Hoek Bridge Anchor

ANALYSIS OF THE STABILITY OF AN ANCHOR BLOCK FOR A SUSPENSION BRIDGE

By Dr Evert Hoek Vancouver February 2003

1. Introduction

The analysis discussed in the following notes deals with one of the anchors for a 500 m long suspension bridge proposed for a major highway project. A detailed analysis was carried out as part of the design of the suspension bridge and my role was to review this analysis on behalf of the owner. In fact, the bridge was not built since an alternative design was chosen for the final construction. However, this does not alter the validity of the design and the valuable lessons that can be learned from this analysis. The layout of the bridge is illustrated in Figure 1 that shows that the suspension cables are anchored directly in the rock. Different options for this anchor, located on a steep rocky outcrop, were considered. Three of these options, one for a gravity anchor block two for tunnelled socket anchors, are discussed here.

Figure 1: Overall view of suspension bridge layout. 2. Geological factors influencing the stability of the anchorage

A plan of the gravity anchor block and of the tunnelled socket anchorage is shown in Figure 2. A section through the proposed gravity anchor block is shown in Figure 3. The anchorages are located on a promontory of thick-bedded sandstone, which is underlain by thinly bedded sandstone/siltstone outcropping to the west of the anchorage. Due to a fold structure that forms the nose of the promontory, the structural geology of the East-facing slope is significantly different from that in the South-facing slope. This difference results in a stable East-facing slope and a less stable South-facing slope. The outline of a landslip on the South-facing slope is shown in yellow in Figure 2 and this landslip has an influence of the layout of the anchorage alternatives. 3. Methods used to assess the stability of anchorage options

The Designer assessed the stability of the gravity anchorage by means of a two-dimensional limit equilibrium analysis (using the program TALREN) and two-dimensional numerical analyses (using the programs SAFE, VISAGE and UDEC). A

Suspension bridge anchor block analysis Page 3

three dimensional study, using the program VISAGE, was also carried out. No analyses were performed for the tunnelled socket options. In reviewing the design report I found that the easiest way for me fully to understand the information presented was to carry out my own analyses, using different software from that used by the Designer. In preparing the models for these analyses I have also reinterpreted the basic data and this has resulted in some slight differences in the parameters included in the analyses. I consider that this is an advantage since it provides an independent view of the stability of the anchor block and an assessment of the behaviour of one of the tunnelled socket options.

N

Figure 2: Layout of alternative anchorages for the bridge cable.


Backfill

Figure 3: Section through the gravity anchor block. 4. Limit equilibrium analysis

The program SLIDE1 was used to check the limit equilibrium analysis carried out by the Designer. The details of the model are illustrated in Figure 4 and the properties of the various materials used in the model, assumed to be fully drained, are given in Table 1.

Backfill Concrete anchor block front open, back filled with rockfill

Excavation damaged rock

5000 kN cable force on anchor

2588 kN reaction on bearing

Thin bedded sandstone

Thick bedded sandstone

Figure 4: Details of limit equilibrium model in SLIDE. The cable force of 150 MN is applied over a 30 m wide gravity block base, giving a force of 5000 kN/m on the cable anchor and a vertical reaction of 2588 kN/m on the saddle bearing. T able 1: Summary of rock mass properties used in the SLIDE analysis.

1 Details are available from www.rocscience.com


Material Properties Comments Thick bedded sandstone Unit weight = 26 kN/m3

Anisotropic strength representing the combined properties of the rock mass (based on Hoek Brown criterion) and two sets of joints (B) or one set of joints and one set of bedding planes (C).

Thin bedded sandstone/siltstone

Unit weight = 26 kN/m3

Anisotropic strength representing the combined properties of the rock mass (based on Hoek Brown criterion) and two sets of joints (B) or one set of joints and one set of bedding planes (C).

Excavation damaged rock Unit weight = 26 kN/m3 c = 0, = 36

Backfill Unit weight = 16.9 kN/m3 c = 0, = 36

Concrete anchor block (concrete construction with rock backfill)

Equivalent Unit weight = 19 kN/m3 (back), = 12 kN/m3 (front) Assumed to be elastic (infinite strength)

Equivalent unit weight based on cross-sectional area and total mass of 380 MN given in the Designers report.

