Editorial 12 - JUNE 2002 IN THIS ISSUE:

Transcription

1 PLAXIS Nº 12 - JUNE 2002 Editorial Bulletin of the PLAXIS Users Association (NL) Plaxis bulletin Plaxis B.V. P.O. Box AN Delft The Netherlands bulletin@plaxis.nl IN THIS ISSUE: Editorial 1 Column Vermeer 2 New developments 4 Note on pore pressure 6 Benchmarking I 9 Benchmarking II 12 Recent Activities 13 Plaxis practice I 14 Plaxis practice II 17 Users forum 22 Some Geometries 22 Agenda 24 Some time has passed since the appearance of our last bulletin no 11, but the PLAXIS team did not sit still. Not only was a new director appointed for PLAXIS B.V. which will be introduced further on, also a number of other new team-members have come to work for PLAXIS. The Plaxis-team has extended with four new people in order to improve the capability to accommodate for the demand on new plaxis developments. The Plaxis-team consist of 14 people. In the next bulletin, we will briefly introduce them to you. New Developments which will be discussed in the contribution by Dr Brinkgreve, the head of our development team. He will discuss further developments such as for the release of Plaxis Version 8, the progress on the PLAX-flow program and the other 3D developments. With respect to PLAXIS 2D, Version 8 is due to be expected after the summer holidays, as Beta testing of this new program is underway, and the users in our regular PLAXIS course in Noordwijkerhout in January and also the attendants of the advanced course have had some opportunity to experience this new program. In his regular column Prof. Vermeer will discuss the use of soil parameters and especially parameter estimation. Not always is it possible to do a direct test for a parameter. Or sometimes in a pre-design stage there is only limited information of the soil stratification. In that case it is often very convenient to have some correlations between different soil-parameters in order to be able to proceed with a geotechnical design. In this issue Prof. Vermeer discusses Oedometer stiffness of Soft Soils. In addition to the aforementioned, Prof. Schweiger who also is a regular contributor to our bulletin discusses the relation between Skemptons pore pressure parameters A and B and the performance of the Hardening Soil model. Furthermore we are fortunate to have new contributions with respect to Benchmarking; two contributions on benchmarking are presented here, one on Shield tunnelling and another on excavations. Again we are glad to have a number of practical applications; Among which are a contribution by Dr. Gysi, on a multi-anchored retaining wall, and another one by Mr. Cheang from Singapore on a complicated retaining wall with Jack-In Anchors. Finally in the Users Forum it is shown how a more complicated 3D situation of a Retaining wall with anchors is practically modelled with PLAXIS 2D. Editorial Staff: Martin de Kant, Plaxis Users Association (NL) Marco Hutteman, Plaxis Users Association (NL) Peter Brand, Plaxis B.V. Scientific Committee: Prof. Pieter Vermeer, Stuttgart University Dr. Ronald Brinkgreve, Plaxis bv 1

2 Fig. 1: Atterberg limits of 21 different soils that were tested by Engel Column Vermeer ON THE OEDOMETER STIFFNESS OF SOFT SOILS For normally consolidated fine-grained soils, we have the logarithmic compression law, e = C c log, where De is the change of the void ratio, C c the compression index and the vertical effectivestress in onedimensional compression. The compression index C c is measured in oedometer tests, together with other stiffness related parameters such as the swelling index and the preconsolidation stress. In this column I will discuss correlations for the compression index C c. It should be realized that Terzaghi and other founding fathers of Soil Mechanics lived in the 10-log-paper period and their findings have to be reformulated for use in computer codes. Hence, we have to change from a 10-log to a natural logarithm in order to obtain the reformulated law, e = - ln, where = C c ln10. On top of this it is convenient to use strain instead of void ratio, which leads to the compression law, where = * ln, * = (1+e) and is a finite strain increment. I will address C c, as well as the modified compression index * and in addition the oedometer modulus E oed. One of the best-known geotechnical correlations reads C c 0.9 (w L - 0.1), where w L is the liquid limit. For details, the reader is referred to the book by Terzaghi and Peck (1967). Wroth and Wood (1978) proposed the seemingly different correlation C c 1.35I P, where I P is the plasticity index. In reality the two correlations are virtually identical, as the plasticity index can usually be approximated as I P 0.73 (w L - 0.1). Indeed, with the exception of sandy silts, data for I P and w L tend to be on a straight line that is parallel to the so-called A-line in Casagrande s plasticity chart (see Fig. 1). On using the I p -w L correlation, the Terzaghi-Peck correlation reads C c 1.23I P, which is very close to the finding of C c 1.35I P by Wroth and Wood. Considering the large amount of evidence on the correlations, C c 1.35I P and I P 0.73 (wl - 0.1), I conclude that we may use both C c 1.35I P and C c w L (1) The latter one is only slightly different from the earlier one by Terzaghi and Peck and to my judgement also slightly better. Let us now address the modified compression index * as used in all advanced Plaxis models. The relationship between the traditional compression index C c and the modified one * is expressed by the equation *= C c C c (1+e) In (2) The approximation follows for e=1. In general it is crude to assume e 1, but it works within the context of the correlations for soft soils. In combination with the correlations for C c it leads to: * 0.3l p and * 0.2(w L - 0.1) (3) For a direct assessment of these correlations, we will consider data by Engel (2001). This database contains modified compression indices for 21 different clays and silts, with a liquid limit ranging from 0.2 up to 1.1 and a plasticity index between 0.03 and 0.7, as can 2

