Dipl.-Ing.Stefan Vogt Zentrum Geotechnik, Technische Universität München Buckling of slender piles in soft soils – Large scale loading tests and introduction of a simple calculation scheme Research work at the Zentrum Geotechnik Motivation load foundation slender piles weiche (very) soft Bodenschicht soil layer firm soil layer Has buckling to be expected ? Research work at the Zentrum Geotechnik Motivation EC 7: „.. check for buckling is not required if cu exceeds 10 kPa..“ Other codes set this limit of undrained shear strength at 15 kPa or 10 kPa (eg. DIN 1054, 2005 or the national technical approvals for micropiles) We asked: Are the standards requirements save enough? Heelis&Pavlovic&West (2004) We asked: Are the published design methods capable to simulate the interaction between the supporting soil and the pile? . Prakash (1987). Wenz (1972).Research work at the Zentrum Geotechnik Motivation Reviewed papers: Vik (1962). Meek (1996). Wennerstrand&Fredriksson (1988). Wimmer (2004). Vogt at the IWM 2004 in Tokyo 1.) The standards rules underestimate the possibility of pile buckling 2.) An elastic approach to describe the lateral soil support is not appropriate 3.Research work at the Zentrum Geotechnik Introduction Literature research Development of a numerical FE-Model Model scaled tests In situ field load test Large scaled loading tests Development of a simple design method Summary of the results obtained in the first step Reported by Prof. N.) Most published calculation methods cannot simulate the pile‘s behavior properly . Research work at the Zentrum Geotechnik Introduction Literature research Development of a numerical FE-Model Model scaled tests In situ field load test Large scaled loading tests Development of a simple design method Aim: Proofing the obtained expertise with large scaled loading tests on single piles Development of a simple design method that can simulate the main effects recognized in the loading tests . Large scaled loading tests Loading of 4 m long single piles Container made up with concrete segments Pile is pinned top and bottom . 0 m lateral deflection 1.Large scaled loading tests Loading of 4 m long single piles Container made up with concrete segments Measuring devices settlement of the pile head axial loading force 1.0 m lateral deflection 1.0 m .0 m 1.0 m lateral deflection 4. Large scaled loading tests Mixing up the soil in a liquid consistency Filling the containers by pumping the liquid soil – following consolidation with the help of the electro osmotic effects surcharge load bridge abutment Draining system necessary settlement hydraulic jack Pumping the liquid soil test pile geotextile drainage rigid foundation . Large scaled loading tests Pile type I: Composite cross section GEWI28 Steel rod d = 28 mm Hardened cement slurry D = 100 mm Pile type II: Aluminum profile Thickness = 40 mm Width = 100 mm . Large scaled loading tests Exemplary illustration of a loading test: Alu-pile surrounded by a supporting soil of cu = 18 kPa . 7 kN/m Mean value 2 Standard deveation = 1.1 % Ic = 0.7 kN/m 2 = 2.1 KN/m 2 Residual shear strength cRv = 12.Large scaled loading tests Shear vane tests: Soil support of cu = 18 kPa Statistical analysis: residual shear strength Normal plastic clay TM w = 40.8.0..53.42.2 KN/m 2 maximum shear strength 0 10 20 30 40 undrained shear strength cu [kPa] .48 Maximum shear resistance cfv Mean value Standard deviation = 18.. Large scaled loading tests Loading characteristic: Soil support of cu = 18 kPa Versuchsnummer: KFL-FLACH40x100-02 250 225 200 16 Settlement of the pile head 20 System: N uO 175 150 125 100 75 50 25 0 0 Sudden increase of the pile head settlement while the axial normal force is decreasing 12 settlement of the pile head [mm] Verschiebung am Pfahlkopf uO [mm] axial pile force [kN] Pfahlnormalkraft N [kN] Querschnitt: 8 No sign in the characteristic of the measured deformations that showed the pile failure in advance! Meßdauer [s] time [s] 4 A Pfahlnormalkraft Verschiebung uo 0 600 1200 1800 2400 3000 3600 4200 4800 5400 6000 6600 7200 7800 8400 9000 . Large scaled loading tests Lateral deflection: Soil support of cu = 18 kPa N Axial force N 50 kN 100 kN w w 220 kN (ultimate) 9 mm 212 kN deflection w 0.9 mm 1.4 mm 0.2 mm . With an increasing soil’s undrained shear strength cu the ultimate bearing capacity rises .Large scaled loading tests Analysis Results: . even in soils with an undrained shear strength of cu > 15 kN/m2 N [kN] 600 500 450 400 350 300 250 200 150 100 50 plastic normal force pile type II plastic normal force pile type I pile type I (Ep·Ip = 55 kNm2) pile type II (Ep·Ip = 38 kNm2) 0 0 5 10 15 20 25 cu [kN/m2] .Buckling regularly determined the ultimate state of the system. 