Geosynthetics and Reinforced Soil Structures Reinforced Soil Walls continued Prof K. Rajagopal Department of Civil Engineering IIT Madras, Chennai e-mail: gopalkr@iitm.ac.inac in
Outline of the Lecture External Stability Calculations Reinforced Soil Walls - 4 /9
External Stability Calculations Stability Against Lateral Sliding Stability against Overturning Stability Against bearing capacity failure Slip circle or overall failure mechanism The length of the reinforced soil block is determined from these calculations. For the purpose of external stability calculations, the reinforced block is treated as a rigid block. Reinforced Soil Walls - 4 3/9
Rankine Lateral Earth Pressures Rankine Lateral Earth Pressures Horizontal ground surface and smooth vertical wall Horizontal ground surface and smooth vertical wall sin 1 sin 1 K a q K K c z K a a a x H/3 H/ qh K H K P a a 1 Cohesion, c is usually neglected K a q K a H q H K H K H q H K H H K M a a a a 3 1 6 1 3 1 q K H K a a K a q Reinforced Soil Walls - 4 4/9 6 3
Rankine s theory Sloped Fill K a cos cos cos cos cos cos cos P P a 1 H cos Reinforced Soil Walls - 4 5/9
Coulomb s Equation for active case K a sin sin sin( ) 1 ( ) sin( )sin( ) sin( ) P = back slope angle = angle at back face of retaining wall = friction angle of the soil = interface friction angle between wall and backfill soil Effect of wall friction is to reduce the active lateral earth pressures Reinforced Soil Walls - 4 6/9
Influence of wall friction For a vertical retaining wall (=90) with horizontal backfill (=0) and friction angle =30, influence of wall friction Wall friction K a 0 1/3 = 0.333 5 0.319 10 0.308 0 0.79 Reinforced Soil Walls - 4 7/9
Design Loads Self weight loads Live loads due to point loads or uniform surcharge Horizontal Loads from the crash barrier Horizontal loads due to breaking forces on bridge abutments Vertical loads from Bridge abutments Seismic loads Reinforced Soil Walls - 4 8/9
Embedment Depth Slope in front of wall Minimum embedment to top of levelling pad Horizontal (wall) H/0 Horizontal (abutment) H/10 3H:1V H/10 H:1V H/7 H V 3H:V H/5 Minimum embedment depth = 500 mm Higher depth of embedment may be required based on plasticity properties of the foundation soil or frost susceptibility, scour depth in river beds, etc. Reinforced Soil Walls - 4 9/9
Height of the Walls, H? H H H L H H L tan Reinforced Soil Walls - 4 10/9
CHECK FOR LATERAL SLIDING (FHWA method) Live load surchage, q L Permanent surcharge, q d 1 k H k q q P ( ) H ab ab d L P h = horizontal load at crest due to crash barrier load, traction load, earth pressure against abutment, etc. P h P h H Reinforced fill L backfill k abh k ab q active pressure coefficient of backfill, k ab 1-sinb 1sin b b = friction angle of backfill soil Reinforced Soil Walls - 4 11/9
CHECK FOR LATERAL SLIDING (FHWA method) shear resistance developed at base ( HL q L ) =friction factor at the base = tan(/3* m ) m = lesser of the friction angles of the reinforced soil and foundation soil d resistance force factor of safety against sliding 1. 5 sliding force Reinforced Soil Walls - 4 1/9
Back to back walls /4+/ Lateral earth pressure varies from 0 to K a depending on the overlap distance K=0 if overlap is 0.3H K=Ka if distance between two blocks are away from each other from the active wedge Reinforced Soil Walls - 4 13/9
overturning FACTOR OF SAFETY AGAINST OVERTURNING (FHWA) moment M 1 1 6 q q k H 3 K ( ) o ab ab d L H P h H resisting moment M. H. L. L / q. L. L R d / Live load contribution for resistance is neglected FS against overturning resisting moment overturning moment Reinforced Soil Walls - 4 14/9
CHECK FOR BEARING CAPACITY OF FOUNDATION SOIL Bearing capacity of the foundation soil is estimated by treating it as a strip footing of width (B) equal to the length of the reinforced block. All permanent and live loads are considered for estimating the foundation pressures R v = HB+(q L +q d )*B + any other permanent loads e=eccentricity = M o /R v Eccentricity: e < B/6 in soils e < B/4inrocks Bearing vb pressure R v B e on foundation soil Reinforced Soil Walls - 4 15/9
