Le ct u r e 3 1 Reinforced Soil Retaining Walls-Design and Construction Pr of. G L Siva k u m a r Ba bu D e pa r t m e n t of Civil En gin e e r in g I n dia n I n st it u t e of Scie n ce Ba n ga lor e 5 6 0 0 1 2 Evolution of RS-RW Cla ssica l gr a vit y r e t a in in g w a lls Re in for ce d con cr e t e t ype s Bu t t r e sse d a n d cou n t e r for t w a lls Pr e fa br ica t e d a n d com pa r t m e n t a lize d gr a vit y w a lls ( cr ibs a n d Bin s, ga bion s) M SE w it h m e t a l r e in for ce m e n t M SE w it h Ge osyn t h e t ic r e in for ce m e n t segmental facing units shear key or mechanical connector geosynthetic reinforcement layer reinforced soil geotextile wrapped drain retained soil granular levelling pad foundation soil Component parts of Reinforced Earth wall (Vidal’s Reinforced Earth system) Steel strips Geotextile materials – Conventional geotextiles nonwovens, woven, knitted and stretch bonded textiles – special geotextiles geosynthetics in two forms geo-grids and geo-composites The principal requirements of reinforcement strength and stability (low tendency to creep), durability, ease of handling, high coefficient of friction and/or adherence with the soil, low cost and ready availability. geosynthetic acts as reinforcement and the most important properties are – tensile strength, – tensile modulus and – interface shear strength General Limit equilibrium approach Two primary forms of stability must be investigated: – External stability – Internal stability Critical state soil properties (’cv and c’cv) Design strength of the grids M I LTS = P c/ ( f m x f e x f d x f j ) External stability Tie back wedge method Coherent gravity method External Forces ws Wall fill c’w, ’w, w H Rv e v L - 2e L Backfill c’b, ’b, b KabwsH 0.5KabH2 H/2 H/3 Foundation Soil c’f, ’f, f 1  sin b K ab  (Rankine ) 1  sin b External Sliding Factor of Safety for sliding is given by: 2   H  w  Re sisting force Fos   Sliding force  H K   H  2w     L w s where  is the coefficient of friction on the base of the reinforced soil block (= tan’w or tan’f ) Target factor of safety is usually 2.0 ab b s Overturning Failure Factor of safety against overturning is given by: Re storing moment Fos   Overturning moment 3  w H  w s   H K ab   b H  3w s    L 2 Target factor of safety is usually 2.0 Seldom a critical failure criterion Bearing Capacity Assume a Meyerhof pressure distribution at the base of the structure Usually, an allowable bearing pressure of half the ultimate pressure is satisfactory providing settlements can be tolerated (i.e. factor of safety = 2.0) The ground bearing pressure is given by v  H w    K   H  3w   H  1   3  H  w   L  w ab s b w 2 s s Allowable bearing pressure given in codes. Slip Failure All potential slip surfaces should be investigated Target factor of safety of 1.5 usually adopted for rotational slip type failures Internal Stability Two main failure mechanisms need to be investigated: – tension failure – pull-out failure Tension Failure Pull-out Failure Tension Failure (1) ws hi vi 45 - ’w/2 Ti Vi Note: Vi is the effective vertical spacing for grid i Potential failure plane Ti has four components: Weight of fill Active pressure from behind RSB Surcharge on top of RSB c’ within RSB (restoring force) Tension Failure (2) Grids carry tension as a result of the self weight of the fill and the surcharge acting on top of the reinforced soil block       h  w   w i s   Ti   K aw  2   2c' w K ab   b h i  3 w s   h i   1     h  w 3   w i s   L        K aw  Vi   Tension Failure (3) A spacing curve approach is used Effective vertical spacing, Vi 55RE 80RE Depth, hi For a given design strength, the maximum vertical grid spacing Vi(max) can be calculated for a range of depths Wedge/Pull-out Failure (1) Consider the possibility of failure planes passing through the wall and forming unstable wedges S1 ws F1 W h  ’w R T Potential failure plane Wedge/Pull-out Failure (2) Assumptions: – each wedge behaves as a rigid body – friction between the facing and the fill is ignored Investigate series of wedges as shown below: Potential failure planes a b c Wedge/Pull-out Failure (3) Mobilising force – At any level, by changing , a value for Tmax can be determined S1 T Tmax For simple cases, Tmax given when  = 45 - ’w/2 F1 W T h  T ws h tan   w h  2ws  2 tan 'w     ’w R Wedge/Pull-out Failure (4) Resisting force – This is normally the design strength of the grid – Account must be taken of the anchorage ws effects Overburden pressure h H  