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Numerical analysis of cargo liquefaction mechanism under the swell motion
Marine Structures 57 (2018) 52e71
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Marine Structures journal homepage: www.elsevier.com/locate/marstruc
Numerical analysis of cargo liquefaction mechanism under the swell motion Samar Daoud a, Imen Said a, *, Samir Ennour b, Mounir Bouassida a a b
ENIT, Universit e de Tunis El Manar, Ecole Nationale d’Ing enieurs de Tunis, LR14ES03-Ing enierie G eotechnique, Tunis, Tunisia MECATER, Rue Ibn Zohr, Immeuble Aliz e, Le Kram, Tunisia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 February 2017 Received in revised form 31 July 2017 Accepted 20 September 2017 Available online 13 October 2017
Cargo liquefaction has been an arising issue since it is the major reason for numerous bulk carriers' capsizes. Many solutions have been adopted by researchers and seafarers to avoid these incidents which can be divided into experimental tests and numerical simulations. The aim of this research is to develop a dynamic numerical model in order to assess the liquefaction potential of a shipped ore. To do so, first, a calibration of experimental cyclic shear test results by means of a non-linear constitutive “UBCSAND” model is elaborated in order to deduce the exact soil parameters. Afterwards, a reproduction of the bulk carrier motions under the swell effect by means of a numerical simulation is conducted. This dynamic model allows analysing the stress distributions in the ore pile as well as spotting the triggering of liquefaction due to pore water pressure build-up. Finally, a parametric study is carried out to determine the variation effect of some key parameters on the cargo liquefaction potential. The numerical calibration results of experimental tests proved that the chosen constitutive model is suitable for the transported ore. Besides, the dynamic model results compared to previous studies and real case observations showed the reliability of this simulation to predict the stress and pore-pressure variation as well as the liquefaction potential under the swell motion. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Dynamic Liquefaction Ore cargo Numerical modeling
1. Introduction Whilst at sea, cargoes are subject to agitation due to the swell impact (Fig. 1). The oscillatory ship movement leads to resettling of the cargo particles and compaction of the inter-granular spaces. This compaction sharply raises the water pressure, forcing the particles apart, potentially leading them to lose direct contact. The cargo loses its shear strength and thus conditions are created for the material to behave like a liquid, i.e. to liquefy [1]. Although in some cases there is no obvious water, the cargoes become soft and loose, even leading to moving. Thus, the ore carrier's stability is greatly reduced, causing a shipwreck. According to [18], from 1988 to 2015, 24 suspected liquefaction incidents were reported. These latters resulted in 164 casualties and the loss of 18 vessels. Conferring to investigations carried out on several case histories, five main potential
* Corresponding author. E-mail addresses: [email protected] (S. Daoud), [email protected] (I. Said), [email protected] (S. Ennour), mounir.bouassida@ fulbrightmail.org (M. Bouassida). https://doi.org/10.1016/j.marstruc.2017.09.003 0951-8339/© 2017 Elsevier Ltd. All rights reserved.
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Fig. 1. Simplified mid-ship section of an ore carrier hold subject to swell motion.
causes have been identified for leading or contributing to cargo liquefaction. The first cause is related to unsafe storage conditions since cargoes are usually stockpiled uncovered and subject to all weather conditions [2]. Second, conforming to the International Association of Classification Societies [3], researches show that insufficient loading plan and improper handling of heavy and high density cargo during loading and unloading cause dangerous situations for ship structure and create excessive stress. The third reason of cargo liquefaction is attributed to poor compliance of some shippers with the testing and certification requirements about moisture test of cargo required by the IMSBC Code, pitiable ships to shore communication, ignorance and deviation from loading plans. The fourth cause was deduced after [4] investigation of a number of ore carriers to understand how cargo liquefaction leads to the loss of stability. They noted that all ore carriers' incidents, including sunken ones, were in good working condition, but experienced extreme voyage conditions. The final identified cause is related to the cargo nature since most casualties commonly involved unprocessed or minimally processed ore cargoes; such as nickel ore, iron ore fines and iron sand. Those cargoes are fine grained soils containing high moisture, although they do not visibly appear wet. In order to reduce the liquefaction risk, many experimental and numerical methods have been developed. For instance, the IMSBC code recommends for materials prone to liquefaction several laboratory tests namely the Flow Table, the Penetration test and the Proctor/Fagerberg test. These tests allow determining the upper bound of the cargo moisture content, which is defined by the Flow Moisture Point (FMP). It is the moisture content permitting the material for passing from solid to liquid state. The IMSBC Code provisions stipulate that cargo must be shipped at moisture content significantly less than the FMP. [5] also suggested a new experimental test procedure for evaluating the shear strength of nickel ore and thus the suitability for carriage of the cargo. The test procedure uses a ‘cone Penetrometer’ to measure the shear strength of a graded sample of nickel ore suitably compacted in a standard container. Unfortunately, no experimental test appears to have accurately captured the cargo behavior due to the scale effect. Therefore, other researchers have resorted to numerical simulations in order to elaborate a more reliable methodology to assess the cargo liquefaction potential. For example [4], used the Level Set Method for the sloshing motion of fluid in a rectangular tank. The simulations have shown that fluid with viscosity can have a negative effect on the stability of ships under the circumstances of beam waves and winds. Warren Springs [1] have also modeled three dimensional flow numerical models to test Canadian Carol Lake Concentrate and some other iron concentrates. These numerical simulations indicated that these cargo types exhibited fast drainage characteristics and a wet base formed within a 35 h voyage. These models of flow were also validated by centrifuge tests at City University, and on-board measurements. Moreover, finite element analysis to model three dimensional flows through voyage was elaborated by the Technical Working Group [6] on Brazilian and Australian Iron Ore Fines. Indeed, scale models of various sizes of holds showed that Australian iron ore fines exhibited some slow drainage behavior and thus the formation of a wet base was not observed. However, a wet base and ‘pooling’ was observed for Brazilian ores. On the other hand [7], and [8] have attempted to simulate a ship's motions within laboratory scale test-work or scale modeling to assess the cargo's liquefaction potential. [9] has also carried out a micro-scale modeling approach to simulate the dynamic behavior of granular materials having physical properties conforming to bulky ship cargos. The researches have varied significantly in terms of the used approach, assessed cargo type and assumptions of motions. Unfortunately, most of these investigators have encountered difficulties when scaling the ships motions (in six degrees of freedom) to a small sample of material. Others have neglected to consider scaling completely. In fact, no scale test-work appears to have accurately captured cargo behavior. In most cases, the scaling issue appears to be due to the difficulties associated with applying scaling laws to the problem (including scaling of accelerations, particle size, relative densities, moisture migration and confining pressures). Given the previously cited issues, previous studies would only give a gross approximation of the ship's motions and their impact on a cargo sample. Taking into account all these features, this paper aims to advance a reliable numerical model
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assessing the liquefaction potential of an overall cargo behavior, in a real scale hold, subject to certain conditions and accelerations observed on typical voyages. In the first part, the UBCSAND constitutive model used in the numerical modeling is presented. Afterwards, a calibration of the numerical model along with cyclic shear tests' results is carried out in order to deduce the UBCSAND input parameters. Finally, a simulation of a cargo hold under the swell effect is conducted to elucidate the processes that could occur within the ore pile, subject to the initial conditions of the cargo and accelerations experienced on voyages. Various journey conditions to determine the cargo behavior during shipment under ship motions in waves are modeled. These calculations are undertaken to assess the overall cargo behavior based upon the parameters determined in the laboratory analysis and calibration results. To conclude, this paper presents a preliminary study to improve the understanding of different parameters affecting the carriage of ore cargoes and to suggest an approach to their safe shipping. It intends to identify the potential of a sufficiently large volume of ore (real scale) to liquefy and/or shift ultimately leading to the loss of ship stability.
