CYCLIC LOAD CAPACITY AND ENDURANCE LIMIT OF MULTI-RING MASONRY ARCHES

Transcription

1 Arch Bridges ARCH 04 P. Roca and E. Oñate (Eds) CIMNE, Barcelona, 2004 CYCLIC LOAD CAPACITY AND ENDURANCE LIMIT OF MULTI-RING MASONRY ARCHES Clive Melbourne*, Adrienn K. Tomor** and Jinyan Wang*** School of Computing, Science and Engineering, University of Salford Newton Building, Salford Crescent, Salford, Greater Manchester, UK M5 4WT, UK * ** *** Key words: Masonry, arch, cyclic, load capacity, endurance limit, S-N curve, ring separation, shear Abstract. A series of large-scale tests have been carried out at the University of Salford on multiring masonry arches to assess their endurance limit and cyclic load capacity. Multi-ring arches represent a significant proportion of the UK bridge stock most of which is over 100 years old. Due to the increasing weight of road and rail traffic their life expectancy and capacity under cyclic loading needs to be predicted. Although there have been a number of small and large scale tests carried out on masonry arches, most of them have been under static loading. There has been however very little work done on load capacity under cyclic loading. The present work entails a series of 3m span two-ring and 5m three-ring brickwork arch tests under cyclic loading at various load levels until failure. The number of load cycles, damage propagation and failure modes have been recorded and recommendations to an endurance limit of such arches have been considered. A few tests under static loading have also been carried out for comparison. While the classical mode of failure of arches under static loading is the four-hingemechanism, all arches within the present test series under cyclic loading have failed by ring separation over the middle section of the arch. Cyclic loading therefore influences the mode of failure. Some theoretical approaches describing the causes of failures have been discussed. 1

2 1 BACKGROUND AND CONTEXT There are over masonry arch bridges in the UK which are being called upon to carry ever increasing levels of loading and increasing volumes of traffic. It is imperative that the bridge stock is not adversely affected by these changes in the loading regime and that appropriate assessment and repair and strengthening techniques are available. Over the past 10 years there has been an extensive programme of research in the UK and abroad which considered various aspects of masonry arch behaviour. One of the conclusions has been the identification of ring separation (delamination) in multi-ring brickwork arch bridges as a major source of concern because its presence reduces the load carrying capacity of the bridge. However, all the experimental work to date has been under monotonic loading conditions and there is a fear that under cyclic loading these phenomena may be aggravated by the incremental deterioration of the brickwork. The current research reported herein addresses some of the issues and offers some guidance. 2 MATERIAL PROPERTIES Class A Engineering bricks (215 x x 65mm) were used throughout the tests with an average compressive strength of 154N/mm 2 and density of 23.7 kn/m 3. 1:2:9 (cement:lime:sand) mortar was used with an average compressive strength of 1.7N/mm 2 and density of 15.5 kn/m 3. The average compressive strength of the brickwork was 25N/mm 2 and the density 20 kn/m Test series A series of 3m and 5m span segmental arches were tested under static and long-term cyclic loading. For dimensions and loading conditions see Table Loading Span (mm) Rise (mm) Ring thickness (mm) Arch width (mm) Number of rings 2 3 Span : rise ratio 4:1 4:1 Dead load 2 x 10kN 2 x 22.5kN Table 1 - Arch dimensions In order to represent the weight of the fill on bridges (with fill height at the crown equivalent to the arch ring thickness and with density of 16kN/m3) dead loads were applied at the ¼ and ¾ points of the arch either by steel weights or by hydraulic jacks (see 2

