Plaxis Bulletin 18

PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES

Plaxis Bulletinissue 18 / october 2005

4D GROUTING PRESSURE MODEL OF A BORED TUNNEL

IN 3D TUNNEL

How a distressed quay wall could be moved back in place…using Plaxis

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Editorial 3

New developments 3

Plaxis Benchmark 4 NO.4: SINGLE PILE 1 - RESULTS ERTC7-BENCHMARK: ULS-DESIGN OF EMBEDDED WALL

Plaxis Practice 7 4D GROUTING PRESSURE MODEL OF A

BORED TUNNEL IN 3D TUNNEL

Recent activities 13

Plaxis Practice 15 HOW A DISTRESSED QUAY WALL COULD BE MOVED BACK IN PLACE… USING PLAXIS

Activities 2005-2006 20

Colophon The Plaxis Bulletin is the combined magazine of Plaxis B.V. and the Plaxis Users Association (NL). The Bulletin focuses on the use of the finite element method in geo-technical engineering practise and includes articles on the practical application of the Plaxis programs, case studies and backgrounds on the models implemented in Plaxis.

The Bulletin offers a platform where users of Plaxis can share ideas and experienceswith each other. The editors welcome submission of papers for the Plaxis Bulletin thatfall in any of these categories. The manuscript should preferably be submitted in an electronic format, formatted as plain text without formatting. It should include the title of the paper, the name(s) of the authors and contact information (preferably email) for the corresponding author(s). The main body of the article should be divided into appropriate sections and, if necessary, subsections. If any references are used, they should be listed at the end of the article.The author should ensure that the article is written clearly for ease of reading.

In case figures are used in the text, it should be indicated where they should be placed approximately in the text. The figures themselves have to be supplied separately from the text in a common graphics format (e.g. tif, gif, png, jpg, wmf, cdr or eps formats are all acceptable). If bitmaps or scanned figures are used the author should ensurethat they have a resolution of at least 300 dpi at the size they will be printed. The use of colour in figures is encouraged, as the Plaxis Bulletin is printed in full-colour.

Any correspondence regarding the Plaxis Bulletin can be sent by email [email protected]

or by regular mail to:

Plaxis Bulletinc/o Dr. W. BroerePO Box 5722600 AN DelftThe Netherlands

The Plaxis Bulletin has a total circulation of 10.000 copies and is distributed world-wide

Editorial Board:

Dr. Wout Broere Dr. Ronald BrinkgreveMr. Erwin BeerninkMr. François Mathijssen

Cover photo: ??????????

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IN THE TIME SINCE THE LAST BULLETIN APPEARED, PLAXIS

HAS CONDUCTED A CUSTOMER SATISFACTION INQUIRY. IN

THIS INQUIRY PLAXIS USERS WERE ASKED ABOUT THEIR

EXPERIENCE WITH THE CURRENT PROGRAMS AND SERVICES

AND THEIR EXPECTATIONS OF FUTURE DEVELOPMENTS. A

FEW KEY RESULTS OF THE INQUIRY ARE DEALT WITH IN THE

RECENT ACTIVITIES COLUMN. MORE ON THE USERS’ EXPEC-

TATIONS FOR FUTURE VERSIONS CAN BE FOUND IN THE NEW

DEVELOPMENTS COLUMN.

In Plaxis Practise, a wide range of different topics is covered. The second paper describes the investigation into a sudden failure of a quay wall. In this case Plaxis V8 has been used to discover the cause of the failure and assist with the subsequent development of a remediation plan. In the first paper, Plaxis 3D Tunnel has been used to simulate the construction of a bored tunnel. The tunnel boring machine and lining construction have been modelled in detail in a step-wise excavation scheme, so that the tunnel boring machine moves step by step through the model. The new copy option in 3D Tunnel has been used to greatly simplify the input needed for this model.

Also found in this Bulletin are the results of the Benchmark that appeared in issue 16. A few people have taken the challenge to calculate the bearing capacity of a bored pile and their anonymised results are presented here. The comparison of their results shows the influence of mesh refinement on the predicted bearing capacity. In this way, the benchmark cases highlight important points for the use of finite elements and this should encourage more users to take part. A new benchmark is also presented, which gives a preview to the upcoming Numerical Methods in Geotechnical Engineering conference, held next year in Graz.

All in all, there is are a lot of interesting Plaxis projects presented in this issue and we hope you will enjoy reading about them.

New Developments Ronald Brinkgreve, Plaxis BV

Recently, two user inquiries have been held among Plaxis users to investigate the main user requirements: One initiated by the Plaxis Development Community (PDC) and another one (world-wide) initiated by Plaxis bv. The first inquiry was meant to make a plan of new developments sponsored by PDC for the period 2006-2010. The second one was meant to have an idea about the broader user requirements, not only in terms of product develop-ments but also in terms of services. In this column the attention will be focused on the requirements for new developments.

There are two user requirements that have been rated with a high priority in both inquiries:• Parameter variation and sensitivity analysis• Safety analysis according to design codesIn fact, these two features are already on the list to be developed for Plaxis 2D Version 9. Details of these features have already been described in Bulletin 15. Another requirement that has been rated with high priority in the world-wide inquiry is the simulation of soil lab tests. Also this feature is considered for Version 9.

The inquiries have also indicated the need for improved ways to check input data and computational results. In the first place there is a need for tools that support users in the selection of model parameters. In this respect, the facility for soil lab test simulations, which has been planned for Version 9, is quite helpful. In addition, facilities can be imple-mented in the output program that help users check the equilibrium of structures or parts of the geometry. Moreover, another tool could help users check the equivalent shear stress against an assumed undrained shear strength profile. The latter is particularly useful when effective strength properties have been used in undrained layers.

In terms of 3D modelling features, the inquiry indicates the need for extended geometric modelling features. Because of the existing program concepts that make 3D modelling with Plaxis easy, the current 3D programs compromise on flexibility. With new ideas, as applied for the 3D Excavation program, the geometrical possibilities will be significantly widened, without compromising on user-friendliness. More details about the development of the 3D Excavation program will be given in the next Bulletin. Another 3D user require-ment with high priority is the possibility to model soil inclusions. Also here, some features are planned for 3D Excavation, like the modelling of ground anchors. Moreover, the embed-ded pile option, which comes available in Version 2 of the 3D Foundation program (see previous Bulletin), enables the modelling of soil inclusions.

