寿命为基础的轨道。

图5

图6

图6显示了最大累积塑性变形测量三个测站5年后（即363mgt）。作为ρ仅仅是整体的塑性应变总结了路基深度图，具有完全相同的形状，如在图5。之前，需要指出的是，累积塑性变形，在这一阶段，远低于破坏极限时。5节将描述如何累积永久变形测量被用来预测设计人生的煤炭铁路重载轨道基础。

5设计寿命预测

根据文献，永久变形是受许多因素的影响，其中可分为三类，即，

（一）装载状态或应力状态；

（二）土壤类型和结构；

（三）土壤的物理状态。

装载状态或应力状态包括规模偏应力和围压，一些重复载入中周期和序列，与应力史。

土壤的类型和结构，包括集料类型，颗粒形状，细粒含量，和级别，也取决于压实方法和压实度，新路基的压实作用力。

土的物理状态的定义是含水率和密度，空隙率，并受环境变化影响。

上述因素，强调在实验室中获得准确的永久变形参数的困难，即使使用复杂的应力路径测试。Bloubank的实地测量，因此，提供了理想的机会做准确考虑中的设计寿命预测轨道基础。Bloubank忠累积吨位的线指示出位363MGT。

40年后的预测累积吨位，每年在这一时期假定吨位将增加10个百分点。该计算出40年后的的总吨位3286MGT。除了10%的增长因素，进一步的安全系数1.2用于解释说明在交通方面的增长的不确定因素，土壤退化，环境因素，和可能的轴重增加。这种计算产生的40年后的总吨位约4000MGT。决定使用这个数字的设计寿命预测如下。

图7

图8

图9

图7至9显示测量累积塑性变形站1，2，和3在第一个5年后以及推断变形直至基础达到年龄为40年（即4000mgt）；这次按数吨位标尺绘图。对数回归分析在上一节讨论，如图4所示是用来推断的基础设计的预期寿命的数据。

对数回归分析在所有三个测量站显示初步改变塑性变形率。然而，经过大约100mgt，强大的线性趋势（以对数尺度）被观察到。一如以往，变形的轨道中心线增长率最高，也是最高的规模。累积塑性变形在各测量站与破坏极限时，很清楚的是，即使是不好的地点（第3站）应提供整个预计40年的设计寿命令人满意的运行状态。使用25mm作为抗剪强度破坏准则，计算站1、2、3的安全系数分别为6.0，2.7，和2.4。

25mm的破坏极限是任意选择的，也可以辩证的说，这可能太保守了。然而，遵循的程序估计在Bloubank计划的轨道基础设计寿命证实轨道基础的性能和预期一样，它应该很容易运输估计总吨位40年或更长。

该图也证实了预期的线性（常数）退化的基础（以对数刻度）与增加吨位。意外或过早地基失效将导致变化的速度累积塑性变形。令人鼓舞的是看到，尽管不好的地点（第3站）的退化是恒定的在图9中，塑性应变和变形不超过363MGT 的阈值。

测量期（5年）比40年的预测要短得多。由于充分引流或发生急剧变化的轴载或交通密度的突然地基失效会危及有效性的预测。为此，实地测量将持续到轨道基础的任何突然变化的退化。所有顾虑已然被采取去确保排水部件是持久和精心设计的，足以在轴重或交通密度的增加的情况下应用安全因素。

6结论

南非煤线上的研究站对累积塑性变形的测量进行了详细的描述。MDDS既被用来衡量的累积塑性应变也用来衡量一段5年26吨/轴装载的轨道基础的累积塑性变形。测量数据被用于预测一段为期40年轨道基础的性能。

三个不同的测量站的预测表明三站很有可能运输安全指数范围从2.4到6预期4000MGT吨位超过40年。这些结果证明，新的设计基础，包括不稳定的分压层，将在实际负荷下提供所需的设计寿命，鉴于一系列的基础条件和不同的环境因素。结果可用于预测的基础设计寿命在其他地点上的线路以及其他重载基础。

鸣谢

对铁路货运公司的有关人员–H.Maree,F.Shaw,D.Potgieter,R.Freyer, R.Furno,J.Kae,N.Tapala,S.Mhlanga,和T.Ratshilumela的贡献表示

感谢。感谢弗雷海德客运站轨道车辆维修人员的帮助。感谢比勒陀利亚大学（铁路工程的首席）土木工程系和铁路货运公司对研究的支持。

作者2010年Design life prediction of a heavy haul track foundation P J Gräbe1∗and F J Shaw2

1Department of Civil Engineering,University of Pretoria,Pretoria,South Africa 2Transnet Freight Rail(Track Technology),Track Testing Centre,Jeppestown, South Africa

The manuscript was received on9December2009and was accepted after revision for publication on17March2010.

