Application of Discrete/Finite Element Algorithms to the Analysis of Masonry Buildings and Bridges

Transcription

1 Industry Sector RTD Thematic Area Date Civil Construction Durability and Life Extension Application of Discrete/Finite Element Algorithms to the Analysis of Masonry Buildings and Bridges Carl Brookes Gifford Consulting Engineers, Southampton, UK Summary The presentation describes the application of discrete/finite element (DE) algorithms to the analysis of masonry buildings and bridges. Several illustrations will be given where these highly non-linear simulations are being used for structural assessment and in the design of strengthening schemes.

2 Introduction Intoduction Discrete Element Technique Applied to Masonry Ancient and modern Application to Masonry Arch Bridges Static coded vehicle loads Unstrengthened and strengthened conditions Application to Buildings - Seismic In-plane behaviour of stone shear walls Earthquake loading Existing and retrofitted structures Application to Buildings - Blast Out-of-plane behaviour of brick/block walls Blast Loading Existing and retrofitted structures

3 Discrete Element analysis A development of the distinct element technique, 1971 Implemented by Rockfield Software Limited in ELFEN, current version 2001 Discrete modelled parts Boundary interface models To deal with contact, gaps, friction along perimeter edges Adaptivity for evolving discrete parts Required if fracturing takes place Overall behavior is highly non-linear Modelled parts are simple

4 Discrete Element Simulation - Blocky 2D seismic analysis to investigate in-plane behaviour of stone façade Artificial horizontal ground motion 0.3g Contours show principal compressive stresses with varying scale.

5 Discrete Element Simulation - Brittle 2D simple cyclic base shearing Mesh adaptivity used to model fracturing process there after DE contact and interface laws apply.

6 Application to Masonry Arch Bridges Application to Masonry Arch Bridges Static coded vehicle loads Unstrengthened and strengthened conditions Prediction and Verification Study looking at past full scale tests of redundant bridges Simulation of more recent laboratory models tested at TRL Aim to concentrate on 2D behaviour (keep things as simple as possible)

7 Torksey Bridge Lincolnshire, 1986

8 Spandrel Splitting from Barrel

9 Arch starting to collapse

10 Arch post failure

11 Arch collapse

12 Collapse failure is not involving spandrel walls

13 Torksey Bridge Simulation First discrete element simulation of arch in D plain strain model. Ignores spandrel walls Contours show principal stresses. Blue shows compression

14 TRL Unstrengthened Arch Carried out in 1997

15 Barrel construction Hand made bricks, radial mortar joints weak mortar, circumferential sand joints to represent ring

16 TRL Unstrengthened Test Simulation Model 18.elf, ELFEN v3.0.0b 2D plain strain model. Ignores spandrel walls. Contours show principal compressive stresses. Blue shows highest compression.

17 TRL Unstrengthened Test Strength Prediction 0 Unstrengthened Arch Test with Simulation in Load Control (contact damping set to 0.5, Fc to 3.5 N/mm 2 ) Load [N] /4 Point 2/4 Point 3/4 Point 1/4 TRL Test Test Data Vertical Intrados Displacement [m]

18 Strengthening Masonry Bridges Background in UK 40,000 Masonry arch bridges in UK (highways, railways, canals) most are over 100 years old many have inadequate strength Environmental deterioration Increased live loading EC directive requires trunk roads to have 40 tonne rating Type of strengthening

19 Formulation of Strengthening and Requirements Requirements minimal change to the bridges appearance minimal impact on bridge users and existing services provide an adequate increase in load carrying capacity exhibit long term durability exhibit a ductile failure mechanism be cost effective Internal strengthening Retrofitted reinforcement (Cintec) stainless steel reinforcement bars bond to masonry by patented grout and sock precision drilling and setting out Rigorously engineered design

20 Mass or Reinforced Concrete Saddle

21 Mass or Reinforced Concrete Saddle Excavation of fill prior to installation of concrete saddle

22 Tangential Reinforcement Retrofitted using Cintec Anchors tangential reinforcement installed from carriageway and, in certain circumstances, from below The System