Grid under consideration Lip L Wedge/Pull-out Failure (5) Resisting force (continued) – Anchorage force, Tai available in a grid is given by: Tai  2L ip  p tan ' w   w h i  w s  factor of safety For each layer of reinforcement cut by the wedge, the lower of the design strength, Tdes or Tai is used to determine the contribution from the reinforcement Compare the mobilising force with the resisting force i.e. T a i or T de s) T Ge osyn t h e t ic Re in for ce d Soil W a lls GRS walls are increasingly becoming popular. geosynthetics Concrete facing Wrapped geotextile facing GRS-RW Features Advantages Stability Considerations: – External stability – Internal stability Design methods (koerner (2001) – Modified Rankine approach-most conservative – FHWA method- intermediate – NCMA approach- least conservative Example masonry concrete segmental retaining wall units Not to scale Different Styles of Facing Blockwork wall Wall in Residential Development Blockwork Wall Adjacent to Highway Construction of Walls Modes of Failure External a) base sliding b) overturning c) bearing capacity (excessive settlement) d) pullout e) tensile over-stress f) internal sliding g) connection failure h) column shear failure i) toppling Internal Facing External Modes of Failure L a) base sliding b) overturning c) bearing capacity (excessive settlement) Internal Modes of Failure d) pullout e) tensile over-stress f) internal sliding Facing Modes of Failure g) connection failure h) column shear failure i) toppling Global Stability Typical Factors of Safety Against (Collapse) Failure Mechanisms a) b) c) d) e) f) g) h) i) Base sliding Overturning Bearing capacity Tensile over-stress Pullout Internal sliding Connection failure Column shear failure Toppling 1.5 2.0 2.0 1.0 1.5 1.5 1.5 1.5 2.0 Global stability 1.3 - 1.5 Construction Details Wall Construction Locking Bar General view on Wall During Construction Placing Facing Blocks Wall Ties Fixing False Facing Locking Geogrid Between Blocks Safety Barriers at Top of Wall Completed Wall with Fence Examples Of Finished Structures Examples Of Finished Structures Examples Of Finished Structures Goegrid-reinforced soil RW along JR Kobe Line (1992) Goegrid-reinforced soil RW along JR Kobe Line (1995) Damaged masonry RW, reconstructed to a GRS RW with a fullheight rigid facing Some examples of poor quality Example calculation An 8 m high wall is to be built using sand fill and polymer-grid reinforcement. The sand has ’ = 300, = 18 kN/m3 and is to be used for the wall and the backfill. A surcharge loading of 15 kPa is to be allowed for, and the maximum safe bearing pressure for the foundation soil is 300 kPa. Two grids of different design strength are available: grid A at 20 kN/m and grid B at 40 kN/m (both have a bond coefficient fb of 0.9). The fill will be compacted in layers 250 mm thick. External stability (sliding) Ka = (1 – sin 300) / (1+ sin 300) = 0.333  = fb tan  = 0.9  tan (30)  0.5. For a factor of safety against sliding of 2.0, the minimum length of layers is: L min FS K ab H  w H  2w  2 μ  w H  w S  S  2x0.333  8  18  8  2  15 L  5.83m. 2  0.5  18  8  15 Therefore adopt a length of 6m. External stability (Overturning) Overturning moments about the toe = Restoring moments about the toe = Factor of safety against overturning = ws H 2 H3  k ab (k ab b ) 6 2 2 w L HL ( )( s ) 2 2 2 3( w H  w s ) k ab ( b H  3w s )(H / L) 2 3(18 x8  15) FS   4.26  2 2 0.333(18 x8  45)(8 / 6) Bearing pressure Using trapezoidal distribution, v max = (18  8 + 15) + 0.333  (18  8 + 45) (8/6)2 = 159 + 112 = 271 kPa. (< 300 kPa) Check that contact stresses at the base of reinforced zone are compressive everywhere (i.e. no tension): v min = 159 – 112 = 47 kPa. (> 0) T = h SV = Kv SV v = (z + wS) + Ka (z + 3wS) (z / L)2 Ti = 0.333 [(18z + 15) + 0.333 (18z + 45) (z/6)2] SV S v max  Pd 2 0.333 18z  15  0.333 18z  45 z 6     Maximum spacing of geogrids, (Sv)max Two different grids that are available the use of above equation results in the values presented in the Table. z (m) Grid A (Pd=20 kN/m) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 2.46 1.73 1.29 1.00 0.79 0.64 0.52 0.43 0.36 0.30 0.26 0.22 0.19 0.16 0.14 0.12 Grid B (Pd=40 kN/m) 4.93 3.46 2.58 2.00 1.59 1.28 1.05 0.86 0.72 0.60 0.51 0.44 0.37 0.32 0.28 0.24 Spacing versus depth plot for grids A and B Maximum vertical spacing (m) 0 0.25 0.5 0.75 1 1.25 Depth below top of wall (m) 0 1 Grid 'A' (20 kN/m) 2 3 4 5 6 7 8 Grid 'B' (40 kN/m) 1.5 Wedge stability check Select trial wedges