3 be seen in Fig. 1. Engel s data for * leads to Figures 2 and 3. From Fig. 2 it can be concluded that the correlation Let us now consider the oedometer stiffness. To this end the logarithmic compression law = *. ln can be written in the differential form d /dln = * and one obtains d / d = / The tangent stiffness in oedometer-compression, also refered to as the constrained modulus, is thus proportional to stress. Hence, E oed = '/ *, where E oed is also denoted as M or E s, depending on conventions in different countries. This linear stress dependency of soil stiffness is nice for finegrained NC-soils, but not for coarse-grained ones. Therefore Ohde (1939) and Janbu (1963) proposed a generalisation of the form: ref E oed = E oed ( '/P ref ) m with P ref = 100kPa (4) Fig. 2: Compression indices as measured by Engel as a function of I p Fig. 3: Compression indices correlate nicely with the liquid limit * 0.3l p has some shortcomings. A close inspection shows that it is nice for clays with plasticity indices above the A-line in Casagrande s plasticity chart, but not for silts with I p below the A-line. To include such silts one could better use the correlation, * 0.2(w L - 0.1) as demonstrated in Fig. 3. On plotting * as a function of the liquid limit, as done in Fig. 3, it is immediately clear that there is an extremely nice correlation. It should also be recalled that the correlation * 0.2(w L - 0.1) is not only supported by Engel s database, but that it is also fully in line with the work of Wroth & Wood as well as Terzaghi & Peck on correlations for C c. where m is an empirical exponent. This equation reduces to the linear stress dependency of soil stiffness for m=1. In the special case of m=1, one thus obtains the logarithmic compression law for finegrained NC-soils. For coarse grained soils, much lower exponents of about m=0.5 are reported by Janbu (1963), Von Soos (2001) and other researchers. The above power law of Ohde, Janbu and Von Soos has been incorporated into the Hardening Soil Model of the Plaxis code. Here it should be noted that the above authors define ref E oed = v. P ref, where v is a so-called modulus number. Instead of the dimensionless modulus number, the Hardening Soil Model involves ref E oed as an input parameter, i.e. the constrained modulus at a reference stress of = p ref = 100kPa. For the coming Version 8 of the Plaxis code, we have also considered the use of alternative input parameters. Instead of ref E oed, we have discussed the modulus number 1/ * as well as the modified compression index itself, as it yields ref * P ref / E oed (5) In fact, this simple relationship between the oedometer stiffness and the modified compression index triggered our thinking on alternative input parameters. Finally we decided 3

4 to go one step further and use the traditional compression index C c by implementing the equations: New Developments ref E oed = P ref (1+e) ln10 =. P ref (6) * C c Within the new Version 8, users will have the choice between the input of E oed and the alternative of C c. Similarly, the so-called swelling index C s will be used as an alternative input parameter for the unloading-reloading stiffness E ur. On inputting C c one also has to prescribe a value for the void ratio. Here, a default value of e=1 will be introduced. This will make the Hardening Soil Model easier to use in the field of soft soil engineering. In a few months, Plaxis version 8 will be released. This new 2D program is one of the results of a recently finished two-years project on Plaxis developments. Another results of this project is the 3D Tunnel program, which was released last year. In this bulletin some new features of Plaxis version 8 will be mentioned. The new features are divided into three groups: Modeling features, calculation options and user friendliness. P.A. Vermeer, Stuttgart University REFERENCES: Engel, J., Procedures for the Selection of Soil Parameters (in German), Habilitation study, Department of Civil Engineering, Technical University of Dresden, 2001, 188 p. Janbu, N., "Soil Compressibility as Determined by Oedometer and Triaxial Tests", Proceedings 3rd European Conference on Soil Mechanics and Foundation Engineering, Vol. 1, Wiesbaden, 1963, pp Ohde, J., "On the Stress Distribution in the Ground" (in German), Bauingenieur, Vol. 20, No. 33/34, 1939, pp MODELING FEATURES Plaxis (2D) version 8 has several new features for the modeling of tunnels and underground structures. Some of these features were already implemented in the 3D tunnel program, such as: Terzaghi, K. and Peck, R. B., "Soil Mechanics in Engineering Practice", 2nd Ed, John Wiley and Sons, New York, 1967, 729 p. Soos von, P., "Properties of Soil and Rock" (in German), Grundbautaschenbuch, Vol. 1, 6th Ed., Ernst & Sohn, Berlin, 2001, pp Wroth, C. P. and Wood, D. M., "The Correlation of Index Properties with Some Basic Engineering Properties of Soils", Canadian Geotechnical Journal, Vol. 15, No. 2, 1987, pp Extended tunnel designer, including thick tunnel linings and tunnel shapes composed of arcs, lines and corners. - Application of user-defined (pore) pressure distribution in soil clusters to simulate grout injection. - Application of volume strain in soil clusters to simulate soil volume loss or compensation grouting. - Jointed Rock model Other new modeling features are aimed at the modeling of soil, structures and soil structure interaction: 4

5 - Input of Skempton's B-factor for partially undrained soil behavior. - Hinges and rotation springs to model beam connections that are not fully rigid. - Separate maximum anchor forces distinction between extension and compression). - De-activation of interface elements to temporarily avoid soil-structure interaction or impermeability. - Special option to create drains and wells for a groundwater flow calculation. CALCULATION OPTIONS Regarding the new calculation options, most new features are in fact improvements of 'inconsistencies' from previous versions. Examples of such improvements are: - Staged Construction can be used as loading input in a Consolidation analysis. - A Consolidation analysis can be executed as an Updated Mesh calculation. - In an Updated Mesh calculation, the update of water pressures with respect to the deformed position of elements and stress points can be included. In this way, the settlement of soil under a continuous phreatic level can be simulated accurately. - Loads can be applied in Staged Construction, which enables a combination of construction and loading in the same calculation phase. The need to use multipliers to apply loading has decreased. This makes the definition of calculation phases more logical and it enhances the flexibility to use different load combinations. - Preview (picture) of defined calculation phase in a separate calculations tab sheet. - Improved robustness of steady-state groundwater flow calculations. Simplified input of groundwater head boundary conditions based on general phreatic level. In addition, a separate program for transient groundwater flow is planned to be released at the end of USER FRIENDLINESS Many new features in the framework of 'user friendliness' are based on users' suggestions from the past. Examples of these features are: - Reflection of input data and applied loads in the output program. - Report generation, for a complete documentation of a project (including input data and applied loads). - Complete output of stresses (effective, total, water), presented both as principal stresses, cartesian stresses; also available in cross sections and in the Curves program. - Equivalent force in cross-section plots of normal stresses. - Force envelopes, showing the maximum values of structural forces over all proceeding calculation phases. - Scale bar of plotted quantities in the output program. - Color plots plotted as bitmaps rather than meta-files. This avoids the loss of colors when importing these plots in other software. - Parameters in material data sets can be viewed (not modified) in Staged Construction. - User-defined material data set colors. A special feature that is available in Version 8 is the user-defined soil models option. This feature enables users to include selfprogrammed soil models in the calculations. Although this option is most interesting for researchers and scientists at universities and research institutes, it may also be interesting for practical engineers to benefit from this work. In the future, validated and welldocumented user-defined soil models may become available via the Internet. More information on this feature will be placed on our web site Registered Plaxis users will be informed when the new version 8 is available; they can benefit from the reduced upgrade prices. Meanwhile, new developments continue. More and more developments are devoted to 3D modeling. We will keep you informed in future bulletins. Ronald Brinkgreve, PLAXIS BV 5