Since the beginning of the Plaxis developments, a lot of effort has been spent on the deve-lopment and implementation of advanced soil models. For such models the emphasis has been on a robust implementation and the use of understandable parameters. Developments on soil models were usually not directly driven by user requirements, but could be consi-dered a “technology push”, resulting from the Plaxis contacts in the field of geotechnical research. Nevertheless, the inquiries indicate that there is interest for even more advanced soil models, such as models for cyclic loading and liquefaction, small-strain stiffness and anisotropy. This gives sufficient basis to continue the soil model development strategy.

It is nice to see that most user requirements with a high priority are already considered in planned developments. This is no surprise, because Plaxis personnel is frequently in contact with their users through sales and support activities, short courses and user meetings. Nevertheless, the inquiries were very useful and also indicated problems that were insufficiently known. The most pronounced example is the problem that calculation phases have to be redefined completely when the geometry is (slightly) changed and the finite element mesh is regenerated. It became clear that users are bothered about this and require a facility that automatically restores the staged construction settings when only small geometric changes are made. We have decided that such a facility will be implemented in Plaxis 2D Version 9.

On behalf of the Plaxis Research and Development team I like to thank all users that have contributed to the inquiries.

Editorial

INTRODUCTION

The PLAXIS Benchmark Problem No. 4, analysis of the load displacement behaviour of a single pile, has been published in Bulletins No. 16 and 17. Geometry of a typical pile load test arrangement was provided together with all input data for the Hardening Soil model. As in the previous benchmark, participation was not in numbers as we would like to see it. Nevertheless the results submitted, named PLT1 to PLT5, are compared in the following. The specification of the Benchmark example is not repeated here; please refer to the Bulletin No.16 or 17 for details.Furthermore a comparison between axisymmetric and three-dimensional analyses using a Beta-version of PLAXIS 3D Foundation V1.5 is presented. This should provide some guidelines for mesh generation, in particular when using the 3D Foundation program.

Comparison of resultsFigure 1 plots the load-displacement curves and it can be observed that with the exception of PLT3 all results are very reasonably in agreement for loading stages up to 4000 kN. The pronounced kink in the curves corresponds to the full mobilisation of shaft friction as follows also from Figure 2. The results of PLT3 do not show the significantly stiffer response for low applied loads suggesting that the interface may have been modelled in a different way.

The second discrepancy in Figure 1 is the maximum load applied or achieved in the different analyses. Assuming that all authors plotted the maximum load for which convergence could be achieved these differences give raise to concern. Internal studies revealed that the results are quite sensitive to local discretisation due to its influence on the calculated error and thus on the convergence with given tolerances. It is impor-tant to note though, that these local differences in the mesh do not have a significant influence on the results in the range of working loads.

Figure 1: Submitted load-displacement curves

Figures 2a and 2b show load-displacement curves split in shaft and base resistance and again all entries show very similar results (Figure 2b is an enlargement of Figure 2a for low applied loads). PLT3 did not provide this particular diagram, but indicated a shaft resistance of 2835 kN which is higher than the other calculations show, again suggesting some differences in modelling the interface behaviour.

Plaxis Benchmark No.4: Single Pile 1 - Results

Helmut F. Schweiger, Graz University of Technology, Austria

Plaxis Benchmarking

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Figure 2: Load-displacement curves: shaft and base resistance, a) full load range, b) limited load range

Influence of discretisation Because internal studies showed that for this type of problems the discretisation may have a larger influence on results even for working load conditions as compared e.g. for deep excavation problems, the results obtained for four different meshes are presented in Figure 3. All analyses were performed with PLAXIS V8.2 in axisymmetric conditions. In Figure 3 coarse represents a mesh of 143 elements (Figure 4) and fine a mesh with 850 elements (Figure 5). Both meshes have been used with 6-noded and 15-noded elements. The result is what can be expected, namely that the coarse mesh behaves much too stiff and that the fine 6-noded mesh gives similar results as the coarse 15-noded mesh but there are still differences to the fine 15-noded mesh. These results clearly emphasize the importance of checking mesh dependence when analysing piles, in particular for higher load levels.

Figure 3: Dependence of calculated load-displacement curves on discretisation (2D-analyses)

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Comparison with 3D-analysis using PLAXIS 3D-Foundation V1.5BetaThe PLAXIS 3D-Foundation programme allows a discretisation in the plan view and automatically extends the mesh into the vertical direction. The discretisation in the third direction can be influenced by specifying “work planes” but if these are not required for modelling the geometry of the problem this is done automatically by the programme. However, as will be shown in the following, care must be taken when using this option because rather coarse meshes are generated in this way, probably leading to unrealistic results. To demonstrate this, the pile benchmark is also analysed with the 3D-Foundation module and different meshes have again been investigated. It is noted here that the equivalent of the 2D 15-noded element is not available in 3D but only quadratic elements can be used. 6 different meshes have been created with refine-ments in the horizontal plane as well as in vertical direction. The latter has been done manually by introducing work planes. Figures 6 and 7 show the extremes of the meshes used, namely a 216 element discretisation in the horizontal plane with a 5 element discretisation in the vertical direction and a mesh with 552x60 elements respectively. In addition meshes with 436x5 and 436x60 elements have been used. It should be mentioned, that the 5 elements generated in the vertical direction is the result of the default mesh generated by PLAXIS.

Figure 8: Dependence of calculated load-displacement curves on discretisation (3D-analyses)

Load displacement curves are plotted in Figure 8 and again the result is what one would expect, i.e. the coarse meshes produce a much stiffer response. It is also evident, that the default discretisation in the vertical direction is not sufficient because even with the fine mesh in the horizontal plane the results are significantly off the axisymmetric analysis (this is considered to be the reference), not only for high load levels but also for moderate loads. However, the fine discretisation in the vertical direction produces results which are comparable to the axisymmetric analysis (there is still a difference in discretisation between these two analyses). Additional studies revealed that an “intermediate” vertical discretisation is also not sufficient. This clearly emphasizes that users should not rely on default settings but make their own judgement on the appropriate discretisation.