2. Materials and methods 2.1. Materials The cargo tested in this study is Nickel ore extracted from New Caledonia mines. This material is known to be an inhomogeneous low-graded soil consisting of very fine clay-like particles and larger rock-like particles. Physical and mechanical characterization tests have been conducted at CERMES laboratories (France) on different New Caledonian Nickel ore samples. 2.1.1. Physical characterization The physical characterization test‘s results concluded that the New Caledonian Nickel ore is divided into three main groups. The first one, known as laterites, is a very fine soil having most particles smaller than 80 mm. It is classified as highly plastic silty sand and characterized by moisture content between 28 and 35%.The second group comprises the earthy saprolites which are sandy silts containing a small fraction of coarse particles (>2 mm) not exceeding 30%. This soil is high plastic silt having high clay content (MBV > 5) and as much as 40% of water content. The third group includes the grainy saprolites that are grainy sands having a high fraction of coarse particles (>30%) and a moisture content varying from 20 to 28%. The average permeability obtained by preliminary oedometer tests is about 5 107 m/s [10]. 2.1.2. Mechanical characterization Preliminary monotonic shear tests were conducted on saturated New Caledonian Nickel ore samples. The response to the applied consolidation stresses of 65 kPa, 130 kPa and 260 kPa, show that the New Caledonian Nickel ore has an apparent cohesion C’ varying from 5 to 10 kPa and an internal friction angle 40 ranging from 30 to 40 depending on the origin and nature of the material. Experimental cyclic triaxial shear tests, performed under undrained conditions with measurement of excess pore pressure (CU þ u), were also conducted under an isotropic consolidation stress s0 c ¼ 65 kPa. The tests were performed on saturated samples and a cyclic shear ratio Rcyc ¼ 0.2 (ie. Deviatoric stress qcyc ¼ ± 26 kPa). The experimental set up of monotonic and cyclic shear tests is detailed in Appendix 1. Two test conditions, detailed in Table 1, were performed on two different samples S1 and S2. Unlike Sample S1, S2 was tested under anisotropic initial consolidation in order to better reproduce the real state of the cargo in the bulk carrier. In fact, a previous quasi-static numerical modeling of the ore carrier hold, showed that 80% of the cargo mass is characterized by an initial shear ratio of Rci ¼ 0.5. Where Rci ¼ qci 2s0 and qci is the initial consolidation deviator stress applied in addition to the 0 c initial consolidation stress sc According to the obtained tests' results, two types of responses are observed. For sample S1, the excess pore pressure becomes high enough so that the effective stress reduces to zero and there is a liquefaction type of failure (cyclic mobility behavior) with progressive accumulation of large deformations. While for sample S2 the pore pressure stabilizes at a residual value which is not high enough to initiate the ratchet phenomenon (accommodation behavior). All tested samples in this study are laterites Nickel ores since they proved to be the most prone Nickel ore type to liquefaction. The experimental shear tests results obtained of the two samples S1 and S2 will be later calibrated by means of a numerical model.
Table 1 Characteristics of cyclic shear tests carried under two different conditions. Test
rd(t/m3)
w (%)
h (%)
rh (t/m3)
SR (%)
q
S1 S2
1.25 1.25
46.2 46.2
31.6 31.6
1.83 1.83
100 100
26 26
cyc
(kPa)
R
cyc
0.2 0.2
NC
Rci
State
36 128
0 0.5
liquefied Non liquefied
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2.2. Methods Combination of physical tests with numerical methods usually leads to the most efficient and robust methods for predicting soil's behavior under dynamic loading, as they couple the strength of the models with the realistic data obtained from experimental tests. In this paper, experimental results from laboratory cyclic triaxial shear tests are used as a tool to calibrate the effective stress constitutive “UBCSAND” [11] model to allow a better understanding of the complex soil behavior. Afterwards, this advanced soil model is used to accurately predict the cargo behavior in a full-scale hold under the swell effects. The methods applied to calibrate cyclic triaxial shear test results and to simulate cargo behavior under the swell effect are detailed in this section. 2.2.1. On the liquefaction constitutive model UBCSAND The UBCSAND soil model is used in this study since it is one of the most popular nonlinear effective stress soil models known in engineering practice for evaluating liquefaction-induced deformation problems. Besides, it is well documented, available for researchers and practitioners, implemented in many numerical programs, and offers potentially important insights into the liquefaction phenomenon. It was developed at the University of British Columbia by Peter Byrne and collaborators [12]. UBCSAND is an effective stress elastic-plastic model which is capable of simulating the liquefaction behavior of sands and silty sands under seismic or cyclic loading. This model is implemented in the widely available finite difference and finite element numerical codes. This model can accurately predict liquefaction-induced lateral displacements and is also able to capture the cyclic build-up of excess pore water pressure and the softening and dilation of soil as it repeatedly crosses the phase transformation line during undrained cyclic shearing [13]. The model input parameters includes elastic stiffness, plastic shear stiffness, strength, flow rule, relative density, and four fitting parameters controlling triggering and post-triggering dilation. In order to determine these specific parameters, empirical relationships are provided based on the corrected standard penetration test (SPT) blow count value, referred to as (N1)60. For instance, generic correlations used to determine these constitutive soil model parameters proposed by Ref. [14] are presented in Table 2. The constant volume friction angle 4cv, the peak friction angle 4p, and cohesion are evaluated from laboratory tests on modeled material. The elastic shear modulus KeG , the plastic shear modulus KpG , and the failure ratio Rf are obtained by curve fitting with the direct shear test results. The elastic bulk modulus KeB is derived from the elastic shear modulus. The elastic shear modulus index ne, elastic bulk modulus index me, and plastic shear modulus index np are generally assigned as 0.5, 0.5 and 0.4, respectively. For this study, the generic correlations presented above are used to evaluate the ability of UBCSAND model to capture and predict deformations by limiting required input to SPT blow count (N1)60. 2.2.2. Numerical calibration of experimental cyclic triaxial shear tests The calibration of cyclic triaxial shear laboratory tests' results is conducted by means of PLAXIS software based of finite element computations. Fig. 2 presents the software interface to model a cyclic shear test. In fact, as earlier mentioned some of the soil constitutive model input parameters (fitting parameters) can only be deduced after experimental tests calibrations. These simulations are also used to evaluate the adeptness of the UBCSAND model and its ability to capture the cyclic pore water pressure increase and corresponding cyclic strain response of the studied soil. In order to reproduce the experimental curves, the actual relative density of laterites (DR z 60%) is used to determine the numerical model parameters detailed in Table 3. 2.2.3. Numerical simulation of a cargo hold under the swell effect In order to assess the liquefaction potential of the cargo under the swell effect, the FLAC 2D software is used in plane strain condition. It is based on the finite difference method to solve the full set of dynamic equations of the swell motion to determine the ore stress and strain behavior. The use of numerical modeling was chosen to gain an understanding of the overall cargo behavior, in a single hold, subject to certain conditions and accelerations observed on typical voyages.