6 Table 1 Parameter sets for Hardening Soil model NOTE ON PORE PRESSURE SOME REMARKS ON PORE PRESSURE PARAMETERS A AND B IN UNDRAINED ANALYSES WITH THE HARDENING SOIL MODEL In undrained analyses Skempton s pore pressure parameters A and B (Skempton, 1954) are frequently used to estimate excess pore pressures. If we consider triaxial conditions, Skempton s equation reads u = B [ 3 + A ( 1-3 ) ] where 1 and 3 are changes in total minor and major principal stresses respectively. For fully saturated conditions, assuming pore water being incompressible, B is 1.0. Furthermore, for elastic behaviour of the soil skeleton, A turns out to be 1/3. A frequently asked question in PLAXIS courses is What pore pressure parameters A and B does PLAXIS use, if an undrained analysis is performed in terms of effective stresses setting the material type to undrained? The answer is You don t know, except for the trivial cases of elastic or elastic-perfectly plastic behaviour. In order to investigate this in more detail undrained triaxial stress paths are investigated with the Mohr Coulomb model with and without dilatancy, and with the Hardening Soil model. In the latter the influence of various assumptions of E 50 and E oed has been studied. Soil Parameters The following parameter sets have been used and the model number given below is referred to in the respective diagrams. A consolidation pressure of 100 kn/m 2 has been applied to all test simulations followed by undrained shearing of the sample. Pore Pressure Parameter B In order to check the value of parameter B in an undrained PLAXIS analysis a hydrostatic stress state has been applied after consolidation. By doing so, the parameter A does not come into picture and B can be directly calculated from u and 3, when using undrained behaviour as material type. PLAXIS does not yield exactly 1.0 because a slight compressibility of water is allowed for numerical reasons and therefore a value of is obtained for the given parameters for the Mohr Coulomb model. For the HS model the value depends slightly on E 50 and E oed, but also on the power m and changes with loading. The differences however are in the order of about 3.0 to 5.0 % for the parameter sets investigated here. So it is correct to say that Skempton s pore pressure parameter B is approximately 1.0 in PLAXIS, when using undrained behaviour as material type. Pore Pressure Parameter A The value of parameter A is more difficult to determine. However one can evaluate A from the results of the numerical simulations and this has been done for various parameter combinations for the Hardening Soil model and the Mohr Coulomb model. Model Number E ref 50 E ref ur E ref oed c ur p ref m K nc 0 R f kn/m 2 kn/m 2 kn/m 2 kn/m 2 - kn/m HS_ / HS_ HS_ HS_ HS_ HS_ Parameters for MC Model: E = kn/m 2 ; = 0.2; = 35 ; = 0 and 10 6

7 Fig. 1 Stress path in p -q-space / MC HS model Fig. 2 q- 1 - diagram / MC HS model Fig. 3 u- 1 - diagram / MC HS model Fig. 4 A- 1 - diagram / MC HS model parameter A excess pore pressure [kn/m 2 ] q [kn/m 2 ] q [kn/m 2 ] Comparison Mohr Coulomb Hardening Soil In this comparison we consider the Mohr Coulomb criterion and the parameter set 1 for the Hardening Soil model for dilatant ( = 10 ) and non dilatant ( = 0 ) behaviour. The p -qdiagramm (Fig. 1) firstly shows that the effective stress path observed in a typical undrained triaxial test is only obtained for the Hardening Soil model because the Mohr Coulomb model remains in the elastic range and thus no change in effective mean normal stress takes place. The well known fact that dilatant behaviour leads to an increase of strength in the undrained case is reproduced by both models in a similar way. It is important to point out that although the effective strength parameters are the same for both models the undrained shear strength is different due to different effective stress paths produced by both models, the Hardening Soil model giving an almost 15% lower value (see also Fig. 2). The pore pressure vs vertical strain diagram in Fig. 3 shows the expected increase of excess pore water pressure followed by a rapid decrease for the dilatant material behaviour. It is worth noting that in the case of the Mohr Coulomb model there is a sharp transition when the excess pore water pressure starts to decrease (at the point where the failure envelope is reached) whereas for the Hardening Soil model this transition is smooth. The pore pressure parameter A (Fig. 4) is 1/3 for the non dilatant Mohr Coulomb model (this is the theoretical value for elastic behaviour) and is independent of the loading stage and thus the vertical strain. For the Hardening Soil model A is not a constant but increases with deviatoric loading to a final value of approx for this particular parameter set. Of course the parameter A tends to become negative for dilatant behaviour. Hardening Soil Influence of E ref 50 and E ref oed The reference parameter set is HS_1 of Table 1. Based on this, the reference values of E 50 and Eoed have been varied (HS_2 to HS_6). Only non dilatant material behaviour is considered. Fig. 5 shows effective stress paths in the p -qspace and it is interesting to see that for E 50 = E oed the stress path is the same for all values of E 50 leading to the same undrained shear strength although the vertical strain (and thus the shear strain) at failure is different (Fig. 6). If E 50 is different from E oed, different stress paths and hence different undrained shear 7