at depths, 1 to 8 m below the top of the wall and calculate the total required force T. Carry out check with and without surcharge ws. For critical wedge angle  = (450 - 'w/2 = 300 for a wedge of height h, the total tension force T is given by T h tan 30 0 18h  2  15  2 tan 30 0  30 0   3h 2  5h For a reinforcing layer at depth z below the top of the wall, the pullout resistance is given by PP = 2 [L – (h – z) tan ]  (z + ws)  0.9  tan 300 / 2. The factor 2 in the numerator denotes the upper and lower surfaces on either side of the geogrid and factor 2 in the denominator refers to the factor of safety. PP = 2 [6 – (h – z) tan 300]  (18z + 15)  0.9  tan 300 / 2. For each reinforcement intersected, the available force is taken as the lesser of the pullout resistance PP and the design tensile strength Pd. For all wedges and both load cases, available force is greater than required force, T. A suitable reinforcement layout is arrived at based on the above considering the thickness of compaction lifts. Calculation of mobilizing and resisting forces for wedge stability Wedge Force to be resisted T (kN/m) Grids Design Tensile force, Depth Involved Pd (m) w = 0 w = 15 kPa s s (kN/m) 1 2 3 4 5 6 7 8 8 22 42 68 100 138 182 232 3 12 27 48 75 108 147 192 2A 4A 6A 9A 13A 15A+2B 15A+6B 15A+10 B 40 80 120 180 260 380 540 700 Pullout resistance Pp (kN/m) ws = 0 42 141 318 732 1495 2538 3905 5639 ws = 15 kPa 16 80 213 548 1189 2092 3301 4859 Available force (kN/m) (minimum of Pd & Pp) ws = 0 40 80 120 180 260 380 540 700 ws = 15 kPa 16 80 120 180 260 380 540 700 Reinforcement Layout (8‐0.25) tan 30o (6‐4.47) = 1.53 m = 4.47 m 0.25 m 1m 2m 1.25 m 3m Pd = 20 kN/m @ 0.5 m c/c. 2.25 m 4m 5m 3.25 m 6m 7m 4.25 m Pd = 20 kN/m @ 0.25 m c/c. 8m 5.25 m 6.25 m 7.25 m 7.75 m L=6m Pd = 40 kN/m @ 0.25 m c/c. Provisions of FHWA Recommended minimum factors of safety with respect to External failure modes Sliding F.S >= 1.5 (MSEW); 1.3 (RSS) Eccentricity e, at Base <= L/6 in soil L/4 in rock Bearing Capacity F.S. >= 2.5 Deep Seated Stability F.S >=1.3 Compound Stability F.S. >= 1.4 Seismic Stability F.S. >= 75% of static F.S. Table1.2: Recommended minimum factors of safety with respect to internal failure modes Pullout Resistance F.S. >= 1.5 (MSEW and RSS) Internal Stability for RSS F.S >= 1.3 Allowable Tensile Strength (a) For steel strip reinforcement 0.55 Fy (b) For steel grid 0.48 Fy (connected to reinforcementpanels concrete Panels or blocks) Empirical curve for estimating probable anticipated lateral displacement during construction for MSE walls Table1.3: Recommended backfill requirements for MSE & RSS construction U.S Sieve Size % Passing For MSE Walls 102 mm 100 0.425 mm 0-60 0.075 mm 0-15 For RSS Walls 20mm 100 4.76mm 100-20 0.425mm 0-60 0.075mm 0-50 Table 1.4: Recommended limits of electrochemical properties for backfills when using steel reinforcement Property Criteria Test Method Resistivity >3000 ohmcm AASHTO pH >5<10 AASHTO Chlorides <100 PPM AASHTO Sulfates <200 PPM AASHTO Organic Content 1% max AASHTO Seismic external stability of a MSE wall under level backfill condition Select a horizontal ground acceleration (A) based on design earthquake • Calculate maximum acceleration (Am) developed in the wall using Am =(1.45-A)A • Calculate the horizontal inertial force (PIR) and the seismic thrust (PAE) using PIR = 0.5 Am γr H2 PAE= 0.375 Am γf H2 Add to static force acting on the structure, 50% of the seismic thrust PAE and the full inertial; force as both forces do not act simultaneously Location of potential failure surface for internal stability design of MSE walls Location of potential failure surface for internal stability design of MSE walls for extensible reinforcement. Distribution of stress from concentrated vertical load Pv for internal and external stability calculations. Distribution of stresses from concentrated horizontal loads for external stability. Distribution of stresses from concentrated horizontal loads for internal stability. Concluding remarks Reinforced retaining walls have evolved as viable technique and contributed to infrastructure in terms of speed, ease of construction, economy, aesthetics etc. It is a technology that needs to be understood well in terms of its response, construction features etc. Failures of RE walls have also been noted in a few places due to lack of understanding of behavour of RE walls. FWHA, NCMA guidelines need to be studied in detail for seismic stability and deformation issues. THANK YOU THANK YOU