Table 2 Correlations proposed by Michael H. Beaty (2011) to determine the UBCSAND model parameters. Parameter
Determination Formula
(N1)60 KeG KeB KpG 4p Rf
(DR/15)2 21:7 20 ðN1Þ0:333 60 KeG 0.7 2 e KG ðN1Þ60 0:003 þ 100 4cv þ ðN1Þ260 =10 ð0:15Þ 1:1 ðN1Þ60
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Fig. 2. Cyclic shear test numerical simulation.
Table 3 UBCSAND model input parameters. Parameter
Input value
(N1)60 KeG KeB KpG 4p Rf
16 1083 758 932 36.6 0.73
In order to fully characterize the cargo behavior during maritime transportation, much information such as bulk carrier motion, wave motions and swell height are required. Indeed, such information constitutes critical input for establishing the force and boundary conditions applied to the hold in numerical modeling. 2.2.3.1. Definition of the model geometry. It is assumed that the hold is in the Full Load condition as defined in the IACS (1997). The waterline of the ship is approximately at the peak of the loaded cargo. The cargo shape and properties used for the numerical modeling and illustrated in Fig. 3 are based on actual measurements and governed by three factors: The shape of the ship's hull. The ore volume in the hold. The ore natural angle of repose. The numerical calculations are performed on a 2D cross-section of a cargo hold. A cargo geometry having a 25 m width and a 5 m height at side and a 10 m height in middle is used to approximate the Nickel ore pile after loading. Fig. 4 shows the numerical grid and meshing modeled on FLAC. In this analysis, the hold was modeled by a structural element, the slope surfaces were assumed to be seepage boundaries, and the bottom of the heap was assumed to be impervious boundaries. Interface elements, allowing slip and separation were placed between the ore pile and the cargo hold. 2.2.3.2. Definition of the applied motion. Understanding and describing the motion and vibrations experienced by the ship (ultimately affecting the behavior of the cargo), across the possible range of sea encountered conditions, constitute critical input for establishing the boundary conditions in the numerical modeling.
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Fig. 3. Modeled cargo shape in a Nickel ore carrier hold.
Fig. 4. The numerical grid modeled on FLAC.
In reality, a ship (and therefore the cargo in the hold) experiences six degrees of motion during a sea voyage: roll, pitch, yaw, surge, sway and heave. From the marine studies work [15] it was concluded that the roll is the most dangerous motion that a cargo can undergo. It is also assumed that contributions from engine vibrations are negligible. Taking these considerations into account, a simple numerical model is designed to apply a roll movement at the hold center of rotation as illustrated in Fig. 5. The swell motion simulated by a sinusoidal velocity is applied along the nodes of the structural element in order to rotate the cargo hold as indicated in Fig. 6. The algorithm developed to simulate this motion is based on rotation equations with respect to the rolling center O (xO,yO) of the hold with a given roll amplitude a. The new coordinates M0 (x’,y’) of a given point M (x,y) are determined by the following equations:
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Fig. 5. Cargo rolling with respect to the hold center of rotation O.
Fig. 6. Velocities applied at each cargo node to reproduce the rolling motion.
x’- xO ¼ (x-xO) cos (a) e (y-yO) sin (a) y’- yO ¼ (x-xO) sin (a) þ (y-yO) cos (a)
(1)
Roll amplitude and period are deduced from real world observations of bulk carriers under similar conditions. In fact, previous ore carriers instrumentations (based on various RAOs and response spectra) reported that the ship roll typically occurs at frequencies in the order of magnitude of 0.14 Hz (i.e. 7s period) [15]. 2.2.3.3. Calculation phases. The calculation phases simulated in the performed FLAC algorithm are detailed below. In this study, initial static stresses are computed from simple gravity. Firstly, a static analysis considering the gravity effect with the Mohr-Coulomb elastic perfectly plastic constitutive model is performed to establish the in-situ stresses before applying the dynamic loading. Afterwards, the water flow is activated during the static solutions. Once initial stress state is established and the soil model is changed to a pore pressure generation constitutive model (UBCSAND model), the effective stress dynamic analysis is started. During these computations, excess pore water pressures are allowed to be generated and their dissipation is modeled. The dynamic calculations are performed in large strain mode.