DOI:10.1243/09544097JRRT371

Abstract:Transnet Freight Rail monitors the behaviour of a new track foundation,constructed in2004,on the South African Coal Line.This site forms part of a major rehabilitation project,aimed at increasing the capacity of the line to sustain future growth in annual tonnage.Sophisticated instrumentation is used to measure resilient and permanent deformation of the track foundation.Preliminary results of this research were published shortly after the construction of the new track foundation. Results of the permanent deformation,gathered over a period of5years,are now presented to provide new insight into the long-term behaviour of track foundations. Permanent deformation measurements are used to calculate the expected design life of a track foundation.The results are used to predict permanent deformation and ultimately the design life of the track foundation under heavy haul loading conditions. The research provides a scientific basis for planning foundation rehabilitation in the light of sustained capital expansion and projected tonnage increase on the Coal Line and other heavy haul lines.

Keywords:permanent deformation,resilient deformation,track foundation, foundation design,design life prediction

1INTRODUCTION

1.1Background

The Coal Line in South Africa is a coal export line linking approximately40 mines in the Mpumalanga coalfields to Richards Bay Coal Terminal(RBCT).The Ogies/Blackhill–RBCT line was opened as a single line in1976and wassubsequently doubled during1983–19.The line was originally designed to handle 76wagon trains at18.5ton/axle load with an annual capacity of21million ton.The line was upgraded over the years to handle200wagon trains(26ton/axle),2.5km long,and grossing20800ton.

The ruling gradient for loaded trains is1:160(0.6per cent)and that for empty trains is1:66(1.5per cent),with a minimum curve radius of500m and a track gauge of1065mm.The track distances from Ogies to RBCT are565km(line1)and560km (line2),respectively.The loaded traffic is carried on line1,which is in most cases also the newest of the two lines.The current tonnage carried on the line is between70 and80million gross ton(MGT)of coal,but it also carries a large proportion of general freight.

Details of the current26ton/axle foundation design,which had a projected design life of40years,are given by Hall and are fully described in the S410 Earthworks Specification.This900mm deep design had stringent subgrade and

sub-ballast criteria,but also included the possibility of stabilizing the sub-ballast layers(thickness of300mm)with cement or lime.An extensive evaluation of the drainage conditions was also included as part of the foundation design and upgrading exercise.A summary of the most important properties of this design is shown in Table 1.

1.2Foundation failure

The first signs of foundation failure on the Coal Line were observed during 1994–1995on the Vryheid–Richards Bay section,approximately20years after its initial construction.According to the literature,the track foundation includes the natural ground(formation),placed soil(fill),and the sub-ballast.In South Africa,the term formation is often used to denote the foundation.These signs included loss of track geometry,white ballast,and hydraulic pumping of the subgrade through the stabilized sub-ballast layer and ballast.An extensive foundation investigation was then initiated to determine the cause(s)of the failure as well as the extent of the problem.

The investigations identified the following main reasons for foundation failureon the line:

(a)cracking of the stabilized sub-ballast layer(s)as a result of inadequate support from the underlying subgrade layers(i.e.an unbalanced design with regard to the layer stiffness);

(b)weathering and decomposition of the constructed layers as a result of cyclic loading,temperature,and moisture changes,leading to a reduction in the functional properties of the materials;

(c)the omission of some of the required earthworks layers(in most cases the A and B layers)at specific locations,especially in cuts;

(d)inadequate drainage and the consequent saturation of the foundation, resulting in reduced stiffness and compressive strength.

Based on the foundation investigations and test results,a condition measurement system was developed,whereby a foundation condition index(FCI)was calculated for each investigated track section.The FCI is a weighted factor that takes into account the material properties,layer stiffness values,moisture condition,and geology of the specific track section under consideration.These values were then used to prioritize the rehabilitation and to give indications of the remaining service life to be expected from each track section.Rehabilitation commenced in1995and continues till the present day.The objective was to rehabilitate all track sections with an FCI value of less than50per cent(both lines).Up to date,roughly200km or18 per cent of the1125km of the track have been reconstructed.

1.3Foundation design philosophy

The philosophy adopted for the new Coal Line foundation design included the following aspects:

(a)the use of high-quality gravels and imported crushed stone;

(b)compaction to high densities;

(c)an extensive drainage design to cope with the high rainfall patterns;

(d)site-specific designs instead of generic designs;

(e)comprehensive quality control measures,specified as part of the design.