8 Fig. 5 Stress path in p -q-space / Hardening Soil Fig. 6 q- 1 - diagram / Hardening Soil Fig. 7 u- 1 - diagram / Hardening Soil Fig. 8 A- 1 - diagram / Hardening Soil parameter A excess pore pressure [kn/m 2 ] q [kn/m 2 ] q [kn/m 2 ] strengths are predicted. The difference between HS_4 and HS_5 is more than 30% which is entirely related to the difference in E oed. This is perhaps not so suprising because E oed controls much of the volumetric behaviour which in turn is very important for the undrained behaviour. However one has to be aware of the consequences when using these parameters in boundary value problems. In Fig. 6 deviatoric stress is plotted against vertical strain and unlike in a drained test where E oed has only a minor influence on the q- 1 -curve both parameters have a strong influence on the results. E 50 governs, as expected, the behaviour at lower deviatoric stresses but when failure is approached the influence of E oed becomes more pronounced. A very similar picture is obtained when excess pore pressures are plotted against vertical strain (Fig. 7). In Fig. 8 the pore pressure parameter A is plotted against vertical strain and it follows that for E oed > E 50 (parameter set HS_4) the pore pressure parameter A is approx. 0.34, i.e. close to the value for elastic behaviour. If E oed < E 50 (parameter sets HS_5 and HS_6) the parameter A increases rapidly with loading, finally reaching a value of approximately A = 0.6. Summary It has been shown that the pore pressure parameters A and B obtained with PLAXIS from undrained analysis of triaxial stress paths using a Mohr Coulomb failure criterion are very close to the theoretical values given by Skempton (1954) for elastic material behaviour, i.e. B is approx. 1.0 and A is 1/3. For more complex soil behaviour as introduced by the Hardening Soil model the parameter A is no longer a constant value but changes with loading and is dependent in particular on the value of E oed in relation to E 50. For a given E 50 the parameter A at failure is higher for lower E oed -values, which in turn results in lower undrained shear strength. E oed < E 50 is usually assumed for normally consolidated clays experiencing high volumetric strains under compression which corresponds to a higher value for A in the undrained case. It is therefore justified to say that PLAXIS predicts the correct trend, care however has to be taken when choosing E oed, because the influence of this parameter, which may be difficult to determine accurately for in situ conditions, is significant and may have a strong influence on the results when solving practical boundary value problems under undrained conditions. 8

9 Fig. 1: Surface settlements - analysis A Fig. 2: Horizontal displacements at surface -analysis A Fig. 3: Displacements of slected points - analysis A Fig. 4: Surface settlements - analysis B Fig. 5: Horizontal displacements at surface -analysis B horizontal displacements [mm] vertical displacements [mm] displacements [mm] horizontal displacements [mm] vertical displacements [mm] Reference Skempton, A.W. (1954). The Pore-Pressure Coefficients A and B. Geotechnique, 4, H.F. Schweiger Graz University of Technology Benchmarking I PLAXIS BENCHMARK NO.1: SHIELD TUNNEL 1 - RESULTS Introduction Unfortunately the response of the PLAXIS community to the call for solutions for the first PLAXIS benchmark example was not a success at all. Probably the example specified gave the impression of being so straightforward that everybody would obtain the same results and thus it would not be worthwhile to take the time for this exercise. However, I had distributed the example on another occasion within a different group of people dealing with benchmarking in geotechnics. In the following I will show the results of this comparison together with the few PLAXIS results I have got. As mentioned in the specification of the problem no names of authors or programs are given, so I will not disclose which of the analyses have been obtained with PLAXIS. I hope, that the summary of the first benchmark example provides sufficient stimulation for taking part in the second call for solutions for PLAXIS Benchmark No.2, published in this bulletin, so that we can go ahead with this section and as awareness for necessity of validation procedures grow, proceed to more complex examples. The specification of Benchmark No.1 is not repeated here; please refer to the Bulletin No.11. Results Analysis A elastic, no lining Figure 1 shows calculated settlements of the 9

10 Fig. 6: Displacements of selcted points - analysis B Fig. 7: Surface settlements - analysis C Fig. 8: Horizontal displacements at surface analysis C Fig. 9: Displacements of selcted points - analysis C Fig. 10: Normal forces and contact pressure - analysis C normal forces [kn]/contact pressure [kpa] displacements [mm] horizontal displacements [mm] vertical displacements [mm] displacements [mm] surface and it follows that even in the elastic case some scatter in results is observed. Some of the discrepancies are due to different boundary conditions. ST5, for example, restrained vertical and horizontal displacements at the lateral boundary, others introduced an elastic spring or a stress boundary condition. The effect of the lateral boundary is not so obvious from Figure 1 but becomes more pronounced when Figure 2, showing the horizontal displacement at the surface, is examined. Figure 3 summarizes calculated values at specific points, namely at the surface, the crown, the invert and the side wall (for exact location see specification). A maximum difference of 10 mm (this is roughly 20%) in the vertical displacement of point A (at the surface) is observed and this is by no means acceptable for an elastic analysis. Results Analysis B elastic-perfectly plastic, no lining Figures 4 and 5 show settlements and horizontal displacements at the surface for the plastic solution with constant undrained shear strength. In Figure 4 a similar scatter as in Figure 1 is observed with the exception of ST4, ST9 and ST10 which show an even larger deviation from the "mean" of all analyses submitted. Again ST5 restrained vertical displacements at the lateral boundary and thus the settlement is zero here. ST9 used a von- Mises and not a Tresca failure criterion which accounts for the difference. The strong influence of employing a von-mises criterion as follows from Figure 4 has been verified by separate studies. It is emphasized therefore that a careful choice of the failure criterion is essential in a non-linear analysis even for a simple problem as considered here. The significant variation in predicted horizontal displacements, mainly governed by the placement of the lateral boundary condition, is evident from Figure 5. Figure 6 compares values for displacements at given points. Taking the settlement at the surface above the tunnel axis (point A) the minimum and maximum value calculated is 76 mm and 159 mm respectively. Thus differences are - as expected - significantly larger than in the elastic case but again not acceptable. 10

11 Fig. 11: Surface settlements analysis A / lateral boundary at 100 m Fig. 12: Horizontal displacements at surface analysis A / lateral boundary at 100 m Fig. 13: Surface settlements analysis A / undrained - drained Fig. 14: Horizontal displacements at surface analysis A / undrained - drained horizontal displacements [mm] vertical displacements [mm] horizontal displacements [mm] vertical displacements [mm] Results Analysis C elastic-perfectly plastic, lining and volume loss Figure 7 plots surface settlements for the elastic-perfectly plastic analysis with a specified volume loss of 2% and the wide scatter in results is indeed not very encouraging. The significant effect of the vertically and horizontally restrained boundary condition used in ST5 is apparent. However in the other solutions no obvious cause for the differences could be found except that the lateral boundary has been placed at different distances from the symmetry axes and that the specified volume loss is modelled in different ways. Figure 8 shows the horizontal displacements at the surface and a similar picture as in the previous analyses can be found. Figure 9 depicts displacements at selected points. The range of calculated values for the surface settlement above the tunnel axis is between 1 and 25 mm and for the crown settlement between 17 and 45 mm respectively. The normal forces in the lining and the contact pressure between soil and lining do not differ that much (variation is within 15 and 20% respectively), with the exception of ST9 who calculated significantly lower values (Figure 10). Results with lateral boundary at distance of 100 m from tunnel axis Due to the obvious influence of the lateral boundary conditions a second round of analysis has been performed asking all authors to redo the analysis with a lateral boundary at 100 m distance from the line of symmetry with the horizontal displacements fixed. As follows from Figures 11 and 12 which depicts these results for case A, all results are now within a small range and thus it has been confirmed that the discrepancies described from the previous chapter are entirely caused by the boundary condition. In addition to finite element results an analytical solution by Verruijt is included for comparison. Vertical displacements are in very good agreement and also horizontal displacements are acceptable in the area of interest (i.e. in the vicinity of the tunnel). For case B similar results are obtained although some small differences are still present. For case C the comparison also matches much better now but some differences remain here and this is certainly due to the fact that the programs involved handle the specified volume loss in a different way. Comparison undrained drained conditions In order to show that the influence of the lateral boundary is especially important under undrained conditions (constant volume) an 11