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The model simulations are undertaken based upon material parameters derived from the results of fully saturated and undrained cyclic triaxial tests, prior to the calibration of the Finite Element Model by Plaxis software as above mentioned. 2.2.3.4. Liquefaction assessment. To distinguish between liquefiable and non-liquefiable zones, the parameter ru is introduced to the FLAC code by a Fish function (an embedded scripting language that enables the user to define new variables and functions as needed). The pore water pressure ratio ru, presented by equation (2), is equal to the pore water pressure divided by the initial effective stress:
. ru ¼ u s0
(2)
ini
This parameter allows identifying the liquefied zones when it exceeds or equals 1. 2.2.3.5. Parametric study. A sensitivity study is carried out to investigate the variation effect of the relative density (DR) of the loaded ore on the soil behavior towards liquefaction (i.e. ru variation) to develop useful insights. Three conditions characterizing the soil density are investigated, as shown in Table 4. 3. Results 3.1. Numerical calibration of experimental cyclic triaxial shear tests results The UBCSAND model parameters listed in Table 3 are adjusted until the numerical model liquefies at the same number of cycles as deduced from the experimental test. When considering Sample S1 results, it is noted from Fig. 7 that the obtained numerical results of the excess pore water pressure evolution are in very good agreement with the experimental ones. Yet, at the onset of liquefaction (after 36 cycles), the experimental curve displays a smoother increase towards a fully liquefied state compared to the numerical predictions.
Table 4 Different density conditions. DR (%)
Density
30 60 90
Loose Moderately dense Very dense
Fig. 7. Excess pore water pressure evolution of sample S1.
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Fig. 8. Axial deformation evolution of sample S1.
Regarding the axial strain evolution illustrated in Fig. 8, the peak-to-peak amplitude remains fairly constant and relatively low (around 0.5%), while there is a rapid and significant compressive axial strain accumulation, reaching high values after 60 cycles. The experimental curve shows a smooth increase of the axial strain. However, for the numerical data, the accumulated deformation remains very small during the first phase of the test (Nc < 36). When approaching the triggering of liquefaction, the axial strain rapidly increases until reaching 4% after 60 cycles. Fig. 9 illustrating the effective stress path for this test shows a densification when the effective mean stress migrates toward the origin and tends to become null. The experimental and obtained numerical results are quite similar. These cyclic shear test results illustrate that the form of this cyclic failure (fully saturated in undrained condition) is rather a cyclic mobility rather than flow liquefaction. This type of behavior is usually witnessed in the case of medium dense to dense soils when subjected to relatively low to intermediate effective confining stresses [16,17]. Actually, during the initial cycles of undrained loading, excess pore water pressures develop and the soil softens and may liquefy in terms of developing excess pore water pressures close to the applied effective confining stresses. However, as the soil deforms in undrained shear, it seems to be able to sustain the applied cyclic stress levels by generating negative excess pore pressures while undergoing axial strains. The second type of response in terms of excess pore pressure, observed on sample S2, is an accommodation behavior due to anisotropic initial stress state. As a matter of fact, Fig. 10 shows that the pore water pressure evolution is limited, stabilizes around 50 kPa and does not reach the initial consolidation stress (failure criteria). Furthermore, an accumulation of the compressive axial strain is observed as illustrated in Fig. 11 (εa >5%). Indeed, the test was stopped after the application of 128 cycles but the axial strain was not yet stabilized, still increasing over 10%, which practically corresponds to a static failure in compression. It is noted that the same maximum value is reached both for the numerical and experimental cases. Yet, the same difference with sample S1 at the liquefaction triggering point is noticed. The corresponding stress path, observed in Fig. 12, also shows a stabilization of the stress state in the (q, p’) plane without crossing boundary of the failure line. This result confirms the accommodation type of response of this sample. Comparison between the results obtained for samples S1 and S2 clearly shows that the existence of an anisotropic state of consolidation stabilizes the material with respect to the cyclic mobility phenomenon and the development of large strains. According to the previous analyses, it is concluded that the UBCSAND model can fairly predict the experimental results of a cyclic triaxial shear test. The major limitations that need to be mentioned of this model are the irregular evolutions of axial strain and effective stresses when the soil approaches the liquefied state. Indeed, Fig. 11 shows that the numerical prediction underestimates the axial deformation under 60 cycles but still reaches the same value at the final equilibrium state. Fig. 12 shows that the predicted range of effective mean stresses are quite different from the experimental ones, however the deviatoric stress is the same. In this regard, the numerical predictions may be affected marginally.
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Fig. 9. Effective stress path of sample S1 (Left: Numerical results, Right: Experimental results).
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Fig. 10. Excess pore water pressure evolution of Sample S2.
Fig. 11. Axial deformation evolution of Sample S2.
Besides, it should be mentioned that typical 2D analysis only considers a single horizontal and vertical direction of loading. Yet, the obtained experimental results of triaxial cyclic tests are affected by loading in three component directions. Therefore, these small differences are expected to occur between laboratory and numerical results. 3.2. Numerical simulation of a cargo hold under the swell effect To examine the modeling exactness, several iso-values are defined to score the variations of soil parameters during swell motion. The results of these simulations are presented and discussed below.
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Fig. 12. Effective stress path of Sample S2 (Left: Numerical results, Right: Experimental results).
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Fig. 13. Deformed mesh (T ¼ 4.25 s/inclination 10 /Quasi-static Initial state).
Fig. 14. Deformed mesh for a loose ore (T ¼ 2098.25 s (~300 cycles)).
Fig. 15. Deformed mesh for a medium dense ore (T ¼ 2098.25 s (~300 cycles)).
3.2.1. Deformed geometry According to the obtained deformed meshes presented in Fig. 14, Fig. 15 and Fig. 16, it is observed that generally local slip failures occur during transport at the edges of the pile precisely at the corners of the slopes, where there is no confinement from the ship bulkheads or side plates. Indeed, comparing the deformed mesh after 300 cycles to the initial cargo's geometry given in Fig. 13, it is noted that the pile slopes which were initially at the ore angle of repose (35 ) gradually flatten. Furthermore, the pile surface settles along the journey under the solicitations generated by the swell on the hold.
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Fig. 16. Deformed mesh for a very dense ore (T ¼ 2098.25 s (~300 cycles)).
It is also worth mentioning that the deformations of the slopes depend on the ore state. When comparing the obtained figures, it is noticed that the ore pile geometry deforms in a more remarkable way when the loaded cargo is looser. It is deduced that the denser the loaded ore is, the less likely to deform it is and thus less prone to plastic failure. 3.2.2. Plastic points Significant plastic shear strains are observed from Fig. 17, Fig. 18 and Fig. 19 at the pile surface and mainly around the slopes. The large amount of plasticity in these zones is not surprising, as the cargo slopes are close to the natural angle of repose of the material and the cargo cohesion is low. Hence, even the slightest roll angle or lateral acceleration would lead to slope failure after exceeding of Mohr-Coulomb criteria (Quasi-static failure). Since the distribution of plastic points is closely dependent on the cargo state, the same conclusions are made. In fact, it can be deduced that the denser the ore is, the less plastic points it develops. 3.2.3. Pore-water pressure evolution The development of the pore pressure depends on the possibility for the air and water in the voids to escape through the grain skeleton. The aptitude of the air and water to escape is governed by the permeability of the loaded material and the distance from zones with higher pore pressures toward drainage zones. In fact, the dissipation starts as soon as inter-granular volume approaches the water volume. Yet, after the generation of the excess pore pressures the dissipation mechanism continues until the pore pressures reach a static equilibrium. According to the pore water pressure evolution graph obtained from the numerical simulation, depicted in Fig. 20, it is witnessed that the curves present two major parts. The first one is characterized by an acute slope traducing the abrupt build-
Fig. 17. Distribution of plastic points for a loose ore (T ¼ 2098.25 s (~300 cycles)).