The major differences between the original S41026ton/axle foundation designand the new design are listed below:

(a)subsurface fin drain systems on both sides of the track foundation.A fin drain is a composite drain that uses a flow net or geogrid sandwiched between layers of geotextile and directs groundwater and/or surface water into a piped drainage system (Fig.1);

Fig.1

(b)a multi-directional geotextile as drainage and separation layer to prevent contamination of the structural layers by the in situ material;

(c)crushed stone sub-ballast layers instead of stabilized layers to prevent premature cracking and consequent foundation failure owing to an unbalanced design with regard to layer stiffness;

(d)the slope on top of the foundation was increased from1:50(2per cent)to 1:25(4per cent)for better surface water run-off.

To verify and to test the performance of the new foundation design,Transnet Freight Rail(Track Technology)initiated a full-scale field instrumentation project carried out at a suitable site,named Bloubank,on the Coal Line.

2SITE DESCRIPTION

The site was described in a previous publication,but for clarity,a summary of the most important characteristics of the site is included here.2.1General

The Bloubank test site is situated60km south of Vryheid,on the Vryheid–Ulundi track section.The geology of the area comprises weathered tillites forming part of the Vryheid geological formation.Tillites are course-grained,sedimentary rocks produced by glaciers and ice sheets.The test site is in a cut on a double line section of the track.Only the newly constructed number1line,carrying the loaded trains,was instrumented.This particular foundation was earmarked for complete rehabilitation and provided the ideal opportunity to carry out full-scale foundation research.

During and after construction of the new foundation,extensive instrumentation was built into the foundation layers.First measurements at the test site were taken when the track was opened to traffic on2April2004,and resilient deformation and long-term permanent deformation of this newly constructed track foundation are monitored at regular intervals,with the last reading being taken inMarch2009.

2.2Foundation design

Figure1shows a diagrammatic presentation of the foundation design that was used for the Bloubank test site.

The design entailed excavation of800mm of old foundation material, reconstruction of4×200mm high-quality structural layers,and an extensive drainage design incorporating fin drains and geosynthetic products for groundwater cut-off and separation.The track structure consisted of60kg/m CrMg rails supported by FY–which is the term used for concrete ties with FIST fastenings and a maximum design axle load of30ton–concrete ties(sleepers)with a centre-to-centre tie spacing of 650mm on270–300mm of ballast between the ties and the foundation.The properties of the selected materials as shown in Fig.1are summarized in Table2.Where applicable,the required minimum specification is stated in square brackets after the actual value of the listed soil property.

2.3Instrumentation

Three measuring stations(stations1,2,and3),eight ties apart,were chosen at the test section.Some of the instrumentation at the test site had to be installed during

the construction of foundation layers.The remainder of the instrumentation was installed just before the track was opened to traffic.Figure2shows a plan view of the site,including all strain gauge and multi-depth deflectometer(MDD)instrumentation. ThreeMDDholes were drilled just outside the left and right rails and at the centre of the rail track.Each of the MDDholes was instrumented with a string of sixMDD modules at the relevant layer interfaces.

At station2,pressure plateswere also installed at the centre of the track foundation between different layers to measure traffic-induced pressures in the track foundation at various depths.Tiemovement was measured with linear variable differential transformers(LVDTs).The instrumentation at the Bloubank site included the following(Figs2and3):

Fig.2

Fig.3

(a)MDDs for the measurement of layer deflections(sixMDDsper location,three locations per station,total=54);

(b)wheel load measurement with strain gauges(one per rail at three stations, total=6);

(c)lateral force measurement with strain gauges(one per rail at three stations, total=6);

(d)tie reaction measurement with strain gauges(one per rail at three stations, total=6);

(e)foundation pressure measurement with pressure plates(five pressure plates at station2);

(f)horizontal and vertical tie movement measurements with LVDTs(only at station2,total=4);

(g)rail movement relative to the tie(station2,total=2);

(h)rail,tie,and ballast accelerations with accelerometers(only at station2,total =3).

This paper focuses on the measurement of permanent deformation because of its influence on track foundation design.The resilient deformation and foundationpressure measurements were described in a previous paper.

2.4Train loading

The majority of the traffic,which was measured at the test site,consisted of20 and26ton/axle coal and general freight wagons.Typically,the coal trains consisted

of either100or200wagons with shorter trains in the case of general freight traffic, all with electric locomotive traction.

3TRACK FOUNDATION DESIGN PARAMETERS

Most railways base their track foundation design on experience and/or empirical or semi-empirical methods.Provided that axle loads are light and train speeds and frequencies are low,these methods generally produce realistic and adequate design values.