CONCLUSION

Unfortunately again only a few PLAXIS users have contributed to this benchmark exercise but, except for one submission, fairly consistent results have been obtained for moderate load levels. The maximum load applied was quite different and internal studies suggest that this is caused by local mesh discretisation. It has to be emphasized though that these loads are well beyond working load conditions. The significant influence of mesh discretisation on the calculated response has been emphasized by means of a number of axisymmetric and 3D analyses. It can be conclu-ded that care must be taken when using the default option for mesh generation in the out of plane direction with the 3D-Foundation program.

The new benchmark example, published in this Bulletin, is a ULS-design of a deep excavation which has been set up by the European Technical Committee on Numerical Methods in Geotechnical Engineering (ERTC7) on the occasion of the next conference NUMGE_06, to be held in Graz in September 2006 (see also www.numge06.tugraz.at).

Figure 4: Axisymmetric mesh: coarse (143 elements)

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Figure 6: 3D mesh: coarse (216x5 elements) Figure 7: 3D mesh: fine (552x60 elements)

ERTC7-Benchmark: ULS-design of embedded wall

Helmut F. Schweiger, Graz University of Technology, Austria

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Plaxis Benchmarking

INTRODUCTION

In order to highlight the consequences of using different design approaches as defined in EC7 for assessing ultimate limit state conditions (ULS) on the design of retaining structures, a benchmark problem has been specified. The significant difference to examples previously examined by various working groups around Europe is that it is the intention here to solve this problem, including determination of the required embedment depth (!), by means of numerical methods, although a check by simple limit equilibrium calculations is certainly recommended. The emphasis is on the ULS design and not on the serviceability limit state (SLS), thus only parameters required for simple elastic-perfectly plastic analysis are provided.

It is anticipated that by solving this benchmark problem suggestions for best way of practice on how to apply the different design approaches in combination with numerical analyses can be established. It is therefore expected that participants in this exercise will use the design approach which will be specified in their respective home countries. However, results employing present standards are also welcome and by extending the invitation to participants worldwide we hope to obtain a comprehensive overview on design assumptions in as many countries as possible.

The results will be presented at the 6th European Conference on Numerical Methods in Geotechnical Engineering in Graz in September 2006.Results should be submitted in electronic form to: [email protected] for submission: January 15th, 2006.

N.B.: The results will be presented and published at the conference in anonymous form, i.e. no names of participants will be disclosed.

PROBLEM SPECIFICATION

The geometry is depicted in Figure 1.The following construction steps should be modelled in the numerical analysis:• initial phase (K0 = 0.5)• activation of diaphragm wall (wished-in-place)• activation of surcharge loads • excavation step 1 to level -2.0 m• activation of strut at level -1.50 m, excavation step 2 to level -4.0 m, • groundwater lowering inside excavation to level -6.0 m• excavation step 3 to level -6.0 m

Notes: • the surcharge of 10 kPa is a permanent load, the surcharge of 50 kPa is a variable

load• bedrock can be assumed at a depth of 20 m below ground surface

Figure 1: Geometric data for benchmark

Required results:• Embedment depth of wall• Design bending moment for the wall• Design strut force

In addition, the following information should be provided:• Design approach employed• Software used (including element type and approx. number of elements)• Element type for modelling diaphragm wall• Element type for modelling wall friction• Wall friction angle (this is not specified because various assumptions are possible

in different countries)• Associated or non-associated plastic flow• Assumptions made for water pressures (hydrostatic, flow calculation, …)

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INTRODUCTION

For some ten years TBM-techniques have been used to construct tunnels in the Netherlands. Ground conditions vary from loose to dense granular soils, sometimes clays. In all cases groundwater is close to ground level. Front stability is maintained by bentonite slurry or earth pressure balance shields. Several research projects have been initiated by the Dutch Centre for Underground Construction (COB) in order to increase TBM applicability in urban areas. The COB has brought authorities, engineering con-sultants and contractors together in research committees.

One COB research committee is investigating the interaction of soil and the tunnelling process using finite element method (FEM) analyses. The grouting pressure applied to fill up the tail void behind the TBM is believed to govern both deformations and internal lining forces.

Several two- and three-dimensional FEM models that include tail void grouting are available. However, they do not describe time-dependent longitudinal lining deformati-ons or bending moments. As part of this COB project Fugro Ingenieursbureau B.V. has developed a 4D FEM model. The model describes the progressive tunnel boring process using PLAXIS 3D Tunnel software.

CASE STUDY

The 4D grouting pressure model was derived from the twin tube Sophia Railway Tunnel constructed in the western Netherlands as part of the Betuweroute railway link between Rotterdam and Germany. Each tunnel is 4.2 km long and has an inside diameter of 8.65 m. Construction used a TBM with a bentonite slurry shield.

Halfway along the tunnels a monitoring section was installed. This consisted of two lines measuring surface displacements laid out parallel and perpendicular to the tunnel axis. Also extensometers and inclinometers were installed. Grouting pressure transducers have been inserted in ring 2080 of the southern tunnel beneath the moni-toring section. This instrumented ring was also monitored after installation. Along with TBM data this monitoring data has been used for achieving a history match with the FEM model.

ANALYSIS OF MEASUREMENT DATA

In order to compare calculation results with measurements at the monitoring section an analysis of the boring process has been performed over some 200 m tunnel length. Major goals are to determine whether the tunnel boring process parameters and res-ponse at ground level at the monitoring section can be correlated and whether they are representative for a larger area.

Data analysis for 140 rings (210 m)Surface settlement at ring number can be compared with front pressure at ring number x —5 in figure 1. The monitoring section is located at ring number 2080. Over the entire length there seems to be some correlation between vertical displacement and front pressure.

In figure 2 the grouting pressure is given for a pressure transducer in the TBM tail. The grouting pressure in the boring phase varies by 100 kN/m² along this stretch. On this large scale there is no clear correlation between grouting pressure and final displace-ment other than that the average grouting pressure is constant at approximately 275 kPa and the average final settlement is 0 mm. In figure 3 the total number of strokes

of the grouting pumps is given. The number of strokes varies considerably. Just like grouting pressure there is no clear correlation between the number of strokes and final displacement other than that the number of strokes is constant as well as the final settlement. On a smaller scale there is some correlation. For example between ring number 2070 and 2105 the final settlement is reduced by an increase in the number of strokes.

F.J.M. Hoefsloot & A. Verweij, Fugro Ingenieursbureau B.V., The Netherlands

4D grouting pressure model of a bored tunnel in 3D Tunnel

Plaxis Practice

Figure 1: Face support pressure at the crown & surface settlement vs. ring number at the monitoring section.