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Fig. 18. Distribution of plastic points for a medium dense ore (T ¼ 2098.25 s (~300 cycles)).
Fig. 19. Distribution of plastic points for a very dense ore (T ¼ 2098.25 s (~300 cycles)).
up of pore pressures, whereas the second part is rather horizontal due to pore pressures' tendency to stabilize after a number of cycles (250 cycles). These results show that the pore water pressure at the ore pile center increases without reaching the liquefaction threshold (initial effective mean stress). Thus, it can be deduced that the pile core is not prone to liquefy even in the case of a very loose ore. 3.2.4. Pore-water pressure ratio According to the obtained simulation results at different dynamic times, it is noted that the distribution of the non-zero values and the maximum reached pore water pressure ratio increase with the number of applied cycles. Therefore, a large number of cycles is needed to generate liquefied zones (ru > 1), which are essentially located under the slopes and at the bottom of the pile. Therefore, it should be concluded that the cargo liquefaction remains localized and does not affect the whole cargo. Fig. 21, Fig. 22 and Fig. 23 show that the distribution of liquefied zones is as important as the cargo is looser. It is thus deduced that a denser ore cargo is less prone to liquefaction than a looser one.
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Fig. 20. Pore water pressure evolution at the center of the hold for a very dense ore (T ¼ 2098.25 s (~300 cycles)).
Fig. 21. Pore-water pressure ratio distribution for a loose ore (T ¼ 2098.25 s (~300 cycles)).
4. Conclusions The present research studied numerically the assessment of cargo liquefaction potential that can result from the swell effect. The following points are concluded from the obtained results: Cyclic shear test results illustrate that the form of cyclic failure of the sample S1 (fully saturated in undrained condition) is a cyclic mobility rather than flow liquefaction. In fact, the material seems to be able to sustain the applied cyclic stress levels by generating negative excess pore pressures while undergoing axial strains. The existence of an anisotropic state of consolidation stabilizes the material with respect to the cyclic mobility phenomenon and the development of large strains as observed on Sample S2.
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Fig. 22. Pore-water pressure ratio distribution for a medium dense ore (T ¼ 2098.25 s (~300 cycles)).
Fig. 23. Pore-water pressure ratio distribution for a very dense ore (T ¼ 2098.25 s (~300 cycles)).
The UBCSAND model can fairly predict the experimental results of a cyclic triaxial test. The major limitation of this model is the irregular evolution of excess pore water pressure or axial strain when the soil approaches the liquefied state. The UBCSAND model showed good agreements with experimental data when used to simulate an anisotropically consolidated test. Regarding the cargo simulation results, it is noted that before the nearly complete loss of strength associated with liquefaction, the strength of the cargo abruptly reduces. This latter result in a tendency to slide, in particular in the remaining slopes of the cargo surface after loading due to plastic failure. Indeed, surface slope failure events occur at the surface where Cyclic Shear Ratios should be high and the angle of repose is reached. These incremental movements may traduce a cyclic mobility phenomenon occurred at the periphery of the cargo where the confining pressures are low. Similar observations were witnessed in the case of the maritime transport of iron ore fines [14]. The central part of the cargo decreases slightly in height but is not subject of any significant horizontal movement. The settlement of the ore pile depends on the number of cycles as well as the amplitude of applied load.
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The obtained deformed meshes and distributions of plastic point show that the swell motion may cause some instability to the peripheral slopes of the cargo but it does not lead to large scale cargo shift required to cause ship instability. The pore water pressure ratio iso-values indicate that the liquefied zones are localized and concentrated in the bottom of the hold. This statement is confirmed by the pore water pressure evolution at the ore pile center which increases without reaching the liquefaction limit. Thus, it is deduced that the pile core liquefaction requires large number of cycles and high solicitation. Finally conforming to the cyclic triaxial test results, the ore may temporarily liquefy and/or dilate under the cyclic rolling. In fact, this corresponds to cyclic mobility/softening where the ore loses its strength but recovers cyclically associated with the rolling of the ship. It should be mentioned that under more severe voyage conditions (i.e. rough seas and bad weather forecast), the cargo is susceptible to liquefy more rapidly. Moreover, a cargo that does not get liquefied after a short voyage may get liquefied after a long one since the duration of loading affects enormously the cargo shear resistance. The conducted parametric study allows assuming that the looser a cargo is, the more prone to slope sliding and pile deformation it is. Therefore, a dense cargo is less susceptible to liquefaction under the swell motion than a loose one. On the basis of simulation results, it is recommended to take account of the cargo density since it appears to be a key parameter in affecting the liquefaction occurrence. Typically, a loaded cargo is denser at the lower part of the pile than the upper part due to confinement and compaction. Thus, it would be more appropriate to define a mean cargo density which corresponds to the upper pile part (3 first meters) to conduct the laboratory tests. It is worth mentioning that the laboratory tests are not enough accurate since they do not precisely reproduce the cargo state (stress distribution, load condition, applied solicitation …) and the obtained results are generally overestimated owing to conservative assumptions. It is recommended for upcoming researches to conduct triaxial tests on unsaturated cargo samples with pore water pressure measurements and simulate these features in a dynamic numerical model of a cargo hold under the swell effect.