It has however been shown that for heavy axle loads,an empirical design method can lead to an inadequate track structure requiring costly maintenance or even resulting in premature failure.This is the result of the effect of principal stress rotation(PSR),which causes very large increases in permanent strain and a reduction in resilient modulus.PSR cannot be modeled by carrying out conventional triaxial tests,and more complex tests,such as cyclic hollow cylinder tests or cyclic simple shear tests,are required to estimate the permanent deformation under track.

The track foundation design method by Li and Selig is based on two parameters,which aim to prevent the two most common track subgrade failures caused by repetitive loading on track foundation.The measurements at Bloubank will be used to evaluate against these norms in the following paragraphs.

3.1Subgrade plastic strain

Subgrade failures can first be related to subgrade cumulative plastic strain(εp) by the following equation developed by Li and Li and Selig whereεp is the cumulative soil plastic strain,N the number of repeated stress applications,σd=(σ1−σ3)

the deviator stress caused by the train axle loads,σs the soil compressive strength, and a,m,b the parameters dependent on soil type.The accompanying design criterion for preventing subgrade progressive shear failure is then given as whereεpa is the allowable plastic strain at the subgrade surface and is2per cent according to the design recommendation by Li and Selig. 3.2Subgrade plastic deformation

Subgrade failures can secondly be related to subgrade cumulative plastic deformation(ρ)by the following equation developed by Li and Li and Selig where T is the subgrade depth.

The accompanying design criterion for preventing the subgrade excessive plastic deformation is then

whereρa is the allowable plastic deformation of the subgrade layer for the design period and is25mm according to the design recommendation by Li and Selig.

Having defined the main track foundation design parameters,the actual field data from the Coal Line heavy haul foundation will now be presented and discussed.

4FIELD MEASUREMENTS

As mentioned before,the Bloubank site was instrumented with an array of MDDs measuring the deformation at three test stations and at various depths. Between April2004and March2009,the Bloubank test site carried approximately 363MGT.The total permanent deformation data for each measuring station,at the left, centre,and right locations,are plotted in Fig.4.Regression analysis was used to fit a curve through all nine sets of raw data.It was found that a logarithmic function of the form y=y0+a ln(x−x0),where y0,x0,and a are variables,y the cumulative permanent peformation,and x the tonnage,provides a sufficiently accurate and close estimate of the permanent deformation development.The regression analysis produced coefficient of determination(R2)values,ranging from0.979to0.995with an average of0.986.Table3contains a summary of the results obtained from the regression analysis on the cumulative plastic deformation data.

Fig.4

The graph in Fig.4shows a typical settlement trend with high initial rates of permanent deformation,reducing considerably as the tonnage increases and almost becoming constant towards the end of the graph.During the measuring period, different rates of permanent deformation can be observed,primarily caused by the seasonal changes in temperature and the resulting subgrade conditions.A reduction in permanent deformation at station1is noted,and the reason for this unexpected change will be investigated when more data are available.

Measurements presented in Fig.4were used to calculate the subgrade cumulative plastic strain(εp)at the three test stations and their individual locations (left,centre,and right).For the purpose of the following calculations,the cumulative strain was obtained by summing the strain occurring in the entire track foundation,i.e. in the subgrade as well as in the special sub-ballast and sub-ballast layers.Table4 shows the MDD hole depths that were measured at the time of installation,which were critical in calculating the individual foundation strains.Figure5shows the maximum plastic strain of the foundation after approximately5years(i.e.363MGT).

Measurements confirm that the maximum total strain(and total deflection)belowa track structure occurs on the track centre-line and not directly below the rails.For shallow depths,this might not be the case,but in terms of cumulative plastic strain, the evidence is clear.This phenomenon was also observed when excavations were done on failed foundations.It should also be noted that with regard to soil conditions, station1was the driest and station3the wettest.This was based on visual observations during the drilling of the MDD holes.Station1could,therefore,be referred to as the‘good’site and station3as the‘bad’site.The increasing plastic strain as observed when moving in the direction from station1to station3supports this fact.

The cumulative plastic strain at each measuring station is well below the failure limit of2per cent for the first5years of this relatively new foundation. Measurements will be used later to predict the cumulative plastic strain over the full design life of the track foundation.

Figure6shows the maximum cumulative plastic deformation measured at three measuring stations after5years(i.e.363MGT).Asρis simply the integral of the plastic strains summed over the subgrade depth,the graph has exactly the same shape as the one presented in Fig.5.As before,it is noted that the cumulative plastic deformation is,at this stage,well below the failure limit of25mm.Section5will describe how the cumulative permanent deformation measurements were used to predict design life of the Coal Line heavy haul track foundation.