Figure 2: Grouting pressure & surface settlement vs. ring number (average uses 5 data points smoothing).

Figure 3: Grout pump strokes & surface settlement vs. ring number.

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Plaxis Practice

Figure 6: Vertical displacement extensometer E 7113 at ground level (GL) , GL —6 m and GL —12.5 m as a function of time. Also plotted is the TBM’s position.

The question can be raised whether these deformations can be directly related to TBM drilling data. They are plotted versus time in figures 7, 8 and 9.

From figure 8 it appears that there is a positive correlation between grouting pressure and vertical displacement: a decreasing grouting pressure in the morning of June 27 results in settlement just as the relatively low grouting pressure in the morning of June 28 (see figure 6); the latter a result of TBM stops. An increase of grouting pressure around mid-night June 29 results in heave at all locations. The correlation of displacement with the number of strokes in figure 9 is less obvious as has been concluded from figure 3.

From the above mentioned it is evident that tunnel boring from rings 2070 to 2090 has not been constant: TBM stops and variation in grouting pressure have resulted in different longitudinal settlement troughs versus TBM position.

Figure 7. Face pressure measured at the crown of the TBM as a function of time.

Figure 8: Grouting pressure measured in the grout injection zone transducer G02 as a function of time.

Data analysis near monitoring sectionOther monitoring results near ring 2080 have been analysed in detail. Surface set-tlement versus time can be plotted as settlement versus TBM position. For a uniform tunnel boring sequence these plots should show the influence of front pressure, TBM volume loss and tail void grouting. Such plots have been given for ground level at the location of three rings in figure 4. Surface settlement has not been constant in relation to TBM position.

Figure 4: Surface settlement ring numbers 2070, 2080 & 2090 vs. position.

In order to find the source of these differences, settlement at ground level and dis-placement of extensometer points are given as a function of time in figures 5 and 6. Extensometer E7113 is located at the tunnel centreline near ring 2080. In these figures the TBM progress has also been plotted; boring for ring number n given on the right hand scale starts at the moment given on the time scale. During boring the centre of this ring is inside the TBM with a decreasing distance of approximately 5.2 to 3.7 m from the tail end.

At all locations settlement occurs at the same time and in most cases due to TBM stops. The largest settlements are found at ring 2090 during TBM stops after boring for ring number 2087, 2088 and 2089. Heave is mainly found during boring for ring numbers 2090 through 2094. In addition the extensometer point at ground level —12.5 m shows heave during boring for ring 2080. At that moment ring 2080 was located within the TBM at a distance decreasing from approximately 5.2 to 3.7 m from the tail end. Thus the measured heave did not originate directly from entering the grouting zone. This heave is limited to the zone directly above the tunnel and does not extend to ground level. Interesting is the response of the extensometer at 12.5 depth to every boring phase at least up to ring number 2094 which is located at 21m distance.

Figure 5: Vertical displacement at ground surface above rings 2070, 2080 and 2090 as a function of time. Also plotted is the TBM position.

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Figure 9: Grouting pump strokes as a function of time.

FEM-MODELLING

Geometry and soil parametersThe model has been built using PLAXIS 3D Tunnel (Brinkgreve & Broere 2004). The model was extended modularly, i.e. first starting with only a tunnel and face support, then adding a new component in order to investigate the model’s response. Subse-quently adding the TBM weight, a grouting pressure zone, jack forces and finally TBM contraction and backup train weight.

Half a tunnel is modelled with standard boundary conditions for soil and lining. The length of one tunnel ring is 1.5 m. In longitudinal direction 70 slices of 1.5 m have been used to model the phased construction. This number of stages is required in order to create a constant bending moment at some distance from both TBM and model boun-daries. The total length and width of the model is 165 m and 75 m respectively. The model base has been chosen at the base of the Kedichem formation (stiff sandy clay). The underlying sand formation is even more stiff regarding unloading (EUR

ref = 150 MN/m²). The major part of the tunnel was bored through Pleistocene sand; only a small part protrudes in the Kedichem clay. Part of the model is sketched in figure 10.

Layer level γsat ϕ c E50ref Eoed

ref EURref

NAP*/** kN/m³ kN/m² MN/m² MN/m² MN/m²Sand -1.5 19 35 1 25 25 85Peat -1.9 11 25 10 2 1 15Clay -8.0 13 28 4 4 2 20Sand*** -13.2 20 38 1 40 40 150Kedichem Clay -24.6 20 32 1 9 6 60Bottom -36.0* NAP = Dutch reference level** Top of the layer*** Pleistocene

Table 1: Hardening Soil parameters

The soil has been modelled using the Hardening Soil model (Brinkgreve & Broere 2004). This model implements soil behaviour under the unloading-reloading conditions gover-ning tunnel construction. Soil parameters were derived from in situ and laboratory tests. Table 1 lists important soil parameters.

Tunnel Boring Machine (TBM)The TBM is modelled by plate elements. The diameter, stiffness and unit weight vary along the length of the TBM. Contraction of the TBM results in volume loss as tunnelling progresses. TBM face pressure is modelled by a pressure at the crown and a pressure gradient of 14 kN/m²/m (measured values). The jack forces measured during tunnelling have been applied on the tunnel lining using point forces. Like the face support they are modelled as external forces not linked to the TBM. The horizontal balance forces of the face support and jack forces have not been modelled. This is because the resulting horizontal force is relatively small, as is confirmed by additional calculations. The bac-kup train is modelled by point loads behind the TBM. Figure 11 displays the different process parameters implemented in the 4D grouting pressure FEM model.

Figure 10: Schematic FEM model geometry

Tunnel liningThe tunnel lining is modelled by plate elements. The bending stiffness in both ring and longitudinal directions have been assessed by FEM analyses accounting for reduced stiffness caused by joints between ring segments. It is possible to select a plate thickness and Young’s modulus such that both ring and longitudinal bending stiffness can be modelled correctly. Three slices of lining have been applied in the tail end of the TBM corresponding to the actual situation. These additional tunnel rings inside the TBM result in a downward force on the lining next to the grouting zone.