3 Figure 1). Live load was applied at the ¼ point for static tests and alternatively at the ¼ and ¾ points for cyclic tests using hydraulic jacks. Cyclic loading was applied at 2Hz frequency to represent the flow of traffic at ca miles/hours speed over the bridge. Cyclic loads were applied for at least 1,000,000 cycles at each load level, starting from a relatively small load. If after 1,000,000 cycles no damage or deterioration was observed the load was increased by 2kN and the process repeated until failure occurred. Formation of a mechanism, ring separation or slippage determined failure. Hydraulic jack Hydraulic jack Steel weights Figure 1 Typical loading system 2.3 Test results Static loading 3m arches under static loading failed at 28 and 29kN and the 5m arch failed at 30kN (Table 2). The relatively small load capacity of the 5m arch is based upon the different modes of failure compared to the 3m arches. 3m arches failed by the formation of a fourhinge mechanism while the 5m arch failed by ring separation between the live load and the nearest abutment (see Figure 2 and Figure 3) at a considerably lower load than formation of hinges would be expected. In the 3m arch radial cracks and hinges occurred gradually and the progress of the damage was visible with the naked eye. The 5m arch, however, failed very suddenly. The current series of tests indicate the pronounced danger of ring separation for multi-ring arches and the importance of assessing arches for the possibility of various modes of failures, i.e. four-hinge mechanism, ring separation, slippage etc. and defining load capacity as whichever is the lowest. Arch Span Loading Max. load (kn) % of static load Number of cycles Failure mode A Four-hinge Static G Four-hinge C ,500 Ring separation 3m E ,000 Ring separation Cyclic F ,000, D ,000, M Static Ring separation 5m O Cyclic ,000 Ring separation Table 2 - Static and cyclic test results 3

4 a) Four-hinge mechanism (3m arch A) b) Ring separation (5m arch M) Figure 2 Failure mechanisms DL + LL DL DL + LL DL + LL Cyclic loading a) Arch M - Static b) Arch O - Cyclic Figure 3 5m arch failure In the cyclic loading test series it has been found that while the arch could be subjected to several million cycles at a certain load level, a small increase in the loading could cause rapid failure. While loaded below the endurance limit a limited number of radial cracks did develop and enabled increased deformation of the arch. The structure still behaved elastically and fully recovered within each loading cycle. When loaded above the endurance limit residual damage in the longitudinal mortar joints occurred within a small number of cycles which led to rapid failure. Under cyclic loading all arches failed by sudden ring separation. In most cases, ring separation under cyclic loading occurred between the ¼ and ¾ point unlike under static loading when ring separation occurred between the ¼ point and the nearest abutment. The reason why arches under cyclic loading generally developed ring separation in the middle section of the arch is that the zone of thrust crosses the mortar joint in the middle section of the arch (if considering a two-ring arch) twice as often as towards the abutments hence causing more frequent change in the direction of shear 4

5 stresses. It is important to note that if the endurance limit for masonry is known, it has to be adjusted, i.e. halved, with regard to the behaviour of the critical section of the arch. A few further tests with reduced longitudinal mortar joints were also carried to represent the effect of loss of bond due to water penetration, longitudinal shear stress overload, etc. It has to be noted that the endurance limit in masonry arches is not necessarily reduced by the presence of radial cracks but is primarily reliant on the loss of mortar bond in the longitudinal mortar joints. As a practical tool for bridge engineers the load capacity as a function of number of cycles is of main interest. which is presented as 3D surfaces separately for 2 and 3 ring arches in Figure 4. For 3m arch series the endurance limit was around 37% (11kN) and for 5m arches around 57% of the static loading (17kN). The 3D surfaces also incorporated the extent of mortar bond and indicate the pronounced effect of mortar bond loss particularly on static load capacity. Although so far only one representative arch type has been tested, arches can vary significantly in their composition. The constituent parts of an arch may comprise stone, brick and mortar. Depending upon their relative strength and endurance each may play a critical role in determining the endurance of the arch. The relative volume of the constituent materials is also important. A dressed stone voussoir arch will probably have less than 2% volume of mortar whilst a multi-ring brickwork arch could have 20% and random rubble arches 40%. In the case of strong bricks and weak mortar it is the volume and strength of the mortar that will dominate. This is evident in Figure 4. It is postulated that the endurance limit E for the arch is dependent on the load range R, these can be related empirically i using equation 1 and is shown in Figure 5 E = 10 H R m (1) The plot will be sensitive to the mode of failure i.e. ring separation, hinging, crushing, etc. The nature of loading in the tests produced a higher shear to bending stress ratio than that which would have been produced by a more distributed load of the same total magnitude. This would mean that the arches were more susceptible to ring separation. However the proposed model does represent a new way forward for arch bridge assessment. It allows the possibility of developing a series of curves using a probabilistic approach with assessment curves set at say 2 (standard deviations) below the characteristic curve and applying Miner s Rule (equation 2) to determine residual life. K=Z K=1 N/E K 1 The Interactive S-N (ISN) diagram could be developed for each bridge based upon standard curves and modified according to an engineer s assessment of the structural condition, thus allowing an assessment of residual life. An example of the ISN curve for ring separation for the 3m arch tests is also shown in (Figure 5). The ISN diagram could be modified to account for any rehabilitation or strengthening and a new residual life determined. The determination of the critical mode of failure will follow from the curves. (2) 5