Fig.5

5DESIGN LIFE PREDICTION

According to the literature,permanent deformation is influenced by a number of factors,which can be grouped into three categories,namely,

(a)loading condition or stress state;

(b)soil type and structure;

(c)soil physical state.

Loading condition or stress state includes the magnitude of deviator stress and confining stress,PSR,the number of repetitive loading cycles and their sequence,and stress history.

Soil type and structure includes aggregate type,particle shape,fines content,and grading and also depends on the compaction method and compaction effort for a new subgrade.

Soil physical state is defined by moisture content,void ratio,and density and is subject to environmental changes.The above-mentioned factors emphasize the difficulty in obtaining accurate permanent deformation parameters in the laboratory,even with the use of complex stress path testing.The field measurements at Bloubank,therefore,offer the ideal opportunity to do accurate design life prediction of the track foundation under consideration.

The cumulative tonnage over the line at Bloubank was stated as363MGT.To predict the cumulative tonnage after40years,it was assumed that the annual tonnage will increase by10per cent per year over this period.This calculation gives a total tonnage of3286MGT after40years.In addition to the10per cent growth factor,a further safety factor of1.2was applied to account for uncertainties in terms of traffic growth,soil deterioration,environmental factors,and a possible axle load increase. This calculation produced a total tonnage of approximately4000MGT after40years.

It was decided to use this number in the design life prediction that follows.

Fig.7

Fig.8

Fig.9

Figures7to9show the measured cumulative plastic deformation at stations1,2, and3after the first5years as well as the extrapolated deformation until the foundation reaches an age of40years(i.e.4000MGT);this time plotted against a logarithmic tonnage scale.The logarithmic regression analyses discussed in theprevious section and shown in Fig.4were used to extrapolate the data to the expected design life of the foundation.

The logarithmic regressions at all three measuring stations show initial changes in the plastic deformation rate.However,after approximately100MGT,a strong linear trend(plotted on a log scale)is observed.As before,the deformation at the track centre-line is increasing at the highest rate and is also the highest in magnitude.

The cumulative plastic deformation at each measuring station is compared with the failure limit of25mm,and it is clear that even the bad site(station3)should provide satisfactory behaviour throughout the projected40-year design life.Using the 25mm as failure criterion,safety factors of6.0,2.7,and2.4were calculated for stations1,2,and3,respectively.The failure limit of25mm was arbitrarily chosen, and one could argue that this might not be conservative enough.Nevertheless,the procedure followed for estimating the projected design life of the track foundation at Bloubank confirms that the performance of the track foundation is as expected and that it should easily carry the estimated total tonnage up to40years and thereafter.

The graphs also confirm the expected linear(constant)degradation of the foundation(plotted on a log scale)with an increase in tonnage.Unexpected or premature foundation failure would have resulted in a change in the rate of cumulative plastic deformation.It is encouraging to observe that the degradation of even the bad site(station3)is constant in Fig.9and that its plastic strain and deformation do not exceed the thresholds after363MGT.

It is realized that the measurement period(5years)is short compared with the 40-year prediction.Sudden foundation failure owing to insufficient drainage or a dramatic change in the axle loading or traffic density would certainly jeopardize the validity of the predictions.For this reason,field measurements will be continued to detect any sudden changes in the degradation of the track foundation.All possible care has however been taken to ensure that the drainage components are durable and well designed and that the applied safety factors are sufficient in the case of axle load or traffic density increases.6CONCLUSIONS

The measurement of cumulative plastic deformation at a research site on the Coal Line in South Africa was described in detail.MDDs were used to measure both the cumulative plastic strain and the cumulative plastic deformation of the track foundation under26ton/axle loading over a period of5years.The measured data were used to predict the performance of the track foundation over a period of40 years.

The predictions at three different measuring stations indicated that all three stations are more than likely to carry the expected tonnage of4000MGT over a period of40years with safety factors ranging from2.4to6.0.These results prove that the new foundation design,comprising unstabilized sub-ballast layers,will provide the required design life under actual loading,given a range of foundation conditions and varying environmental factors.The results can be used to predict the foundation design life at other sites on the Coal Line as well as on other heavy haul foundations. ACKNOWLEDGEMENTS

The contributions of the Transnet Freight Rail personnel–H.Maree,F.Shaw,D. Potgieter,R.Freyer,R.Furno,J.Kae,N.Tapala,S.Mhlanga,and T.Ratshilumela–are gratefully acknowledged.The track maintenance staff of the Vryheid Depot are thanked for their assistance.The University of Pretoria(Chair in Railway Engineering) in the Department of Civil Engineering and Transnet Freight Rail are thanked for supporting this research.

©Authors2010