12 Fig. 1: Geometric data benchmark excavation analysis has been performed for case A with exactly the same parameters except for Poisson's ratio, chosen now to correspond to a drained situation, i.e. deformation under constant volume is no longer enforced (for simplicity the difference of Young's module between drained and undrained conditions has been neglected). It follows from Figure 13 that for the drained case the surface settlements are virtually independent of the distance of the lateral boundary (results for mesh widths of 50 m and 100 m are shown respectively). The horizontal displacements (Figure 14) show some differences of course but in the area of interest they are negligible in the drained case. Summary The outcome of this benchmark example clearly emphasizes the necessity of performing these types of exercises in order to improve the validity of numerical models. Given the discrepancies in results obtained for this very simple example much more scatter can be expected for real boundary value problems. One of the lessons learned from this example is that the influence of the boundary conditions can be much more severe in an undrained analysis than in a drained one and whenever possible a careful check should be made whether or not the placement of the boundary conditions affects the results one is interested in. One may argue that this is a trivial statement, practice however shows that due to time constraints in projects it is not always feasible to check the influence of all the modelling assumptions involved in a numerical analysis of a boundary value problem. It is one of the goals of this section to point out potential pitfalls in certain types of problems which may not be obvious even to experienced users and to promote the development of guidelines for the use of numerical modelling in geotechnical practice. Helmut F. Schweiger, Graz University of Technology Benchmarking II PLAXIS BENCHMARK NO. 2: EXCAVATION 1 The second benchmark is an excavation in front of a sheet pile wall supported by a strut. Geometry, excavation steps and location of the water table are given in Figure 1. Fully drained conditions are postulated. The soil is assumed to be a homogeneous layer of medium dense sand and the parameters for the Hardening Soil model, the sheet pile wall and the strut are given in Tables 1 and 2 respectively. Table 1. Parameters for sheet pile wall and strut EA EI W V kn/m kn 2 /m kn/m/m - Sheet pile wall 2.52E Strut 1.5E6 The following computational steps have to be performed in a plane strain analysis: - initial phase (K 0 = 0.426) - activation of sheet pile, excavation step 1 to level 2.0 m dry wet E ref 50 E ref ur E ref oed c ur p ref m K nc 0 R f R inter T-Strength kn/m 3 kn/m 3 kpa kpa kpa kpa - kpa kpa Table 2. Parameters for HS-model 12

13 - 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 - phi-c-reduction REQUIRED RESULTS 1. bending moments and lateral deflections of sheet pile wall (including values given in a table) 2. surface settlements behind wall (including values given in a table) 3. strut force 4. factor of safety obtained from phi-creduction for the final excavation step Note: As far as possible results should be provided not only in print but also on disk (preferably EXCEL) or in ASCII-format respectively. Alternatively, the entire PLAXIS-project may be provided. Results may also be submitted via e- mail to the address given below. Results should be sent no later than August 1st, 2002 to: Prof. H.F. Schweiger temporary occupied the chair on behalf of MOS Grondmechanica BV. Since the very beginning Dr. Bakker has been actively involved in the program(ming) of PLAXIS and is a key figure in the PLAXIS network. In his last position he was Head of Construction and Development at the Tunnelengineering department for the Dutch Ministry of Public Works. Furthermore he is a lecturer at Delft University of Technology. COURSES In 2001 over 400 people attended one of the 13 Plaxis courses that were held in several parts of the world. Most of these courses are held on a regular basis, while others take place on an single basis. Institute for Soil Mechanics and Foundation Engineering Computational Geotechnics Group Graz University of Technology Rechbauerstr. 12, A-8010 Graz Tel.: +43 (0) Fax: +43 (0) schweiger@ibg.tu-graz.ac.at Recent Activities NEW DIRECTOR OF PLAXIS B.V. We are pleased to introduce the new director of PLAXIS BV, Dr. Klaas Jan Bakker. Dr. Bakker who started the first of February takes over the chair of Mr. Hutteman, who Regular courses: Traditionally, we start the year with the standard International course Computational Geotechnics that takes place during the 3rd week of January in the Netherlands. The Experienced users course in the Netherlands is traditionally organised during the 4th week of March each year. Besides these standard courses in the Netherlands, some other regular courses are held in Germany (March), England (April), France (Autumn), Singapore (Autumn), Egypt, and the USA. For the USA the course schedule is a bit different, as we plan to have an Experienced users course per two years and two standard courses in the intermediate periods. In May, 2002, we had the Experienced users course in Boston, which was organised in cooperation with the Massachusetts Institute of Technology (MIT). For January 2003, a standard course is scheduled in Berkeley in 13