Figure 11: Tunnel boring process parameters featured in the 4D grouting pressure FEM model

Figure 12: Close up of the tunnel, showing the location of the point loads representing the backup train

GROUT

During boring of the second tunnel the grouting pres-sure has been measured at 14 locations along the circumference of one instrumented ring. Both the measured pressure and pressure gradient vary with distance. They also differ during periods of excavation (high pressure (gradient)) and standstill (lower pressure (gradient)). The grouting pres-sure has been modelled for a length of six rings behind the TBM. The modelled pressure and pressure gradient are given in figure 13. Behind the grouting pressure zone, the grout is assumed to behave like a soil and is therefore modelled by volume elements as an elastic material with a Young’s modulus assumed equal to the surrounding soil.

Calculation processThe tunnel boring process has been modelled by a staged construction calculation with PLAXIS 3D Tunnel V2, where in approximately 60 stages one ring per stage is ‘bored’. This version includes a copy option whereby the features (e.g. loads, structures, state of soil elements, water pressures etc.) of one stage can be easily copied to the next. This results in an efficient modelling procedure and a minimisation of input errors.

RESULTS 4D FEM ANALYSIS

Introduction After performing the modular construction of the model and assessing the governing process parameters the final model was constructed using best estimate values for every possible input parameter. This calculation is called the standard run. The standard run is equipped with:• measured (applied) face pressures• real bending stiffness for TBM • values of contraction of the TBM fully supplied• measured (applied) jack forces• real bending stiffness lining in both ring and longitudinal direction• measured grouting pressures

Where possible, the results of the standard run have been compared with measured soil deformations. In addition a series of calculations have been conducted in order to determine the model’s sensitivity to certain parameter variations.

Results of the standard run: surface settlementThe results show that the maximum of the calculated final surface settlement is about 10 mm (figure 14 and 15 depict the transverse and longitudinal troughs). The final

Plaxis Practice

Figure 14: Standard run: calculated and measured transverse settlement troughs.

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Figure 13: Modelling the grouting pressure Figure 15: Standard run: calculated longitudinal settlement trough

deformations at surface level measured at the monitoring section varied between approximately 15 mm heave and 10 mm settlement. Hence the 4D model with best estimate parameters calculates the maximum of the measured settlements.

The calculated transverse trough is symmetric, while the measured one is not. This asymmetry is probably caused by variations in grouting pressure at the monitoring section and / or the presence of a safety shaft constructed before the tunnels. The cal-culated longitudinal trough is one of three possible troughs found during the passage of the TBM underneath the monitoring section (see also figure 4).

Results of the standard run: tunnel displacementWhen performing a staged construction calculation with PLAXIS 3D Tunnel, every new ring is added in a stressless situation. In obeying this condition the new ring is placed with an offset onto the tunnel. This repeated process causes a displacement of the tunnel as displayed in figure 16, where uplift is plotted against distance from the front of the model. After having modelled 60 rings this displacement is about 60 mm. This phenomenon is believed to stem from the stressless procedure in PLAXIS, excluding real life construction effects. This means that in reality newly added rings are probably built in warped (intentionally or unintentionally) and / or a downward force is exerted on the tunnel by the TBM (see figure 18).

Figure 16: Calculated displacement of the tunnel over 60 rings

The calculated net uplift of a tunnel segment caused by grouting pressures after installation is displayed in figure 17. Also shown are the measured displacements of ring 2080, the only ring monitored after installation. The measured uplift is about 20 mm and occurs over a distance of approximately 12 m after installation. The calculated uplift is only 4 mm and occurs over a length of 9 —12 m. The difference is significant. Figure 17 indicates that further uplift is suppressed by backup train loads

Figure 18: Warped position of newly placed tunnel rings (left) or downward force exer-ted by TBM on tunnel (right)

Results of the parameter variation studyIn order to assess the sensitivity of the 4D FEM model to parameter variations, additio-nal calculations were performed. The most important variations were carried out for:• tunnel bending stiffness reduced by a factor 0.5• soil stiffness EUR

ref reduced by a factor 0.7• modelling TBM without contraction

The results of the variations study are presented in tables 2a and 2b, where the focus is on the maximum final surface settlement and the calculated net uplift of the tunnel construction respectively. The results can be compared with the results of the standard run, given in the top row.

standard run 10 mm settlement tunnel bending stiffness x 0.5 no effectsoil stiffness x 0.7 8 mm settlementfront pressure +10 kN/m² * no effectgrouting pressure +20 kN/m² ** 8 mm settlementgrouting pressure +50 kN/m² *** 2 mm settlementgrouting pressure +100 kN/m² **** 30 mm heaveno contraction TBM 2 mm settlement* +10 kN/m² equals +5% ** +20 kN/m² equals +6 to +10% ***+50 kN/m² equals +14 to +25% ****

+100 kN/m² equals +28 to +50% ***** N/I = not investigated

Table 2a: Maximum value calculated surface settlement

standard run 4 mm tunnel bending stiffness x 0.5 7 mm soil stiffness x 0.7 4 mm front pressure +10 kN/m² 4 mm grouting pressure +20 kN/m² 5 mm grouting pressure +50 kN/m² 6 mmgrouting pressure +100 kN/m² N/I *****

no contraction TBM N/I *****

Table 2b: Maximum value calculated net uplift tunnel

Finally the measured and calculated horizontal displacements are plotted in figure 19. The shapes match well. When omitting TBM contraction the calculated curve shifts toward the measured one. On raising the grouting pressure uniformly by 50 kN/m² the calculated curve closely matches those measured.

Correlating the calculated surface settlements and the results from figure 19 indicate that either the applied contraction is too high or the grouting pressures are too low in the standard run. Possibly a combination of these two should be implemented to match the measured ground deformations.`

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Figure 17: Displacements of 1 tunnel ring after installation. Small triangles represent backup train wheel loads.

Plaxis Practice

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Figure 19: Inclinometer results showing measured values and calculated values for three calculations (s.r. means standard run; c = 0 means zero contraction; +50 kN/m² indicates the raised grouting pressure ).

Figure 21: bending moments M11 in the tunnel linng

Figure 20: Bending moments at various cross sections in the 3D Tunnel model

Bending moments and normal forces in the tunnel liningApart from displacements, also the forces and moments in the tunnel lining can be derived from the calculation. In figure 20 the bending moments in various cross secti-ons are given for various distances to the TBM. In cross section 1 the moments are given in the lining, just before the lining exits the TBM tail. In section 2 the lining is loaded by the grout pressure and the point load from the wheels of a backup train. The influence of this wheel load can be clearly seen. The other sections are taken further back and show a diminishing influence of the wheel loads. Figure 21 shows the distribution of these moments over the entire lining.