23 Tangential Reinforcement Mode of Behaviour To prevent classic 4 hinge failure

24 TRL ARCHTEC Test First Test Carried out in 1998

25 Modelled Cintec Anchors tension Axial stress compression Separate finite element mesh Shear coupling model for bond Axial formulation for elastic and non-linear material behaviour

26 Failure of Inner Ring

27 Failure of Inner Ring

28 Failure of Inner Ring Exposing Cintec Anchors

29 Test After Inner Ring Collapse

30 TRL First ARCHTEC Strengthened Simulation Model 24.elf, ELFEN v D plain strain model. Ignores spandrel walls. Contours show principal compressive stresses. Blue shows highest compression.

31 First ARCHTEC Test Strength Predictions TRL Test Strengthened in Load Control Load [N] /4 Point 2/4 Point 3/4 Point TRL Test 1/4 TRL Test 2/4 TRL Test 3/ Vertical Intrados Displacement [m]

32 Comparison of TRL Laboratory Test Results Load Reaction [N/m] Tonnes 41.5 Tonnes Both Archtec arches more than double the capacity of the unstrengthened arch Unstrengthened First Archtec Second Archtec Tonnes Intrados Displacement [m]

33 Conclusions Application to Masonry Arch Bridges CONCLUSIONS The performance of unstrengthened and strengthened arches can be simulated using the discrete element technique Compared with conventional methods DE assessments give best possible estimate of strength Best possible live load assessments can be carried out. Over 60 bridges have now been strengthened using DE based designs

34 Application to Buildings Seismic Shear wall investigation Application to Buildings - Seismic In-plane behaviour of stone shear walls Earthquake loading dynamic loads Existing and retrofitted structures Macro-block - weak mortar Ancient masonry with very weak or no mortar Brittle material - strong mortar Ideally suited to model masonry where mortar and block strengths are similar Sensitivity analysis various retrofitted reinforcement arrangements

35 Masonry shear wall details (all dimensions in mm)

36 General arrangement of idealised building

37 Typical ashlar wall

38 Unstrengthened simulation 0.3g loading Principal compressive stresses in N/m 2

39 Strengthening arrangements (13,19,20,21) Horizontal, Vertical and diagonal Cintec anchors installed from the roof and at the corners

40 Strengthened simulation 0.3g loading Principal compressive stresses in N/m 2 Combined arrangement No. 21

41 Conclusions Application to Buildings Seismic CONCLUSIONS Indications are that the overall performance of masonry acting compositely with retrofitted reinforcement can be predicted Predicted damage looks similar to that occurring in actual buildings Verified for other masonry applications, static and high speed dynamic Numerical modelling is valuable as a virtual test bench for strengthening Currently strengthening of non-engineered buildings is often based on how designs faired after Earthquakes Full-scale testing is very expensive

42 Application to Buildings Blast Out-of-plane behaviour of brick/block walls Application to buildings - Blast Out-of-plane behaviour of brick/block walls Blast Loading Existing and retrofitted structures Very fast dynamic load Load applied typically in 5ms Strain rate in materials very important Sensitivity analysis Experimental test programme various retrofitted reinforcement arrangements

43 Strengthening to Resist Blast Strengthened hollow concrete block wall subjected to severe blast load Before front view After front view

44 Strengthening to Resist Blast Strengthened hollow concrete block wall subjected to severe blast load Before rear view After rear view

45 Strengthened Simulation decoupled analysis, Elfen & Air3D The wall was subjected to a blast load from 200kg TNT 12.5m; 534kPa, 1274kPa-ms (440lbs TNT 41ft; 77psi, 185psi-ms).

46 Unstrengthened Simulation decoupled analysis, Elfen & Air3D The wall was subjected to a blast load from 200kg TNT 12.5m; 534kPa, 1274kPa-ms (440lbs TNT 41ft; 77psi, 185psi-ms).