14 cooperation with the University of California. For August, 2003, another standard course is organised in Boulder in cooperation with the University of Colorado. It is our intention to repeat this scheme of courses for the Western hemisphere. For the Asian region, we have planned a similar schedule that also includes an experienced users course once every two years. Other courses: Besides the above regular courses, other courses are organised in different parts of the world. In the past year, courses were held in Mexico, Vietnam, Turkey, Malaysia, etc. On the last page of this bulletin, you can see the agenda, which lists all scheduled courses and some other events. Our web-site on the other hand will always give you the most up-to-date information. PLAXIS Practice I 1. Introduction In Würenlingen (Switzerland), for the temporary storage of nuclear waste, an extension of the existing depository was required. To facilitate this, a m deep excavation was necessary. This bordered immediately adjacent pre-existing structures. Furthermore, along one of it s sides there is a route used for the transportation of nuclear waste. Photo 1: Participants in the Experienced users course, March 2002, the Netherlands. 2. Project Length of excavation: 98 m Width of excavation: 33 m Maximum depth: 9 m Start of works: Spring 2001 End of construction: Summer 2001 Photo 2: Plaxis short course, October 2001, Mexico 3. Geotechnical conditions In the Würenlingen area, significant deposits of the Aare River dominate, which comprises predominantly gravels and sands. The groundwater table lies at a depth of ca. 9.5 m below the surface prior to excavation. The gravels and sands are known as good foundation material, with some low apparent cohesion, allowing for the temporary construction of vertical cuttings of low height. Photo 3: Plaxis short course, November 2001, Vietnam. 4. Construction procedure Due to space restrictions, a sloped earthworks profile is not possible. Therefore, it was concluded to undertake the excavation using Model Behavior unsat sat E ref 50 E ref oed m E ref ur ur c R inter - kn/m3 kn/m3 kpa kpa - KPa - kpa - HS Drained Table 1. Soil parameters 14

15 Fig. 1: Typical section with horizontal displacements a soil nailing option. Correspondingly, the excavation had to proceed in benched stages. Each bench had a height of 1.30 m and a width of 4.5 to 6.0 m. The free face was immediately covered with an 18 cm thick layer of shotcrete and tied back with untensioned soil nails. The bond strength of the soil nails was established by pullout tests. Usually the soil nails are cemented along their full length. For the pullout tests, however, the bond length was reduced to between 3.0 and 4.0 m with a total length of 7.0 m. The individual nails have a cross-sectional area of 25 mm and yield strength of 246 kn. During the pullout tests, it was possible to tension the nails to yield point without any indication of creep or failure. In total five benches were necessary to reach excavation depth. The wall itself is vertical, with nail spacing of 1.5 m and 1.3 m, horizontal and vertical respectively. The nails were tightened three days after installation with a torque key, to secure a fast seat to the shotcrete. A pretensioning with fully cemented nails is not sensible (see fig. 1). 5. Calculations The initial calculations were performed with the usual statical programs based on beam theory and limiting equilibrium loading. Due to the particular safety requirements in connection with nuclear transport additional deformation predictions were made. These calculations were carried out with Plaxis version 7. Geotextile elements were used to model the nails. Due to the good bonding of the soil nails proven by the pullout attempts, no reduction was made for loading transfer along the geotextile elements. The calculations were performed with the following parameters: Hardening soil model Plane strain with 6 node elements 649 elements Due to the simple geology, only one soil layer was used (see table 1) Due to good bonding between soil and shotcrete wall no reduction in interface friction was made. The calculations were performed without groundwater. Shotcrete wall of 18 cm thickness with reinforced wire mesh, modeled as beam elements. EA = 5.4 x 10 6 kn/m, EI = x 104 knm 2 /m and = 0.2 Soil nails are modeled as geotextile elements. EA = 6.87 x 10 4 kn/m and = 0. Results Final excavation stage Maximum deformation of shotcrete wall; 17 mm (see fig. 2a and fig. 3). Maximum horizontal deformation of shotcrete wall; 14 mm (see fig. 2d). Maximum force in geotextile element; 49 kn/m, or 73.5 kn per nail (see fig. 4). Maximum bending moment in shotcrete wall; 11.5 knm/m (see fig. 2b). Maximum axial force in shotcrete wall; -67 kn/m (see fig. 2c). It must be noted, that the tensile forces in the geotextile elements at the final excavation stage did not calculate to zero at the toe of the nail, as should be in reality. This could be due to a too wide FE-net around the geotextile elements, additionally due to the use of only 6-nodes instead of the more precise 15-node element. 6. Measurement on site In total, deformation of the excavation was taken at five stations. Prior to excavation clinometers were placed ca. 1.0 m behind the proposed shotcrete wall, with a depth of 7 m below excavation level. Figure 7 shows the measured horizontal deformations of two cross-sections with equal depths (7.2 and 9.0 mm). Figure 6 contains the calculated horizontal deformations along a vertical line 15

16 Fig. 2: Output in shotcrete wall Fig. 3: Deformation of geotextile 1m behind the shotcrete wall (14.9 mm). A comparison shows that the calculated deformations are greater than the measured. Conspicuous is, that below the excavation base there is practically no movement measurable. Plaxis, however, has predicted some 4 mm deformation. This may be due to an initial offset or due to stiffer behavior at the bottom of the excavation. The maximum measured horizontal deformation was between 7.2 and 9.0 mm at the wall head. Plaxis calculated 14.9 mm horizontal deformation at this point. If only relative measurements are considered, assuming that no movement takes place at the wall toe, then the prediction from Plaxis lays very close to the actual maximum measured. The forms of the measured and calculated deformation curves correspondwell well with each other. Fig. 4: Axial Forces in geotextile 7. Conclusions The calculated deformation of the nailed wall corresponds well with the measured values, especially if the predicted deformations of Plaxis below excavation level are not considered. The soil parameters used correspond to conservative average values, evaluated from a large number of previous sites under similar conditions. It is plausible that the deformation parameters are underestimated. Fig. 5: Measured displacements Fig. 6: Calculated displacement The Plaxis calculation illustrates comprehensively, that the soil nailing system (soil-nail-wall) works as an interactive system. It shows further, that the maximum nail force does not necessarily act at the nail head, but according to the distribution of soil movements may also lie far behind the head of the nail. This means that displacements are necessarily taking place before the nail force is activated. On the one hand, it shows that the shotcrete wall in vertical alignment is stressed by bending and compression, and that the wall s foot transmits compressive stresses to the soil. On the other hand, the shotcrete wall in horizontal alignment is only loaded by bending, whereby in the absence of lateral restrictions of deformation there could also be tension. Finally it is clear to see, that nail head support and pullout failure should be considered (see fig. 4). 16