6 This will help decide the appropriate repair technique and quantify the new residual life for a given load regime m + 5m Arches Endurance Limit (Approx. 30%) 50% % of static loading 100% m (3 ring) Arch Endurance Limit (Approx. 57%) 3m (2 ring) Arch Endurance Limit (Approx. 37%) Number of load cycles Arch Max Cycles load (kn) 1 A* G* C* 14 23,500 4 E* 12 25, ** 10 20, A* M* ** 26 50,000 7 O* ,000 8 O* 20 38, ** 10 50, ** 10 50,000 * Tested by Tomor **Tested by Alnuaimi ii 0% Mortar bond (%) Test Results Figure 4 Load vs. Number of cycle surfaces Log (Number of load cycles) Ring separation Mechanism Log (Stress) Log (Number of load cycles) 1E+13 1E+12 1E+11 1E+10 1E+09 1E+08 1E+07 1E H 3m Test Data Slope m 1 10 Log (Load) 100 Figure 5 Interactive S-N diagram 3 SHEAR TESTING In order to gain a clearer understanding of the shear capacity of mortar-brick joints a series of triplets and large-scale arch sections have been tested under static and cyclic loading. There are two types of mortar bond that needs to be distinguished when dealing with masonry arches: radial and longitudinal joints. In the radial joints rough brick surfaces are connected where else longitudinal joints connect the smooth narrow sides of the bricks. 6

7 3.1 Triplet tests In order to represent radial joints a series of triplets have been tested. In the mortar joints of both triplets and the large-scale arch tests a number of voids have been observed due to imperfections in the construction process. This issue, however, needs to be raised when dealing with large scale arches. Static shear capacity of the triplets was plotted against their bonded surface area in Figure 6 (see trendline for Static tests) and indicate exponential relationship with significant reduction of shear capacities for less than 90% bonded surface area. When assessing real structures it needs to be noted that material properties gained from smallscale samples with 100% mortar bond do not necessarily represent the real structure and proportional reduction of the shear capacity gained from perfect samples is still likely to largely overestimate the capacity of the structure. 3.2 Large-scale sample tests Figure 6 Shear tests In order to compare the shear capacity of the real arch with those gained from smallscale triplet tests large blocks were taken out and tested from one of the 5m arches after failure. Even though the arch has already been subjected to a large number of load cycles as well as the sudden impact during collapse, they still show noticeably greater shear capacities compared to the triplet tests (see Large blocks in Figure 6). The reason behind the significantly smaller shear strength of triplets is mainly due to the edge effects which for single brick surfaces (triplets) are considerably greater compared to large blocks. 3.3 Cyclic tests Shear strength (N/mm 2 ) Trendline for static tests Triplet tests Joint shear strength Bonded surface area (%) A series of cyclic load with no pre-compression at 2Hz tests on triplets has also been carried out. Some of the samples failed whilst increasing the cyclic loading and are included as dynamic tests in Figure 6. Cyclic shear capacity and the maximum number of loading cycles seems to be independent from the extent of bonded surface area and was significantly smaller compared to monotonic loading. Cyclic shear capacity of brickwork is the stress level at which the mortar joint can deteriorate to an extent that the reduced surface bond is no longer able to transmit the stresses. Stress levels below the endurance limit do not seem to initiate cracks or cause deterioration of the mortar. For that reason 95 Static Dynamic (Failure during loading) Cyclic Large blocks