The bearing pressure at the foundation soil should be less than the allowable bearing pressure. Allowable bearing pressure is that t pressure that t will have adequate factor of safety against bearing failure and the resulting settlements are within the limits. Reinforced Soil Walls - 4 16/9
Types of bearing capacity failures General shear failure in case of dense soils, over consolidated d clays Local shear failure in case of loose sands, normally consolidated clays Punching shear failure in case of extremely soft soils Vesic (1960) Reinforced Soil Walls - 4 17/9
q nu c Vesic s Bearing capacity Theory and IS6403 Net ultimate bearing capacity, N c s c d c i c q' ( N q -1) s q d q i q 1 B N Net safe bearing capacity, q ns = q nu /FS Bearing capacity factors N c, N q, N are functions of friction angle of soil N q = e tan tan 4 + c q s d N = (N 1) cot i W' N = (N q 1) tan S c, S q, S =shape factors 1 d c, d q, d = depth factors1 i c, i q, i =load inclination factors 1 (IS 6403 1981) Reinforced Soil Walls - 4 18/9
Empirical correlations for soil strengths Empirical Correlations with SPT N values for cohesive soils (Bowles 1988) N value U.C.C. consistency (kpa) < < 5 very soft -4 5-50 soft 4-8 50-100 medium 8-16 100-00 stiff 16-3 00-400 very stiff > 3 > 400 hard cohesive strength 6SPT N value (kpa) Empirical Correlations with corrected SPT N values for cohesionless soils (Bowles 1988) N value relative density (%) description < 4 5-30 0 very loose 4-10 7-3 15 loose 10-30 30-35 65 medium 30-50 35-40 85 dense > 50 38-43 100 very dense Reinforced Soil Walls - 4 19/9
Local shear failure (incomplete failure surface) Terzaghi s approximation cm = c 3-1 m = tan tan 3 Reinforced Soil Walls - 4 0/9
MethodofAnalysisBasedonRelative of on Density & void ratio Relative density void ratio condition Analysis method > 70% < 0.55 dense general shear failure <0% > 0.75 loose local shear failure 0 70% 055 0.55 075 0.75 medium interpolate between above. Reinforced Soil Walls - 4 1/9
Water table correction factor, W Varies between 05and 0.5 10 1.0 W=0.5 B B W=1.0 Reinforced Soil Walls - 4 /9
Types of settlements Immediate settlements Primary consolidation settlements Secondary consolidation i settlements Reinforced Soil Walls - 4 3/9
S i q n B (1- ) E Approximate relations for Young' s clayey sand : Elastic settlements I Sands : Saturated sands : gravelly sand and gravel : clay soils, E Poisson' s f E 100 to 500 c q n = net pressure at foundation level E = Young s modulus of foundation soil I f = influence factor = 3.38 for strip footings = Poisson s ratio of foundation soil modulus of (kpa) 500 (N 15); to 4 q E (kpa) 50 (N 15) E (kpa) 100(N 6) uu E 30 (N 15); 3 to 6 q ratio of clays (saturated) : sands :0.3 to 0.4 soils : 0.4 to 0.5 rock : c clays (dry) : 0.1to 0. soils 0.1 to 0.3 c Reinforced Soil Walls - 4 4/9
Primary consolidation settlements S c 1 Cc e o H log 10 ' o ' ' o S c = m v H Settlement at any time, t S(t) = U(t) S c for U 53%, Tv = (/4) U; for U > 53%, Tv = 1.781 0.933 [log10(100 U%)] Time factor, T v = c v t/d v v Reinforced Soil Walls - 4 5/9
Secondary consolidation settlements S s C H log t 1 e 10 f C = secondary consolidation coefficient i = slope of the timesettlement graph in the secondary compression region Happens at constant effective stress after primary consolidation Predominant in organic clays like peat More important in case of thin soil deposits compared to width of foundation Reinforced Soil Walls - 4 6/9
Slip Circle Failure Analysis h T r N = W.cos i ; T = W.sin i H w i i R = c.+n.tan w i i T N FS R T c L a tan wi cosi T w sin i i r h Reinforced Soil Walls - 4 7/9
Global slip circle failure of a reinforced soil retaining wall due to deep seated failure Reinforced Soil Walls - 4 8/9
Recap This lecture has discussed the different calculations for satisfying the equilibrium of thereinforced soil block Reinforced Soil Walls - 4 9/9