17 Thanks to prior deformation calculation with Plaxis and measurement control by clinometer installation during the construction stage, the safety of the works in relation to nuclear transportation could be assessed at all times. H.J. Gysi, G.Morri, Gysi Leoni Mader AG, Zürich - Switzerland Calculation procedure Phase 1: Initial stresses, using Mweight = 1. Phase 2: Live load (5 kn/m 2 and 10 kn/m 2 ) Phase 3: Excavation to top level of wall (-0.80 m). Phase 4: First excavation stage, including shotcrete of wall and installation of first row of soil nails (-2.10 m). Phase 5: Second excavation stage with shotcrete wall (-3.40 m). Phase 6: Installation of second row of soil nails. Phase 7: Third excavation stage with shotcrete wall (-4.70 m). Phase 8: Installation of third row of soil nails. Phase 9: Fourth excavation stage with shotcrete wall (-6.00 m). Phase 10: Installation of fourth row of soil nails. Phase 11: Fifth excavation stage with shotcrete wall (-7.30 m). Phase 12: Installation of fifth row of soil nails. PLAXIS Practice II FINITE ELEMENT MODELLING OF A DEEP EXCAVATION SUPPORTED BY JACK-IN ANCHORS filled layer of very loose silty sand and very soft peaty clay varies from 11m to 13m. Due to the presence of very soft soil condition and the fast track requirement of the project, Contiguous Bored Pile (CBP) walls supported by soil nails were used to support the excavation process. This hybrid technique was envisaged and implemented due to its speed in construction and the ability of the Jack-in Anchors 1) in supporting excavations in collapsible soils, high water table and in soft soils conditions (Cheang et al., 1999 & 2000, Liew et al, 2000). The use of soil nailing in excavations and slope stabilisation has gained wide acceptance in Southeast Asia, specifically in Malaysia and Singapore due to its effectiveness and huge economic savings. Adopting the observational method, numerical analyses using PLAXIS version 7.11 a finite element code were conducted to study the soil-structure interaction of this relatively new retaining system. Numerical predictions were compared with instrumented field readings and deformation parameters were back analysed and were used in subsequent prediction of wall movements in the following excavation stages. 2. SUBSURFACE GEOLOGY The general subsurface soil profile of the site, shown in Table 1 consists in the order of succession of loose clayey SILT, loose to medium dense Sand followed by firm to hard clayey SILT. The residual soils (Figure 1) are interlayered by 9m thick soft dark peaty CLAY. For analysis purposes the layers were simplified 1) Jack-in Anchor Technique is a patented product by Specialist Grouting Engineers Sdn. Bhd. Malaysia 1. INTRODUCTION A mixed development project that is located at UEP Subang Jaya, Malaysia consists of three condominium towers of 33 storeys and a single 20-storey office tower. Due to the huge demand for parking space, an approximately three storey deep vehicular parking basement was required. The deep excavation, through a Photo 1: Jack-in Anchor Technique 17

18 into representative granular non-cohesive and cohesive material, such as: Photo 2: The Retaining System: Contiguous Bored Pile Wall Supported by Jackin Anchors that function as Soil Nails DEPTH (m) DESCRIPTION SPT N VALUE LAYER 1 0 to 9 Clayey SILT <12 LAYER 2 9 to 18 Soft Dark Silty CLAY 0 LAYER 3 18 to 27 Medium Dense SAND >18 LAYER 4 27 to 35 Dense SILT >50 Fig. 1: Typical Subsurface Profile Table 1. Soil Layers 3. THE RETAINING SYSTEM In view of the close proximity of commercial buildings to the deep excavation, a very stiff retaining system is required to ensure minimal ground movements the retained side of the excavation. Contiguous Bored Pile that acts as an earth retaining wall during the excavation works were installed along the perimeter of the excavation and supported by jack-in anchors. The retaining wall system consist of closely spaced 1000mm diameter contiguous bored piles supported by hollow pipes which functions as soil nails are installed by hydraulic jacking using the Jacked-in Soil Anchor Technology as shown in photo 3. Figure 2 illustrates the soil nail supported bored pile wall system. Fig. 2a: The Retaining System Photo 3: Hydraulic Jacking Fig. 2b: The Retaining System 18

19 Fig. 4: Geotechnical Instruments This method has proven to be an efficient and effective technique for excavation support, where conventional soil nails and ground anchors have little success in such difficult soft soil conditions. Such conditions are sandy collapsible soil, high water table and in very soft clayey soils where there is a lack of shortterm pullout resistance. Relatively, larger movements are required to mobilise the tensile and passive resistance of the jacked-in pipes when compared to ground anchors. However it was anticipated that the ground settlement at the retained side and maximum lateral displacement of the wall using this system would still be within the conditions and the close proximity of the commercial buildings to the deep excavation, a performance monitoring program was provided. Firstly, as a safety control. Second, to refine the numerical analysis using field measurements obtained at the early stages of construction and third, to provide an insight into the possible working mechanisms of the system. The geotechnical instrumentation program consists of 18 vertical inclinometer tubes located strategically along the perimeter within the Contiguous Bored Pile wall and 30 optical survey makers (surface settlement points) near the vicinity of the commercial buildings. The locations of these instruments are detailed in Fig. 4 for the inclinometers. Fig. 5 illustrates the restrained trend of horizontal displacement of the wall as measured through inclinometers installed at the site Fig. 5: Measures deflection profile required tolerance after engineering assessment. 4. GEOTECHNICAL INSTRUMENTATION In view of this relatively new excavation support technique used for in-situ soft soil 5. FINITE ELEMENT MODELLING EQUIVALENT PLATE MODEL Equivalence relationships have to be developed between the 3D structure and 2D numerical model. Non 2-D member such as soil nails must be represented with equivalent properties that reflect the spacing between such elements. Donovan et al. (1984) suggested that properties of the discrete elements could be distributed over the distance between the elements in a 19