CONCLUSIONS & RECOMMENDATIONS

The results presented in this paper show that state of the art FEM software and compu-ter technology combined with the practical experience currently available it is feasible to model tunnel boring with a 4D approach. Process parameters can be modelled wit-hout difficulty and their individual influence on model response can be evaluated with certain parameters can be varied easily (soil / tunnel properties) and the PLAXIS copy

option now available limits repetitive data entry and minimises input errors. However, changing contraction or grouting pressure distribution demands means defining and running a new calculation. This is more time consuming.

Both monitoring and TBM data show that the boring process has not been constant at the section used for the history match with the FEM model. However, the case study and parameter variations show that recalculation of a tunnel boring process in terms of soil displacements is feasible.

Grouting pressures and TBM contraction govern soil displacements. Hence, these parameters should be carefully assessed. Measured grouting pressures provided the input for this 4D FEM model. In future predictions grouting pressure distribution can be determined using the recently developed grout consolidation model as presented by Bezuijen & Talmon (2003). It is questionable whether TBM contraction should be fully applied. In practice contraction might be limited by either face or grouting pressures. REFERENCES

• Bezuijen, A. & Talmon, A. 2003. F220-E-03-109 Groutdruk-metingen Sophiaspoortunnel – Metingen en analyse beide buizen. Gouda: COB (The Netherlands)

• Brinkgreve, R.B.J. & Broere, W. (eds.) 2004. PLAXIS – 3D Tunnel version 2 - user manual.

Recent activities

43%

Fully coupleddeformation-

porepressureanalysis

Small strainstiffnessmodelling

Cyclicloading &

Liquefactionmodel

Extendedphi-c

reductionprocedure

Parametervariation

(sensetivityanalysis)

Simulation ofsoil lab test

Anisotropy Geometryimport,

preferredformat...

35%40%

58%63%

48%

24%

33%

Improved ways to check calculations and results (Quality control) 1

Extension of geometrical modelling functionality 2

Improved robustness/stability of GUI software 3

Improved robustness/stability of the calculation kernel 4

Improved extension manuals 5

Simplification of import- and exportpossibilities with other software packages 6

Increase quality of support during difficult projects 7

More user friendly products 8

Improved Price/Quality ration 9

Integration of 2D and 3D software10

Faster feedback in cases of questions or problems11

Extension export functionality12

More attention to wishes of clients13

More active in contacts and coaching on a local level14

More accessible courses15

More frequent distribution of upgrades16

Improved availability of helpdesk17

Improved customer focus of the helpdesk18

Better anticipation of new marketdevelopment19

Usermeetings on a more frequent basis20

MARKET RESPONSE ANALYSIS

On behalf of Plaxis an independent Market Survey Company called Service check carried out a Customer Satisfaction Analysis. This has been carried out in the first half of 2005 and with over 200 participants the results are very reliable and a guideline for new deve-lopments of our products and services. A huge thank you to all our respondents. We appreciate the time and thought given to answering the questionnaire and we value your input. Plaxis is committed to addressing all the issues that have been notified to us, in the imme-diate future and everyone will shortly receive notice of our plan of action.

13

PLAXIS STAFF

Plaxis extended her staff with three persons; Mrs. Wendy Veenstra, Mr. Lars Beuth and Mr. Micha van der Sloot.

• Wendy studied sociology and has a background in legal risk management. She will be responsible as a coordinator in all our Marketing and Sales activities.

• Lars Beuth studied Civil Engineering and graduated at the Technical University of Kaiserslautern in southwestern Germany, specializing on geotechnical engineering

Figure 2: Priority Analysis over the total results.

The questionnaire contained a range of questions con-cerning the satisfaction of the use of Plaxis software, our agents, helpdesk support, courses, user meetings, website and mailings.

Concerning the user satisfaction of Plaxis software: the scores on most aspects are good to very good. The software in general, its user friendliness, functionality and the concept of the program are all rated very well but also, of course, our shortcomings were exposed. The graph below shows the results of the vote for suggested improvements/extensions. As can be concluded from this graph, parameter variation is the improvement most wanted by Plaxis users (63% of the participants).

The need to improve the software also comes forward in the over all priority analysis: improved robust-ness/stability of the GUI software and the calculation kernel come third and fourth in line of all measures of improvement (see graph). Respondents give even more priority to the improvement of the ways to check calcu-lations and results, and to the extension of geometrical modelling functionality. This is a priority graph over all our products and services.

Figure 1: Desired adjustments in Plaxis 2D.

and information sciences in Civil Engineering. His main activity within Plaxis will be the synchronization and further development of the Output programs of the Plaxis product range. Furthermore Micha van der Sloot joined the Plaxis R&D team.

• Micha studied Civil Engineering, and graduated at TU Delft, specializing in Hydraulic Engineering and Probabilistic Design. His main activity is the quality control of all Plaxis products. Additional Plaxis still has vacancies for a Junior and Senior GUI Software Developer and for a course coordinator.

Ronald Brinkgreve, Plaxis BV

Recent activities

THE FIFTH INTERNATIONAL SYMPOSIUM OF TC 28 ON UNDERGROUND CONSTRUCTION IN SOFT GROUND WAS HELD LAST JUNE IN AMSTERDAM

Last summer from 15–17 June Technical Committee 28 for Underground Construction in Soft Ground held its three yearly symposium in Amsterdam. From Plaxis bv, Klaas Jan Bakker and Wout Broere, due to their relation as lecturers with Delft University of Technology were involved with the organization of the Symposium.

T28 is a committee of the International Society for Soil Mechanics and Geotechnical Engineering and was established in 1989, with the main purpose to provide a forum for interchange of ideas and discussion using representatives from many countries with an active interest in tunneling and deep excavations in the urban environment. During the previous symposium in TOULOUSE (2002), the Netherlands was asked to host the next symposium, as the activities in Underground Construction in the past decade, e.g. the Green Heart tunnel, the Western Scheldt tunnel and the plans for the new North South metro line for Amsterdam attracted international attention.