8 cyclic shear capacity of the mortar joint does not seem to be directly related to the amount of bonded surface area but mainly be a function of the stress level unless there is considerably large loss of mortar bond. When assessing arches for shear under static loading for newly built arches allowance can therefore possibly be made for good quality mortar bond. For cyclic loading the shear capacity is however not directly related to the extent of mortar bond and considerably lower shear capacity needs to be assumed compared to static loading. 4 MODELLING AND ASSESSMENT METHODS 4.1 Finite elements Modelling the behaviour of multi-ring arches was carried out using the Finite Element program Ansys. At present, Ansys can only be used for modelling arches under static loading as there is currently not enough information available for calibrating and modelling arches under cyclic loading. The arch was modelled as a continuum using the Solid 65 element as distinguishing between brick and mortar joints with Ansys is not easily possible. A continuum can be conveniently used when modelling radial cracks for single ring arches (i.e. four-hinge mechanism under static loading); however, it is not suitable for modelling multi-ring arches when ring separation is an issue. Since in the continuum model used in Ansys the maximum load capacity is determined primarily by the formation of a mechanism and weakness at the longitudinal mortar joint has been neglected, the determined maximum load capacity by the program does not represent the real behaviour of the arch. Shear stresses along the longitudinal mortar joint were therefore abstracted manually. Ansys shows good resemblance of the failure mechanism of the 3m laboratory arch tests (four-hinge mechanism) however it significantly underestimates the load capacity. At this stage it is felt that Ansys modelling may be reliably used to give qualitative understanding of the relative performance of masonry arches however its quantitative output has to be dealt with extreme caution. For the 5m arch model which failed by ring-separation Ansys shows significant increase in shear stresses at the top mortar joint after the opening of the first (radial) crack (see Figure 7). The effect of radial cracks locally increase the longitudinal shear stresses which can cause ring separation at a significantly lower load than that associated with the formation of hinges. The very similar failure loads of the 3m and 5m arches (28kN, 29kN and 30kN) are therefore due to the fact that formation of the four-hinge mechanism in the 3m arch seems to coincide approximately with the opening of the first crack in the 5m arch and therefore with the sudden increase of the longitudinal shear stresses up to the critical shear value. 8

9 Shear Stress (N/mm 2 ) m Unreinforced 5m Arch Arch Element Shear Shear stresses Stresses at top at Top mortar Joint joint DL+LL + LL DL 4.2kN 6.5kN 9.5kN 12.5kN 15.3kN st Crack LL DL Horizontal location (mm) Figure 7 Ansys longitudinal shear stress vs. Load level results 5 CONCLUSIONS - Ring separation for multi-ring arches can occur at a considerably lower load level than that associated with a four -hinge mechanism failure. - Cyclic load capacity and endurance limit of multi-ring arches can be around 60% lower than the static load capacity and can modify the mode of failure. - S-N curve as 3D surfaces are a function of mortar bond as has been shown for the present series of tests. - A model for an Interactive S-N (ISN) curve to allow assessment of residual life and fatigue performance for general arch bridge assessment has been proposed. - Shear capacity of mortar-brick joints seems to be exponentially related to the extent of mortar bond under static loading however it appears to be independent of mortar bond under cyclic loading. - Shear capacity of small and large-scale samples have demonstrated the significance of the size of the test sample and the necessary consideration of the extent and quality of the mortar bond. - Ansys can conveniently be used for modelling arches as a continuum for a mechanismtype failure under static loading; however, it is not directly suitable for modelling multi-ring arches where there is the possibility of ring separation. 9

10 6 ACKNOWLEDGEMENTS The authors wish to acknowledge the support of EPSRC, UK and Marshall Products Limited and the technical support of the University of Salford. REFERENCES i D.J. Oehlers and M. A. Bradford, Elementary Behaviour of Composite Steel & Concrete Structural Members, Butterworth & Heinemann, 1999, ii Matar Alnuaimi, The Behaviour of Strengthened Masonry Arches, PhD Thesis, University of Salford,