20 uniformly spaced pattern by linear scaling. Unterreiner et al. (1997) adopted an approach similar to Al-Hussaini and Johnson (1978) where an equivalent plate model replaces the discrete soil-nail elements by a plate extended to full width and breadth of the retaining wall. Nagao and Kitamura (1988) converted the properties of the 3-D discrete elements into an equivalent composite plate model by taking into account the properties of the adjacent soil. The twodimensional finite element analysis performed hereafter uses the composite plate model approach. Fig 6: 2-Dimensional finite element mode Finite Element Analysis The finite element analyses were performed using PLAXIS (Brinkgreve and Vermeer, 1998). The Contiguous Bored Pile wall and steel tubes were modelled using a linear-elastic Mindlin plate model (Figure 6). The nails were pinned to the CBP wall. The soil-nail soil interface was modelled using the elastic-perfectly-plastic model where the Coulomb criterion distinguishes between the small displacement elastic behaviour and slipping plastic behaviour. The surrounding soils were modelled using the Mohr-Coulomb soil model. Table 2 and 3 shows the properties used for the analyses. Figure 7: Lateral Deflection of Soil Nailed Contiguous Bored Pile Wall 6. COMPARISON OF FIELD INSTRUMENTED AND PREDICTED DISPLACEMENT READINGS Measured And Predicted Lateral Deflection Figure 7 compares the in-situ, predicted and back analysed lateral deflection of the soil nail supported wall. The measured lateral deflection Table 2: Soil Properties Layer 1 Layer 2 Layer 3 Layer 4 E (kn/m 2 ) soil (kn/m 3 ) C Table 3: Nail and Contiguous Bored Pile Wall Properties E NAIL 2.90E+06 kn/m 2 E CONC. 2.00E+07 kn/m 2 Figure 8: Lateral Deflection of Stiff and Flexible Soil Nail System is showing a trend of restrained cantilever and the jack-in anchors are restraining the horizontal displacement of the wall. Initial finite element prediction (Prediction No.1) based on soil strengths correlated from laboratory 20

21 Figure 9: Influence of Nail Stiffness results. Excavation involves mainly the unloading of adjacent soil, the ground stiffness is dependent on stress level and wall movements. These aspects were taken into account in prediction no.2, the trend is similar and a better prediction was obtained. Subsequent finite element runs were made base on the improved parameters. system. Soil-nail lateral resistance is dependent not only on the relative stiffness and yield strengths of the soil and nail, but also on the local lateral displacement across the shear zone. Due to the hybrid nature of this system, the results indicated that the relative stiffness of the nail and wall too governs the development of bending i.e., lateral resistance of the soil nail. In soft soils, numerical results indicated greater bending moments in the nails due to larger wall deflection. The implication of this study is additional analysis of different working mechanisms in various soil types should be envisaged. 7. SOIL-NAIL-SOIL-STRUCTURE INTERACTION Lateral Bending Stiffness of Soil Nails A flexible nail system with a bending stiffness of 1/220 of the stiff nail system was numerically simulated. It was hypothesised that if bending stiffness of the inclusions were insignificant in the performance of the nail system, there would be no difference in the lateral displacement of the wall. However figure 8 shows that bending stiffness is significant, at least in a soil nail supported embedded wall. With a stiff nail system, the lateral displacement was significantly reduced. Figure 9 illustrates that the influence increases as excavation proceeds further, this is due to the fact that larger movements are required to mobilised lateral bending resistance of the nails. 8. CONCLUSION The soil-nail-soil-structure interaction of a nailed wall is complex in nature. Soil nails are subjected to tension, shear forces and bending moments. The outcome of this numerical investigation of a real soil-nailed supported Contiguous Bored Pile wall in soft residual soils is that nail bending stiffness has a significant effect as deformation progresses, at least in this hybrid support 9. REFERENCE 1. Al-Hussaini, M.M., Johnson, L., (1978), Numerical Analysis of Reinforced Earth Wall, Proc. Symp. On Earth Reinforcement ASCE Annual Convention, p.p Brinkgreve, R.B.J., Vermeer, P.A., (1998), Plaxis- Finite Element Code for Soil and Rock Analyses- Version 7.11,A.A.Balkema. 3. Cheang, W.L., Tan, S.A., Yong, K.Y., Gue, S.S,, Aw, H.C., Yu, H.T., Liew, Y.L., (1999), Soil Nailing of a Deep Excavation in Soft Soil, Proceedings of the 5Th International Symposium on Field Measurement in Geomechanics, Singapore, Balkema. 4. Cheang, W.L., Luo, S.Q., Tan, S.A., Yong, Y.K., (2000), Lateral Bending of Soil Nails in an Excavation, International Conference on Geotechnical & Geological Engineering, Australia. ( To be Published) 5. Donovan, K., Pariseau, W.G., and Cepak, M.,(1984), Finite Element Approach to Cable Bolting in Steeply Dipping VCR Slopes, Geomechanics Application in Underground Hardrock Mining, pp new York: Society of Mining Engineers. 6. Liew, S.S., Tan, Y.C., Chen, C.S., (2000), Design, Installation and Performance of Jack-In-Pipe Anchorage System For Temporary Retaining Structures, International Conference on Geotechnical & Geological Engineering, Austraila. ( To be Published) 7. Nagao, A., Kitamura, T., (1988), Filed Experiment on Reinforced Earth and its Evaluation Using FEM Analysis, International 21

22 Symposium on Theory and Practice of Earth Reinforcement, Japan, pp Unterreiner, P., Benhamida, B., Schlosser, F., (1997), Finite Element Modelling Of The Construction Of A Full-Scale Experimental Soil- Nailed Wall. French National Research Project CLOUTERRE, Ground Improvement, p.p W.L.Cheang, Research Scholar, engp9168@nus.edu.sg, S.A.Tan, Associate Professor, cvetansa@nus.edu.sg, Modelling a row of piles or a row of grout bodies in the z-direction can be done by dividing the EA real and EL real by the centre-to-centre distance Ls. For a beam: EA real =E real *d real *b real [kn] EA plaxis = EA real /Ls [kn/m] For a grout body: EA real =E real *d real *b real [kn] EA plaxis = EA real /Ls [kn/m] K.Y.Yong, Professor, Department of Civil Engineering, National University of Singapore Users Forum BEAM TO PILE PROPERTIES IN PLAXIS Properties for anchors are entered per anchor so : EA = [kn] per anchor Ls = [m] is spacing centre to centre Fig 1. Partial geometry for shieldtunnel project Beams and geotextiles are continuous in the z-direction (perpendicular to the screen). Therefore, a beam /geotextile will be a continuous plate/textile in the z-direction. The properties are entered per meter in the z-direction EA = [kn/m], EL = [kn/m 2 /m] Some geometries In the past bulletins, a few articles were related to experience with the 3D Tunnel program. Since it s release last year, the 3D Tunnel program has been used in practice for some interesting projects. In the below graphs, without further explanation you will find a brief overview of possible projects and geometries. The printed figures also indicate that the 3D Tunnel program can deal with projects beyond tunneling. 22

23 Fig 2. Partial geometry for pileraft foundation Fig 3. Displacement contours for shield tunnel project Fig 4. Partial geometry for anchored retaining wall. Fig 5. Deformed mesh for interacting tunnels. 23