Acknowledgements This work was supported by the CNRT (Centre National de Recherche Technique "Nickel et son Environnement") and SEM (Syndicat des Producteurs-Exportateurs et Exportateurs de Minerai de Nickel de NC) in the scope of Rheolat I and II projects 2011e2016. We thank them both for providing insight and expertise that greatly assisted this research. We would also like to show our gratitude to the CERMES-Navier laboratories who are part of this project and conducted the physical characterization and the Cyclic Triaxial tests. Appendix 1
Monotonic shear test set up Consolidated undrained tests (CU tests) with measure of pore water pressure u are carried out on saturated samples. The specimens are prepared initially dry and then saturated. In order to easily reconstitute the samples, the dry density selected is about 0.9rd,opt. The specimens are reconstituted layer by layer and compacted manually. A confining pressure of 50 kPa is applied to the sample. The saturation phase is then carried out by first circulating carbon dioxide under a pressure of 15 kPa for 15 min, then by flowing de-aired water through the specimen under a hydrostatic head of about 10 kPa. A minimum back-pressure u0 equal to 200 kPa is applied and the Skempton coefficient B is measured to ensure a good level of saturation (B > 0.98). The specimen is finally isotropically consolidated to the selected consolidation pressure, during a period of 16 h. Shearing is then performed under undrained conditions, at controlled strain-rate according to standard NF P [94-074] (0.05% axial strain per minute). For a given ore, three tests are carried out for three different consolidation pressures, which allows to determine the parameters of the Mohr-Coulomb criterion (angle of internal friction 40 and apparent cohesion c’), and undrained shear strength cu. Cyclic shear test set up In order to evaluate the liquefaction properties of the nickel ores under cyclic loading, cyclic triaxial tests are conducted to determine the shear resistance of a specimen. The corresponding tests are usually carried out on servo controlled triaxial setups allowing to run stress-controlled cyclic tests with measurement of pore water pressure. The experimental setup used to perform cyclic tests is composed of self-contained triaxial cell, electronic test control unit and data acquisition computer (see Fig. 24). The triaxial cell possesses an upper piston driven by a pneumatic servo-controlled system which allows applying force-controlled or displacement-controlled cyclic deviatoric loadings to the specimen. The specimens have a diameter of 70 mm and a height of 140 mm.
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Fig. 24. Experimental set up of cyclic triaxial shear test.
Two criteria are used to determine if a specimen has reached a state of liquefaction: Criterion n 1: the excess pore water pressure reaches the value of the consolidation stress Du ¼ s0 c. Criterion n 2: the peak-to-peak axial strain within a cycle is equal to εa ¼ 5%. References [1] International Maritime Organization (IMO). Solid bulk cargoes code [IMSB code 268(85)]. IMO publishing; 2012. ISBN: 978-92-801-1535-2. [2] The Swedish Club. Carriage of nickel ore and iron ore fines. Detailed Bulletin. [Available Online and Accessed on March 2016]. 2012. [3] International Association of Classification Societies (IACS). Bulk carriers, guidance and information on bulk cargo loading and discharging to reduce the likelihood of over - stressing the hull structure. IACS publishing; 1997. [4] Zou Y, Shen C, Xi X. Numerical simulations on the capsizing of bulk carriers with nickel ores. J Navig 2013;66:919e30. https://doi.org/10.1017/ S0373463313000349. [5] Ota SM, Ura T, Tanaka M. Study on prevention of nickel of sliding ore in bulk. J Soc Nav Archit Jpn 2000;187:301e7. [6] TWG. Submission for evaluation and verification. Reference Tests [Online]. Available: http://ironorefines-twg.com/report-4-reference-tests/; 2013a. Accessed 20 May 2016.
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[7] Atkinson JH, Taylor RN. Moisture migration and stability of iron ore concentrate cargoes. In: Leung Lee, Tan, editors. Proc int. Conf. Centrifuge 94, Singapore (31st Aug-2nd Sep 1994). Rotterdam: A.A. Balkema; 1994. ISBN: 9054103523. [8] Koromila IA, Spandonidis CC, Spyrou KJ. Experimental investigation of cargo liquefaction and impact on the stability of a bulk - carrier. In: Proceedings of the 13th international ship stability workshop. Pp. 1e7; 2013. [9] Spandonidis CC, Spyrou KJ. Micro-scale modeling of excited granular ship cargos: a numerical approach. Ocean Eng J 2013;74(2013):22e36. [10] CERMES/Navier laboratories, Evaluation of the liquefaction properties of three reference nickel ores, September 2014. [11] Byrne PM, Park SS, Beaty MH, Sharp MK, Gonzalez L, Abdoun T. Numerical modeling of liquefaction and comparison with centrifuge tests. Can Geotech. J 2004;41(2):193e211. [12] Beaty MH, Byrne PM. An effective stress model for predicting liquefaction behavior of sand. In: Dakoulas P, Yegian M, Holtz RD, editors. Geotechnical earthquake engineering and soil dynamics III, ASCE geotechnical special publication No. 75, vol. 1, proceedings of a specialty conference (pp. 766e777); 1998. [13] Shriro M, Bray JD. Seismic assessment of earth structures overlying potentially liquefiable soils. 2011. [14] Beaty MH, Byrne PM. UBCSAND constitutive model version 904aR [Online]Available:http://www.itascaudm.com/media/download/UBCSand/ UBCSAND_UDM_Documentation.pdf. 2011. Accessed May 2015. [15] TWG. Submission for evaluation and verification - marine report [Online]. Available:. 2013. http://ironorefines-twg.com/report-5- Marine Report/. Accessed 20 May 2016. [16] Seed HB. Soil liquefaction and cyclic mobility evaluation for level ground during earthquakes. J Geotech. Eng Div ASCE 1979;105(No. GT2). [17] Seed HB, Idriss IM. Ground motions and soil liquefaction during earthquakes. California: Berkley: Earthquake Engineering Research Institute Publication; 1982. [18] Munro M, Mohajerani A. ‘Liquefaction incidents of mineral cargoes on board bulk carriers’, in Advances in Materials Science and Engineering. ISSN1687-8442. United States: Hindawi Publishing Corporation; 2016. p. 1e19.