00 6.0 maximum interaction of the internal force Interaktionskurve des variables (pile type II) Pfahles FLACH40x100 400.Large scaled loading tests Analysis Results: No failure due to a limited pile‘s material strength! N [kN] 1000.0 cu = 18.0 0.00 .7 kN/m2 200.0 800.0 600.00 2.5 kN/m2 cu = 0 kN/m2 Even the backing moment out of the lateral soil support is not considered 0.0 ? ? cu = 10.00 M [kNm] 4. Large scaled loading tests Analysis Results: For lower axial forces the lateral deflections of the pile remain very little (stiff behavior) The failure of the micro piles occurred suddenly (no sign of failure from the measured deformations) The halve waves of the buckling pile‘s bending curve were always smaller than the full pile‘s length (from joint to joint) . Introduction of a simple design method . LHw N z .Introduction of a simple design method Finding a static system Substituted mechanical system with a buckling length of LHw the length of the effective buckling figure’s half wave LHw can develop freely for the most conditions in situ at the upper and lower boundaries of the soft soil layer the large scaled loading tests showed that the length of the buckling figure’s half waves were smaller than the maximum possible length of 4 m. an infinite long pile can be assumed for the calculations. M w0.M .Introduction of a simple design method Finding a static system All forces acting on the static system with a length of LHw zp P Lateral soil support p(z) T = 0 N Bending moment in the middle MM LHw N T=P z LHw wN. M .M + imp − P ⋅ zp MM p(z) T = 0 N LHw LHw Force from the lateral soil support is defined piecewise in order to a elastic-plastic soil resistance wN.M w0.Introduction of a simple design method Derivation Setting up equilibrium: Condition ∑M = 0 at the pinned top P zp N T=P z LHw MM = N ⋅ w N. M .M deformation wN.M < wki for: wN.M > wki the lateral supporting force is remaining constant LHw kl 1 wki wN.M w0.M ⋅ L Hw π L Hw P = k l ⋅ w ki ⋅ π for: wN.Introduction of a simple design method Derivation Force P from a bi-linear approach of the supporting soil: N T=P zp P MM p(z) T = 0 N LHw P = k l ⋅ w N.M ≥ wki z supportion force P pf for a deformation of wN. M + imp defined picewise .Introduction of a simple design method Derivation Assumption: The pile‘s material remains elastic Condition ∑M = 0 at the pinned top LHw MM = N ⋅ w N.M + imp − P ⋅ zp MM = −E p ⋅ Ip ⋅ w N.M ″ π2 1 2 wN.M ⋅ 2 ⋅ Ep ⋅ Ip + 2 ⋅ pM ⋅ LHw π LHw N= LHw wN. M + Hw imp perfect elastically bedded beam buckling load according to ENGESSER (elastically bedded beam): imperfect elastically bedded beam imperfect bilinear bedded beam perfect unsupported beam imperfect unsupported beam wki buckling load according to EULER (unsupported beam): wN.Introduction of a simple design method Presentation N = F (wN. LHw and the soil support: pf and wki) N perfect bilinear bedded beam 1 π2 2 wN. Ep·Ip.M. imp.M ⋅ 2 ⋅ Ep ⋅ Ip + 2 ⋅ pM ⋅ LHw LHw π N= L wN.M . for which the buckling load Nki is minimal Vary LHw to find the minimum and therefore effective buckling length! effective Nki effective LHw LHw 1 π2 2 w ki ⋅ 2 ⋅ Ep ⋅ Ip + 2 ⋅ w ki ⋅ kl ⋅ LHw LHw π Nki = L w ki + Hw imp Nki .Introduction of a simple design method Presentation LHw is unknown! For defined parameters (soil support. imperfection and flexural rigidity) there is one length of LHw. gb.de .bv.) Check if the pile’s material strength governs the maximum bearing capacity (this means: “does the pile’s material yield before the buckling load is reached”) You may download an Excel-Sheet at www.) Calculate the buckling load Nki 5.tum.) Define an imperfection and the flexural rigidity of the pile’s cross section 3.) Evaluate the effective buckling half wave's length LHw 4.Introduction of a simple design method Summary of the calculation sequence: 1.) Define the parameters of the lateral soil support pf und wki 2. Introduction of a simple design method Back-calculation of the large scaled tests Pile type I 500 450 400 350 pf = 10 · cu · b kl = 100 · cu imp = 600 Used: half side cracked cross section (no tension stresses in the hardened cement) N [kN] 300 250 200 150 100 50 0 0 5 10 15 20 25 pf = 6 · c u · b kl = 60 · cu imp = 300 50 mm hardened cement: C20/25 100 mm GEWI28: BSt 500 S Ep·Ip = 55 kNm2 cu [kN/m2] . 