3D modeling of progressive deformation of Ko±ciuszki's mound at Kraków

3D modeling of progressive deformation of Ko±ciuszki's mound at Kraków A. Truty, K. Piotrowski, K. Dziewo«ski Cracow University of Technology, Institute of Geotechnics Department of Environmental Engineering Z_Soil Day 27.08.2007 Page 1 of 25

History 19.07.1820: decision to build the mound devoted to Tadeusz Ko±ciuszko Construction of the mound basis (litography by Józef Brodowski 1840 Page 2 of 25 Begining of the construction 15.10.1820 End of construction 23.10.1823

Galician autonomy Construction of the fort 1850 1854 Page 3 of 25 Fort Ko±ciuszko in 1915 r. (Wikipedia.org)

Geometry of the structure Page 4 of 25 Slopes: 40 o 60 o Height: 34 m Radius at the base: 40 m Elevation: 327.78 m.a.s.l.

Characteristics of soils Mound is constructed of loess type clays Such soils are very sensitive to the saturation ratio Higher water content yields reduction of stiness and strength Page 5 of 25

Major damage of the structure (during ood 1997) Page 6 of 25

Repair of the structure 5.12.1999: begining of the repair The repair process consisted of the following steps: 1. Installation of injection anchors 2. Cutting top part of the mound ( 1 3 from the top) and its reconstruction 3. Installation of the dranaige systems 4. Rehabiliation of the masonary retaining walls Page 7 of 25

Repair scheme in the cross section JJ II J I Page 8 of 25

JJ II J I Page 9 of 25

However,... During construction, in the period of intensive raining (April and July 2001) excessive deformations of the mound were observed These deformations did not stabilize till now Page 10 of 25

Results of inclinometer measurements I-4 I-3 I-2 I-1 Page 11 of 25 I-3 I-4 I-2 I-1

Numerical model - assumptions and hypothesis Sources of the excessive deformation: 1. Additional loading of the bottom part of the mound (load increase by 6 to 12 %) 2. Secondary consolidation 3. Articial irrigation (causes increase of the water content both in the upper and lower part, increase of the body forces and reduction of the strength and stiness) 4. An eect of the steel surface grid is neglected 5. Two numerical models are analyzed: simplied singlephase (for assumed water content) coupled two-phase (consolidation caused by wetting) Page 12 of 25

Weak form of the problem of consolidation of partially saturated two-phase medium Ω Ω ε ij (w) σ tot ij dω = Ω w i b i dω + Γ t w i t i dγ (1) q ε kk dω q,k vk F dω q Ω Ω q q dγ Γ q n S K + n S F p ṗ dω+ Γ S q k v (p p ext ) dγ = 0 (2) Term Γ S q k v (p p ext ) dγ is useful for modeling inltration processes as it may cut-o compressive pressures caused by the prescribed uid ux. Page 13 of 25

3D model within Z_Soil environment JJ II J I Page 14 of 25 N

Rys. 6.7 Kotwy w modelu Kopca Modeling repair stages ANALIZA PRZYCZYN POSTĘPUJĄCEJ DEFORMACJI KOPCA KOŚCIUSZKI 41 ANALIZA PRZYCZYN POSTĘPUJĄCEJ DEFORMACJI KOPCA KOŚCIUSZKI Rys. 6.7 Kotwy w modelu Kopca Rys. 6.8 Membrana PEHD w modelu Kopca JJ II J I 43 Page 15 of 25 Politechnika Krakowska. Wydział Inżynierii Środowiska Rys. 6.11 Inklinometry w modelu Kopca Rys. 6.8 Membrana PEHD w modelu Kopca

Material properties for M-C model at the bottom part of the mound S r = 1.0 dla w = 0.35 w L = 0.35 w p = 0.18 Parameters for dierent saturation ratio w S r I L E ν φ c n e o γ d γ [-] [-] [-] [kpa] [-] [] [kpa] [-] [-] [kn/m 3 ] [kn/m 3 ] 0.21 0.62 0.2 20000 0.32 18 31 0.48 0.9 14 17.5 0.25 0.75 0.4 13000 0.32 14 24 0.48 0.9 14 18.2 Page 16 of 25

Material properties for M-C model at the top part of the mound Parameters for dierent saturation ratio w S r I D E ν φ c n e o γ d γ [-] [-] [-] [kpa] [-] [] [kpa] [-] [-] [kn/m 3 ] [kn/m 3 ] 0.075 0.43 0.9 140000 0.25 36 0 0.31 0.45 18.2 18.5 0.127 0.74 0.9 140000 0.25 36 0 0.31 0.45 18.2 20.5 Page 17 of 25

Single-phase model: evolution of parameters in time Page 18 of 25

Safety analysis just after repair Page 19 of 25

Safety analysis during wetting Page 20 of 25

Deformation of inclinometers Page 21 of 25

modelu obliczeniowym zasymulowano adnianie Kopca, przez wprowadzenie na wierzchni Coupledobciążenia model w postaci strumienia cieczy. Page 22 of 25

Deformation of inclinometers Page 23 of 25

Politechnika Krakowska. Wydział Inżynierii Środowiska przemieszczenie bezwzględne u(t) [m]. Evolution of deformation in time (tip of inclinometer I-1) 0.1 0.09 0.08 0.07 0.06 0.05 Wykres 5 - Przemieszczenia inklinometru I-1 (gł. ok 7,5 m) w czasie Page 24 of 25 0.04 0.03 0.02 0.01 0 0 1000 2000 3000 4000 5000 6000 7000 czas t [dni] przemieszczenia inklinometru I-1 listopad - minimalne nawodnienie czerwiec - minimalne nawodnienie prognoza postępującej deformacji ANALIZA PRZYCZYN POSTĘPUJĄCEJ DEFORMACJI KOPCA KOŚCIUSZKI 57

Conclusions Uncoupled model indicates a relatively low safety factor SF = 1.09, coupled model yields SF = 1.20 Simulations indicate that irrigation should denitely be eliminated for some period of time to see the eect For more realistic predictions a dedicated constitutive model of unsaturated soil (like Barcelona) should be used More testing is needed to have the knowledge on the distribution of the water content in the structure and to asess strength and stiness Deformation can grow for several years Page 25 of 25