Contents lists available at ScienceDirect
Marine Structures journal homepage: www.elsevier.com/locate/marstruc
Numerical analysis of cargo liquefaction mechanism under the swell motion Samar Daoud a, Imen Said a, *, Samir Ennour b, Mounir Bouassida a a b
ENIT, Universit e de Tunis El Manar, Ecole Nationale d’Ing enieurs de Tunis, LR14ES03-Ing enierie G eotechnique, Tunis, Tunisia MECATER, Rue Ibn Zohr, Immeuble Aliz e, Le Kram, Tunisia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 February 2017 Received in revised form 31 July 2017 Accepted 20 September 2017 Available online 13 October 2017
Cargo liquefaction has been an arising issue since it is the major reason for numerous bulk carriers' capsizes. Many solutions have been adopted by researchers and seafarers to avoid these incidents which can be divided into experimental tests and numerical simulations. The aim of this research is to develop a dynamic numerical model in order to assess the liquefaction potential of a shipped ore. To do so, first, a calibration of experimental cyclic shear test results by means of a non-linear constitutive “UBCSAND” model is elaborated in order to deduce the exact soil parameters. Afterwards, a reproduction of the bulk carrier motions under the swell effect by means of a numerical simulation is conducted. This dynamic model allows analysing the stress distributions in the ore pile as well as spotting the triggering of liquefaction due to pore water pressure build-up. Finally, a parametric study is carried out to determine the variation effect of some key parameters on the cargo liquefaction potential. The numerical calibration results of experimental tests proved that the chosen constitutive model is suitable for the transported ore. Besides, the dynamic model results compared to previous studies and real case observations showed the reliability of this simulation to predict the stress and pore-pressure variation as well as the liquefaction potential under the swell motion. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Dynamic Liquefaction Ore cargo Numerical modeling
1. Introduction Whilst at sea, cargoes are subject to agitation due to the swell impact (Fig. 1). The oscillatory ship movement leads to resettling of the cargo particles and compaction of the inter-granular spaces. This compaction sharply raises the water pressure, forcing the particles apart, potentially leading them to lose direct contact. The cargo loses its shear strength and thus conditions are created for the material to behave like a liquid, i.e. to liquefy [1]. Although in some cases there is no obvious water, the cargoes become soft and loose, even leading to moving. Thus, the ore carrier's stability is greatly reduced, causing a shipwreck. According to [18], from 1988 to 2015, 24 suspected liquefaction incidents were reported. These latters resulted in 164 casualties and the loss of 18 vessels. Conferring to investigations carried out on several case histories, five main potential
* Corresponding author. E-mail addresses: [email protected] (S. Daoud), [email protected] (I. Said), [email protected] (S. Ennour), mounir.bouassida@ fulbrightmail.org (M. Bouassida). https://doi.org/10.1016/j.marstruc.2017.09.003 0951-8339/© 2017 Elsevier Ltd. All rights reserved.
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Fig. 1. Simplified mid-ship section of an ore carrier hold subject to swell motion.
causes have been identified for leading or contributing to cargo liquefaction. The first cause is related to unsafe storage conditions since cargoes are usually stockpiled uncovered and subject to all weather conditions [2]. Second, conforming to the International Association of Classification Societies [3], researches show that insufficient loading plan and improper handling of heavy and high density cargo during loading and unloading cause dangerous situations for ship structure and create excessive stress. The third reason of cargo liquefaction is attributed to poor compliance of some shippers with the testing and certification requirements about moisture test of cargo required by the IMSBC Code, pitiable ships to shore communication, ignorance and deviation from loading plans. The fourth cause was deduced after [4] investigation of a number of ore carriers to understand how cargo liquefaction leads to the loss of stability. They noted that all ore carriers' incidents, including sunken ones, were in good working condition, but experienced extreme voyage conditions. The final identified cause is related to the cargo nature since most casualties commonly involved unprocessed or minimally processed ore cargoes; such as nickel ore, iron ore fines and iron sand. Those cargoes are fine grained soils containing high moisture, although they do not visibly appear wet. In order to reduce the liquefaction risk, many experimental and numerical methods have been developed. For instance, the IMSBC code recommends for materials prone to liquefaction several laboratory tests namely the Flow Table, the Penetration test and the Proctor/Fagerberg test. These tests allow determining the upper bound of the cargo moisture content, which is defined by the Flow Moisture Point (FMP). It is the moisture content permitting the material for passing from solid to liquid state. The IMSBC Code provisions stipulate that cargo must be shipped at moisture content significantly less than the FMP. [5] also suggested a new experimental test procedure for evaluating the shear strength of nickel ore and thus the suitability for carriage of the cargo. The test procedure uses a ‘cone Penetrometer’ to measure the shear strength of a graded sample of nickel ore suitably compacted in a standard container. Unfortunately, no experimental test appears to have accurately captured the cargo behavior due to the scale effect. Therefore, other researchers have resorted to numerical simulations in order to elaborate a more reliable methodology to assess the cargo liquefaction potential. For example [4], used the Level Set Method for the sloshing motion of fluid in a rectangular tank. The simulations have shown that fluid with viscosity can have a negative effect on the stability of ships under the circumstances of beam waves and winds. Warren Springs [1] have also modeled three dimensional flow numerical models to test Canadian Carol Lake Concentrate and some other iron concentrates. These numerical simulations indicated that these cargo types exhibited fast drainage characteristics and a wet base formed within a 35 h voyage. These models of flow were also validated by centrifuge tests at City University, and on-board measurements. Moreover, finite element analysis to model three dimensional flows through voyage was elaborated by the Technical Working Group [6] on Brazilian and Australian Iron Ore Fines. Indeed, scale models of various sizes of holds showed that Australian iron ore fines exhibited some slow drainage behavior and thus the formation of a wet base was not observed. However, a wet base and ‘pooling’ was observed for Brazilian ores. On the other hand [7], and [8] have attempted to simulate a ship's motions within laboratory scale test-work or scale modeling to assess the cargo's liquefaction potential. [9] has also carried out a micro-scale modeling approach to simulate the dynamic behavior of granular materials having physical properties conforming to bulky ship cargos. The researches have varied significantly in terms of the used approach, assessed cargo type and assumptions of motions. Unfortunately, most of these investigators have encountered difficulties when scaling the ships motions (in six degrees of freedom) to a small sample of material. Others have neglected to consider scaling completely. In fact, no scale test-work appears to have accurately captured cargo behavior. In most cases, the scaling issue appears to be due to the difficulties associated with applying scaling laws to the problem (including scaling of accelerations, particle size, relative densities, moisture migration and confining pressures). Given the previously cited issues, previous studies would only give a gross approximation of the ship's motions and their impact on a cargo sample. Taking into account all these features, this paper aims to advance a reliable numerical model
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assessing the liquefaction potential of an overall cargo behavior, in a real scale hold, subject to certain conditions and accelerations observed on typical voyages. In the first part, the UBCSAND constitutive model used in the numerical modeling is presented. Afterwards, a calibration of the numerical model along with cyclic shear tests' results is carried out in order to deduce the UBCSAND input parameters. Finally, a simulation of a cargo hold under the swell effect is conducted to elucidate the processes that could occur within the ore pile, subject to the initial conditions of the cargo and accelerations experienced on voyages. Various journey conditions to determine the cargo behavior during shipment under ship motions in waves are modeled. These calculations are undertaken to assess the overall cargo behavior based upon the parameters determined in the laboratory analysis and calibration results. To conclude, this paper presents a preliminary study to improve the understanding of different parameters affecting the carriage of ore cargoes and to suggest an approach to their safe shipping. It intends to identify the potential of a sufficiently large volume of ore (real scale) to liquefy and/or shift ultimately leading to the loss of ship stability.