A B/C

A

B A

-75 -90

-45

25

45 90

A : c = 352 kPa, = 54 B : c = 0 kPa, = 30.2 C : c = 0 kPa, = 18

A

A

B A

-75 -90

-45 B/C

25

45 90

A : c = 182 kPa, = 41 B : c = 0 kPa, = 29.3 C : c = 0 kPa, = 16

The program SLIDE has a number of options for automatic non-circular failure surface searches and one of these options was used to produce the results shown in Figure 5 and 6. The General Limit Equilibrium method is a very powerful non-circular analysis method that was used in this study. A wide range of material models, including the Hoek-Brown failure criterion and user-defined anisotropic criteria, can be included in the model. Hence, I believe that the failure surfaces shown in Figure 5 and 6 are realistic for this slope. The structural geology of the rock mass forming this slope varies significantly across the width of the slope and, in order to cover this variation, I have carried out two sets of analyses. The first of these assumes that the structure in the plane of the analysis is controlled by two sets of orthogonal joints (B in Table 1, with the results shown in Figure 5) while the second assumes one set of joints and a set of bedding planes dipping approximately parallel to the slope (C in Table 1, with the results shown in Figure 6). The failure surfaces shown in Figure 5 indicate that potential sliding is controlled by a combination of sliding along joints and failure through the rock mass. The global factor of safety of 3.5 involves the entire rock mass from the crest to the toe of the slope. The local factor of safety of 3.9 is typical of the numerous failure surfaces generated in the immediate vicinity of the anchor block. These factors of safety were checked for a range of cable load factors and were found to be almost independent of this load up to a cable load of six times the design load.


Figure 5: Most critical failure surfaces for the East-facing slope on which the proposed gravity anchor block is located. Factors of safety are shown for three of the surfaces. In the case of the model with the bedding planes dipping approximately parallel to the slope, Figure 6 shows a number of failure surfaces with a minimum factor of safety of 2.81. The bedding planes in the thick bedded sandstone are assumed to have a shear strength defined by c = 0 and = 18 while, for the thin bedded sandstone, I have assumed c = 0 and = 16, based on some laboratory shear test results. Once again, the stability of the slope is independent of the load applied to the cable anchor block. I believe that these two models represent the extremes of the behaviour of the slope and that the actual situation probably lies somewhere between these extremes. These studies confirm the conclusion reached by the Designer that the factors of safety of the slope determined by two-dimensional limit equilibrium analyses, exceed the factor of safety of 1.25 required by Euro Code 7 by a substantial margin.


Figure 6: Most critical failure surfaces for the model with bedding planes dipping approximately parallel to the slope. Sliding along the base of the block controls stability of the gravity anchor. The factor of safety for this failure mode was not calculated since it depends upon the material properties assumed and the geometry of the shear key on the base of the block. It is a simple matter to change this geometry and I am in complete agreement with the Designer that an adequate factor of safety against sliding on the base can be achieved. I have not carried out any detailed seismic loading studies but a few checks gave results consistent with those reported by the Designer. 5. Numerical analyses of gravity anchorage stability

The limit equilibrium analyses described above suffer from the disadvantages that some form of predefined failure path must be assumed and that displacements in the slope are not taken into account. These disadvantages can be overcome by using a numerical analysis method in which the progressive failure and deformation of the entire system can be simulated. The Desugners used the continuum finite element models SAFE and VISAGE and the discrete element finite difference UDEC to carry out two-dimensional analyses on the gravity anchorage. The program VISAGE was used for three-dimensional studies. In


order to understand the behaviour of these models and to check the results of the analyses, I have carried out a series of studies using the two-dimensional continuum finite element model PHASE22. Details of the gravity anchor block model that I have used are illustrated in Figure 7. In this model the thick-bedded sandstone and the thin-bedded sandstone/siltstone have been modelled as Hoek-Brown materials. A set of orthogonal joints have been superimposed on the thick bedded sandstone to simulate the most unfavourable joint orientations that can be derived from the structural geology observations. A 2 m wide zone of excavation damaged material has been wrapped around the base of the gravity anchor block. The properties of all the materials included in this model are given in Table 2. An additional set of analyses were carried out in which bedding planes dipping approximately parallel to the slope were included, as in the case of the limit equilibrium model used to generate the results shown in Figure 6. The results given by these two finite elements models were not significantly different and I have only reported the results from the first of these models here. The Phase2 model was run in the following four stages:

1. The overall model, consisting of thick bedded sandstone and thin bedded sandstone/siltstone, was subjected to gravity loading with a ratio of horizontal to vertical stress of 0.25:1. The model was run to equilibrium to simulate the consolidation of the rock masses. Some slip on the joint systems occurred during this consolidation process.