The symposium was held in the Novotel Hotel in Amsterdam from 15 to 17 june. The first two days where spend for technical discussion sessions and on the last day technical visits were organized to the Amsterdam North South Metro project, to the Green Heart tunnel and to the Rotterdam Randstadrail project. Apart from the opening lecture by Professor Emeritus Arnold Verruijt on typical Dutch tunnel engineering issues, special lec-tures were given by Prof Robert J. Mair of Cambridge on “Reflections on advances over 10 years TC28”, and by Mr Nick Shirlaw on “Deep excavations in Singapore Marine Clay”.

The themes for the symposium were, to begin with, Design methods for tunnels, influences on foundations and secondly, Bored Tunnels; construction, further Mitigating measures e.g. to prevent unwanted settlements, Numerical analysis of tunnels and deep excava-

tions, and further Monitoring of underground constructions, and Deep excavations. The general reports give an overview of the different papers for the six technical sessions.

The symposium was succesfull in the sense that over 200 delegates from 34 countries attended and discussed over 122 papers, which was well above the number anticipated for. Papers where presented either orally of by poster presen-tation. Among these papers quite a number of contributions illustrate the use of Plaxis computer codes for tunneling and deep excavations. Among these was a paper by Mr Hoefsloot et al, which explains the results that can be obtained with the latest version 2 of the Plaxis 3D Tunnel program. A sum-mary of that paper is also reproduced in this bulletin.

The Symposium was sponsored by the Dutch Public Works Department (Rijkswaterstaat) and by various companies from The Netherlands and abroad among which also Plaxis BV.

Dr ir K.J. BakkerDirector Plaxis BVChairman of Organizing committee TC28 IS-AmsterdamPlaxis Course in Old Trafford (Manchester United)

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EVENTS

In september Plaxis gave acte de presence at 2 Conferences; China Tunnel 2005 in Shanghai and the important 16th Intenational Conference on Soil Mechanics and Geotechnical Engineering in Osaka. On both conferences Plaxis demonstrated respecti-vely the Chinese and Japanese version of Plaxis V8.

Our course program has experienced a novelty in August with courses in Australia. In corporation with local and international specialist two courses have been succesfully carried out in Perth and Sydney. In the line of new courses we also planned the first experienced Plaxis course in Mexico from October 24 till 27. In november the 12th European Plaxis User Meeting will held in Karlsruhe. For detailed information on these and other upcoming conferences, seminars, courses, user meetings and other Plaxis related events check out on regular base our agenda on our website.

Japanese version of Plaxis V8

How a distressed quay wall could be moved back in place… using Plaxis

B. Simon, Terrasol

Figure 1: Schematic quay cross section (CM: datum at lowest astronomical tide)

15

INTRODUCTION

Chef de Baie 1 Quay was built in 1982 in La Rochelle harbour. It is 180m long and 23.5m high. It receives ships with cargoes of bulk timber and containers. It is an essential piece of the port facilities as it receives more than 30% of all quantities of wood and other similar products which are imported into France.

DESCRIPTION

The quay is a combined wall of steel tubular piles and sheet piles with one row of tie-back anchors connected to a parallel anchorage wall. Pile spacing is 1.7m with one sheet pile between. The quay is built at the toe of an existing reclaimed fill slope.

Each tie rod, 30m long, consists of three steel pieces connected by two cast iron con-necting sleeves. There is one tie rod per pile.

The whole structure is designed as an anchored frame supporting the crane rails. The front wall is designed using a subgrade reaction approach.

New fill consists of well graded limestone material up to 600 mm size.The front wall is installed with tie rods only supported at their ends and on the inter-mediate pile row.

It can be established that filling operations were carried out in a rather crude way with fill material simply pushed against the front wall from the existing platform across tie rods.

DEFECTS

Defects appeared quite suddenly on 12th February 2001 between 12 noon and 1 p.m. without any witnesses. Misalignment of the rails and decimetric settlements of the platform were readily apparent. Horizontal displacement of the capping beam reached some 30 to 40cm on a 100m stretch.

Figure 2 and figure 3: Platform settlement and rail misalignment

Emergency backfilling in front of the wall could stop this progression and restore safety.

Because of the utmost importance of this quay for the operations of La Rochelle har-bour, thorough investigations were started to find the cause of such defects and to be able to propose appropriate remedial works.

Plaxis Practice

It could be observed that some tie rod caps were in loose contact with their piles while others had punched and torn up the pile envelopes.

Excavation of the quay platform made clear there was no difference of piezometry between fill and basin at low tide.

This course of action combined historical survey and specific geotechnical borings. It led us to ascertain without any doubt, and in less than four months, that the defects were caused by accidental breakage of a few of the anchor tendons which had sustained excessive stresses for a time period back to construction. The construction procedure had created the conditions for quite erratic tensions between adjacent anchors, some of them having probably failed since that very early stage without anybody noticing it. A cast-iron piece connecting two elementary tendon pieces was recovered and inspected to confirm it broke a long time ago.

ANALYSIS WITH PLAXIS OF THE CAUSES OF THE DEFECT

At first, it was decided to check the stresses in the tie rods before filling, when they simply hung between the front and back wall with one temporary support line in bet-ween. Only updated mesh analysis provides reliable results as can be seen in figure 4 where they are compared to results from standard analysis. Updated mesh analysis demonstrated that tie rods could be submitted to significant tensions, which combined with the bending stresses led to stresses as high as 20% of the tendon yield stress. A significant strength amount had thus already been consumed in that preliminary stage and this clearly should not have been neglected in the design.

A complete and rather simple model of the quay (including the emergency fill) was prepared. It comprised 347 6- noded elements.

Mohr Coulomb model was used for all layers. Fill strength parameters were derived from the results of Menard pressuremeter tests carried out following the disorder. Limestone Young’s modulus could be ascertained from the results of one pile lateral loading test carried out during the construction, which was partially documented.

γ/γsat(kN/m³) c (kPa) φ (°) ψ (°) E (MPa) νFill 18/21 5 35 5 50 0.25Limestone 18/21 500 0 0 1000 0.20

Table 1 Model parameters.

Rinter value was set at 0.5 for all layers.

The filling operations (slope in limit equilibrium) could be properly modelled by activa-ting clusters laid parallel to the initial slope (this feature could not be incorporated in the initial design by the subgrade reaction approach).