5 40 mm 100 mm 200.0 Alu-pile: Al Mg Si 0.0 400.Introduction of a simple design method Back-calculation of the large scaled tests Pile type II 1000.0 kl = 70 · c u pf = 7 · c u · D 0.0 0 5 10 cu [kN/m2] 15 20 25 Ep·Ip = 38 kNm2 .0 kl = 100 · c u pf = 10 · cu · D kl = 100 · cu pf = 7 · c u · D N [kN] 600.0 800. .Viscous influence creep and relaxation . The insecurities upon the design method is based and which are recognizable comparing the theoretical results with the data form the pile load tests must be covered by partial safety factors on the structural part and the soil resistance.Soil resistance (wki.Summary In (very) soft soils pile buckling should always be verified! With the help of the presented design method the main effects of the loading tests can be considered in basic. pf) .Compound effects steel-concrete . Thank you for your Attention! . . Research work at the Zentrum Geotechnik Introduction Literature research Development of a numerical FE-Model Model scaled tests In situ field load test Large scaled loading tests Development of a simple calculation scheme characteristic of the lateral reaction forces elastisch or elastisch-plastisch supporting force beam supported by springs N lateral deflection . Research work at the Zentrum Geotechnik Introduction Literature research Development of a numerical FE-Model Model scaled tests In situ field load test 100 Loading tests on 80 cm long model piles Varying soil strengths and cross sections Comparison of the test results with the predicted buckling loads (both numerical FEM and published calculation methods) elastic characteristic of the springs elastic-plastic characteristic of the springs buckling load [kN] Knicklast Nk [kN] Large scaled loading tests Development of a simple calculation scheme 80 60 40 20 0 0 5 10 15 20 25 30 35 undrained shear strengh cu [kN/m2] undrainierte Scherfestigkeit cu [kN/m²] . Research work at the Zentrum Geotechnik Introduction Literature research Development of a numerical FE-Model Model scaled tests In situ field load test Large scaled loading tests Development of a simple calculation scheme Loading test of a GEWIpile in soft. organic soil Sudden pile failure at a load very little above the design load . M [mm] .Large scaled loading tests Results of the loading tests of three unsupported composite piles Why to use an aluminum pile? 100 90 89 kN 80 Buckling load of the unsupported pole (EULER II) Axial pile force N [kN] 70 60 50 40 30 Nu Loading an pile with such an inelastic behavior due to its cross section material (unpredictable crack propagation of the concrete) is improper to qualify the lateral soil support! Nu 20 10 0 0 Nu wu 20 40 60 80 wu 100 120 140 160 180 200 Lateral deflection in the middle of the pile wN. 5 40 mm 100 mm Ep·Ip = 38 kNm2 . 100 mm GEWI28: BSt 500 S Ep·Ip = 55 kNm2 Aluminum profile Al Mg Si 0. Solution: A aluminum pile that has a similar flexural rigidity compared to the cracked composite cross section.Large scaled loading tests Pile type II: Aluminum profile Composite cross section. cracked half side Cement: C20/25 50 mm Some pile is needed which behaves elastically over a wide range of lateral displacements and which reproduces the buckling load according to EULER in the unsupported case. Large scaled loading tests Test results obtained by loading of an unsupported alu-pile Ultimate bearing capacity of the 200 unsupported composite-piles: Nk = 55. 180 22 und 19 kN 160 140 axial pile force N [kN] 120 100 80 60 40 20 0 0 600 time [s] 100 80 60 40 Alupile: always Nk = 22 kN 20 0 1200 lateral displacement in the middle of the pile w [mm] . M ⋅ sin L ⋅ z Hw z Assumption of sinus shaped bending curves π w N (z) = w N.M .M w0.Introduction of a simple design method Derivation Assumption of a sinus shaped deformation due to imperfection N T=P zp P MM p(z) T = 0 N LHw π w 0 ( z) = w 0.M ⋅ sin L ⋅ z Hw This yields to a sinus shaped form of the load per unit length due to the lateral soil support LHw π p( z) = pM ⋅ sin L ⋅ z Hw wN. In this case the pile‘s material strength governs the ultimate load. axial pile force N case 2 wM.Introduction of a simple design method Is the decisive buckling load Nki the ultimate axial load Nu of the micropile? D w M.pl C α N = 2 ⋅ 1 − Npl π ⋅ Ep ⋅ Ip Mpl ⋅ LHw 2 The pile‘s material may yield before the buckling load is reached.pl case 1 B case 1 N α M = Mpl ⋅ 1− Npl A lateral deformation wN.pl case 2 wM.M .