2. The open cut excavation required to accommodate the concrete gravity anchorage structure was excavated and the stresses and displacements in the model were again allowed to reach equilibrium.

3. The concrete gravity anchorage was cast in place and the rear compartment was backfilled.

4. The loads were applied to simulate the thrust on the saddle bearing and the loads on the cable anchorage. The final run to equilibrium was completed and the results of the modelling process interpreted.

Figure 8 is a typical printout from one of these interpretations. The displacement vectors show that most of the displacements are of the anchor block itself and the rock in the immediate vicinity of this block. This confirms the finding from the limit equilibrium studies that the overall stability of the slope is not significantly influenced by the application of the cable load. There is a slight tendency for the block to rotate but the magnitude of this displacement is very small. Since the behaviour of the anchorage is very local, the logical approach to analysing its stability is to examine its response to increasing cable loads. In order to provide a basis for comparing all of the anchorage options, the total displacement of the saddle bearing has been measured in the Phase2 analyses. As far as I can ascertain, the same measurement point was used by the Designers in their analyses in which the cable load was increased until failure of the model occurred.

2 Details are available from www.rocscience.com.


Figure 7: Phase2 finite element model of the gravity anchor block and the underlying slope. T able 2: Mechanical properties assumed in the Phase2 model

Material Properties Comments Thick bedded sandstone

Unit weight = 0.026 MN/m3 Hoek-Brown material defined by GSI = 40, mi = 17, ci = 40 MPa giving E = 3556 MPa, mb = 1.99, s = 0.0013. Joints defined by c = 0, = 36

Based upon Hoek-Brown parameters quoted by the Designer

Thin bedded sandstone/siltstone

Unit weight = 0.026 MN/m3 Hoek-Brown material defined by GSI = 30, mi = 10, ci = 15 MPa giving E = 1633 MPa, mb = 0.98, s = 0.0007.

Based upon Hoek-Brown parameters quoted by the Designer

Excavation damaged rock

Unit weight = 0.026 MN/m3 c = 0, = 38

Assuming typical rockfill properties

Backfill

Unit weight = 0.017 MN/m3 c = 0, = 36

Concrete anchor block (concrete construction with rock backfill in rear compartment)

Equivalent Unit weight = 0.019 MN/m3 (back), = 0.012 MN/m3 (front) Assumed to be elastic (infinite strength)

Equivalent unit weight based on cross-sectional area and total mass of 380 MN given in the Designers report. Distribution of unit weights to simulate filled rear compartment and open front compartment.


Figure 8: Typical results given by the finite element program Phase2 for the gravity anchorage. Slip on the joints during consolidation is shown in dark red/brown while slip resulting from the application of the cable load is shown in red. The displacement vectors indicate the total movements of the anchor block and rock mass as a result of the application of the cable load, i.e. they are the difference in displacements between the third and fourth stages of the model.

Figure 9: Displacement of the saddle anchor for different anchorage options for increasing cable force, expressed as a factor on the design load of 150 MN.


Figure 9 shows the results of the Phase2 analysis of the gravity anchorage block and compares it with the displacements measurements on the SAFE, UDEC and VISAGE models used by the Designer. Considering the differing assumptions included in these models, the agreement between these results is considered to be excellent. Note that I have assumed deformation modulus values of approximately one third of those used by the Designer and this accounts for the larger initial deformations exhibited by the Phase2 model. The plot also includes results for two tunnelled socket options that will be discussed later. In these analyses, failure is defined as a sudden change in the slope of the load deformation curve, as shown by the VISAGE solution for a load factor of approximately 2.5. Less pronounced failure points are shown by the other models but, in all cases, the load factor is well in excess of the load factor of 1.4 required by Euro Code 7. 6. Analysis of tunnelled socket options

In addition to the gravity anchorage solution discussed above, the Designer has also carried out a conceptual study of four tunnelled socket anchorage options. A cross-section through Option 1 is reproduced in Figure 10. The other three options are generally similar but, for Options 3 and 4, the tunnel portion has been skewed in a horizontal plane. The basic aim in all of the designs is to avoid intersecting the landslip which is shown in plan in Figure 2 and outlined in red in Figure 10. The Designer did not provide any stability studies on these tunnelled socket anchorage options but they did present detailed drawings and estimated costs.