A comparison was made between Plaxis calculations assuming tie rods acting either as node to node anchors or as geogrids with the same axial stiffness per ml. In the first case no interaction is assumed between fill and tendons while the latter assumes a complete interaction where tendons are carrying the full weight of overlying fill. The model neglecting fill/tie rod interaction led to less horizontal displacement with higher stresses found in the front piles.

Ymax M+ M- T (cm) (kNm/ml) (kNm/ml) (kN/ml)Subgrade reaction model 8.4 1820 2280 650Plaxis modelwithout interaction 9.4 1480 2160 623with interaction 7.5 1265 1820 771

Table 2 Results.

Plaxis model

tendon 80 mm under its ownweight

Updated mesh analysis

Standard analysis

11 m 20 m

y = 0.15 m

M = 1.18 kNm T = 103 kN

y = 0.08 m

M = 13.0 kNm

0.2σebending moments

Figure 5: Plaxis model of the quay

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Plaxis Practice

Figure 4: Hanging rod analysis

T = 125 kN/ml y(0) = -0.3 cm

17

The same model was used to study how the displacement at the top of the wall evolved when the tie rod tension was decreased by steps. This showed that tie rod reaction had to be kept at around 75% of the installed capacity to account for displacement around 30 to 40cm as observed just before emergency fil-ling. Thus it could be concluded that not all the tie rods were broken or else the displacements would have been much higher. In addition the Plaxis model pointed out that maximum stress in the front tubular piles remained less than 75% of yield stress despite the amplitude of their displacement.

These piles could then still be reused. Checks of the structural integrity of other quay components led to the conclusion that the concrete capping beam could also be reused while the transverse and rear beams which suffered too much cracking had to be rebuilt.

USE OF PLAXIS MODEL TO EVALUATE REPAIR SOLUTIONS

The agreement found between the numerical model and the recorded displacements led us to consider that the model could help exploring various solutions for moving back the wall. This complementary study proved the wall alignment could be restored by combining controlled excavation behind the wall, down to elevation -7.6 CM, and pre-stressing the temporary tie anchors. Tension forces varied between 125 kN/ml and 145 per ml to move the front line between 0.6cm and 1.8cm back its theoretical initial position.

The Plaxis model greatly helped convincing the Owner that realignment of his quay was feasible!

Figure 6: quay displacement and bending moment versus remaining tie-rod capacity

Figures 7a and 7b: Modelling the repair actions

18

Plaxis Practice

REPAIR WORKS AND COMPARISON WITH PLAXIS PREDICTIONS

From then on the detailed design of these remedial works could be prepared by a team set up by the Owner with one structural expert and one geotechnical expert. This inclu-ded a detailed description of all successive stages. Tenders were asked of specialised contractors in the same way as for a new structure.

Works started in May 2003 less than 26 months after the accident with the following steps:• Temporary fill to improve passive thrust in front of rear anchoring wall • Temporary tie rods (2 tie rods every 5 piles : one per 4.75 ml)• Controlled excavation down to -7.6 CM together with tensioning of the temporary tie

rods (in successive runs)• Rebuilding the rear beam (piles and transverse beams)The quay could be moved back along its initial alignment with accuracy less than a few centimetres.Measured tensions in the temporary tie rods at final stage are plotted in figure 8. Average value is slightly higher than the estimated tension for a final displacement of 1.8cm beyond the theoretical line. Since achieved displacement was slightly more (bet-ween -2 and -3cm), Plaxis predicted tension values match closely the observations.

CONCLUSION

This case illustrates quite remarkably how a numerical model supported by careful in situ observations, specific borings and historical survey can help decision making: decisions about either restoring safety soon after the accident or choosing the most appropriate remedial solution later on.

Figure 8: measured tensions in the temporary tie-rods

19

Plaxis BVP.O. Box 572

2600 AN Delft

The Netherlands

Tel: + 31 (0)15 2517720

Fax: + 31 (0)15 2573107

Email: [email protected]

Website: http://www.plaxis.nl

PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES

Activities200524 – 27 October 2005 International Course for Experienced Plaxis Users (English)Santiago de Querétaro, Qro. México

9 – 10 November 2005Construction Computing 2005, The Barbican, London, UK

9 – 11 November 2005 12th European Plaxis User Meeting, Karlsruhe, Germany

16 – 18 November 2005 Short Course on Computational Geotechnics (French)Paris, France

24 November 2005 Norwegian Plaxis User Meeting, Oslo, Norway

2 – 7 December 2005 Plaxis Workshop, Kuwait Research Institute

December 2005Plaxis User meeting, Delft, The Netherlands

200616 – 18 January 2006International course on Computational GeotechnicsNoordwijkerhout, the Netherlands

3 – 5 January 2006Course Computational Geotechnics, New York, U.S.A.

1 February 2006Workshop User defined soil models (WildeFEA Limited)Manchester, UK

13 – 17 February 2006Course Computational Geotechnics, South Africa

26 February – 1 March 2006GeoCongress 2006, Atlanta, Georgia, U.S.A.

7 March 2006Introduction to Geotechnical Finite Element Analysis (WildeFEA Limited), London, UK

8 March 2006Introduction to Geotechnical Finite Element Analysis (WildeFEA Limited), Manchester, UK

13 – 15 March 2006Course Computational Geotechnics (German), Stuttgart, Germany

20 – 23 March 2006International course for experienced Plaxis users, Antwerp, Belgium

22 – 27 April 2006 ITA-AITES 2006: 32nd World Tunnel Conference, Seoul, Korea

April-May 20062nd Asian Course for Exp. Plaxis UsersKuala Lumpur, Malaysia

April – May 20061st Asian Users Day, Kuala Lumpur, Malaysia

18 – 22 April 2006100th Anniversary Earthquake ConferenceSan Fransisco, U.S.A.

22 – 27 April 2006ITA 2006, Seoul, South Korea

31 May – 2 June 200610th Piling and Deep FoundationsAmsterdam, the Netherlands

2 – 4 June 2006 GeoShanghai International Conference, Shanghai, China

7 – 9 June 2006Danube-European CoGE+Course, Ljubjana, Slovenia

20 – 22 June 2006Course Computational GeotechnicsManchester, United Kingdom

28 – 30 June 2006ICDE 2006 Deep Excavations, Singapore

6 – 8 September 2006 6th European Conference on Numerical Methods in Geotechnical Engineering, Graz, Austria

29 – 30 September 2006Baugrund Tagung, Bremen, Germany