Figure 10: Section through tunnelled socket anchorage Option 1.


A complete analysis of these options requires a three-dimensional model since it is not possible to represent the tunnel portion of the anchorage correctly in two dimensions. However, for comparative purposes, an acceptable approximation can be made by representing the tunnel as a slot and using the same type of analyses as were used for the gravity block option. Figure 11 shows the results of one such study in which tunnelled socket Option 1 has been analysed by means of the program Phase2. The plot is similar to that given in Figure 8 and the measured displacements of the saddle bearing are included in Figure 9. Comparing Figures 8 and 11 shows that more of the rock mass is involved in the movements associated with the tunnelled socket option. However, these movements are still localised and have a negligible influence on the overall stability of the East-facing slope. Since no base sliding is involved, as for the gravity anchor, there is no distinct failure load within the scale of cable forces plotted in Figure 9. This relative crude analysis suggests that it is entirely feasible to anchor the cable by means of a tunnelled socket system such as that illustrated in Figure 10. Hence the choice of the anchorage method can be made on the basis of other considerations including cost.

Figure 11: Displacement vectors obtained in a Phase2 model of tunnelled socket anchorage Option 1. 7. Consideration of a vertical shaft socket anchorage

In view of the uncertainty about the long-term stability and possible extent of the landslip, one obvious approach is to move all the components of the anchorage as far away as possible from the landslip. One way to do this is to anchor the cable in a vertical shaft. This option is possible because of the fact that the stability of the overall slope has been shown to be independent of the anchorage forces and that the


reaction to these forces is confined to the rock mass immediately surrounding the anchorage. Figure 12 shows the results of a crude Phase2 analysis of this option and the measured displacements of the saddle bearing are included in Figure 9. While the displacements are somewhat larger than for the tunnelled socket Option 1, the behaviour is still more than adequate in terms of the EC 7 requirements. From a purely practical point of view, I consider that there are significant advantages to a vertical shaft as compared with any of the inclined shaft options studied by the Designer. Not only is excavation of a vertical shaft easier but the arrangement of ladderways and services is also simpler. Drainage can be by gravity through a large diameter borehole exiting in the slope face.

Figure 12: Displacement vectors obtained in a Phase2 model of a possible vertical shaft anchorage. Note that many more joints have been included in the upper part of the rock mass as compared with the model shown in Figure 11. 8. Conclusions and recommendations

All of the anchorage options studied by the Designer and the vertical shaft anchorage option discussed in this report can be constructed with confidence that they will provide adequate stability, not only of the anchorage but also of the East-facing slope below the cable. I agree with the recommendation by the Designer that the gravity anchorage option is the simplest and cheapest solution. I consider that the question of the landslip on the South-facing slope requires further consideration. The Designer has pointed out that the long-term behaviour of this landslip is difficult to quantify, particularly under earthquake conditions. Based on the


various analyses that I have carried out, I agree with this assessment. However, there is a possibility that further movement of the landslip could result in the formation of a steep back scarp which could undercut the cantilevered rear compartment of the anchor block. I believe that it is necessary to deal with this issue, in spite of the fact that it does not influence the sliding stability of the anchor block. I consider that it is necessary to carry out additional site investigations with the aim of clearly defining the present and future limits of the landslip in the immediate vicinity of the anchor block. Based on this investigation, a stabilisation scheme should be devised, including anchorage of the thick-bedded sandstone if necessary, to ensure that retrogressive failure of the landslip does not result in undercutting of any portion of the anchor block. If such an investigation proves that it is not possible or that it is too expensive to stabilise this back scarp, then consideration has to be given to the use of an anchorage system, such as the vertical shaft option proposed in this review, that isolates the anchorage from the landslip to the maximum extent possible.

IntroductionGeological factors influencing the stability of the anchorageMethods used to assess the stability of anchorage optionsLimit equilibrium analysisNumerical analyses of gravity anchorage stabilityAnalysis of tunnelled socket optionsConsideration of a vertical shaft socket anchorageConclusions and recommendations

Hoek Bridge Anchor

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