2. Materials and methods 2.1. Materials The cargo tested in this study is Nickel ore extracted from New Caledonia mines. This material is known to be an inhomogeneous low-graded soil consisting of very fine clay-like particles and larger rock-like particles. Physical and mechanical characterization tests have been conducted at CERMES laboratories (France) on different New Caledonian Nickel ore samples. 2.1.1. Physical characterization The physical characterization test‘s results concluded that the New Caledonian Nickel ore is divided into three main groups. The first one, known as laterites, is a very fine soil having most particles smaller than 80 mm. It is classified as highly plastic silty sand and characterized by moisture content between 28 and 35%.The second group comprises the earthy saprolites which are sandy silts containing a small fraction of coarse particles (>2 mm) not exceeding 30%. This soil is high plastic silt having high clay content (MBV > 5) and as much as 40% of water content. The third group includes the grainy saprolites that are grainy sands having a high fraction of coarse particles (>30%) and a moisture content varying from 20 to 28%. The average permeability obtained by preliminary oedometer tests is about 5 107 m/s [10]. 2.1.2. Mechanical characterization Preliminary monotonic shear tests were conducted on saturated New Caledonian Nickel ore samples. The response to the applied consolidation stresses of 65 kPa, 130 kPa and 260 kPa, show that the New Caledonian Nickel ore has an apparent cohesion C’ varying from 5 to 10 kPa and an internal friction angle 40 ranging from 30 to 40 depending on the origin and nature of the material. Experimental cyclic triaxial shear tests, performed under undrained conditions with measurement of excess pore pressure (CU þ u), were also conducted under an isotropic consolidation stress s0 c ¼ 65 kPa. The tests were performed on saturated samples and a cyclic shear ratio Rcyc ¼ 0.2 (ie. Deviatoric stress qcyc ¼ ± 26 kPa). The experimental set up of monotonic and cyclic shear tests is detailed in Appendix 1. Two test conditions, detailed in Table 1, were performed on two different samples S1 and S2. Unlike Sample S1, S2 was tested under anisotropic initial consolidation in order to better reproduce the real state of the cargo in the bulk carrier. In fact, a previous quasi-static numerical modeling of the ore carrier hold, showed that 80% of the cargo mass is characterized by an initial shear ratio of Rci ¼ 0.5. Where Rci ¼ qci 2s0 and qci is the initial consolidation deviator stress applied in addition to the 0 c initial consolidation stress sc According to the obtained tests' results, two types of responses are observed. For sample S1, the excess pore pressure becomes high enough so that the effective stress reduces to zero and there is a liquefaction type of failure (cyclic mobility behavior) with progressive accumulation of large deformations. While for sample S2 the pore pressure stabilizes at a residual value which is not high enough to initiate the ratchet phenomenon (accommodation behavior). All tested samples in this study are laterites Nickel ores since they proved to be the most prone Nickel ore type to liquefaction. The experimental shear tests results obtained of the two samples S1 and S2 will be later calibrated by means of a numerical model.
Table 1 Characteristics of cyclic shear tests carried under two different conditions. Test
rd(t/m3)
w (%)
h (%)
rh (t/m3)
SR (%)
q
S1 S2
1.25 1.25
46.2 46.2
31.6 31.6
1.83 1.83
100 100
26 26
cyc
(kPa)
R
cyc
0.2 0.2
NC
Rci
State
36 128
0 0.5
liquefied Non liquefied
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2.2. Methods Combination of physical tests with numerical methods usually leads to the most efficient and robust methods for predicting soil's behavior under dynamic loading, as they couple the strength of the models with the realistic data obtained from experimental tests. In this paper, experimental results from laboratory cyclic triaxial shear tests are used as a tool to calibrate the effective stress constitutive “UBCSAND” [11] model to allow a better understanding of the complex soil behavior. Afterwards, this advanced soil model is used to accurately predict the cargo behavior in a full-scale hold under the swell effects. The methods applied to calibrate cyclic triaxial shear test results and to simulate cargo behavior under the swell effect are detailed in this section. 2.2.1. On the liquefaction constitutive model UBCSAND The UBCSAND soil model is used in this study since it is one of the most popular nonlinear effective stress soil models known in engineering practice for evaluating liquefaction-induced deformation problems. Besides, it is well documented, available for researchers and practitioners, implemented in many numerical programs, and offers potentially important insights into the liquefaction phenomenon. It was developed at the University of British Columbia by Peter Byrne and collaborators [12]. UBCSAND is an effective stress elastic-plastic model which is capable of simulating the liquefaction behavior of sands and silty sands under seismic or cyclic loading. This model is implemented in the widely available finite difference and finite element numerical codes. This model can accurately predict liquefaction-induced lateral displacements and is also able to capture the cyclic build-up of excess pore water pressure and the softening and dilation of soil as it repeatedly crosses the phase transformation line during undrained cyclic shearing [13]. The model input parameters includes elastic stiffness, plastic shear stiffness, strength, flow rule, relative density, and four fitting parameters controlling triggering and post-triggering dilation. In order to determine these specific parameters, empirical relationships are provided based on the corrected standard penetration test (SPT) blow count value, referred to as (N1)60. For instance, generic correlations used to determine these constitutive soil model parameters proposed by Ref. [14] are presented in Table 2. The constant volume friction angle 4cv, the peak friction angle 4p, and cohesion are evaluated from laboratory tests on modeled material. The elastic shear modulus KeG , the plastic shear modulus KpG , and the failure ratio Rf are obtained by curve fitting with the direct shear test results. The elastic bulk modulus KeB is derived from the elastic shear modulus. The elastic shear modulus index ne, elastic bulk modulus index me, and plastic shear modulus index np are generally assigned as 0.5, 0.5 and 0.4, respectively. For this study, the generic correlations presented above are used to evaluate the ability of UBCSAND model to capture and predict deformations by limiting required input to SPT blow count (N1)60. 2.2.2. Numerical calibration of experimental cyclic triaxial shear tests The calibration of cyclic triaxial shear laboratory tests' results is conducted by means of PLAXIS software based of finite element computations. Fig. 2 presents the software interface to model a cyclic shear test. In fact, as earlier mentioned some of the soil constitutive model input parameters (fitting parameters) can only be deduced after experimental tests calibrations. These simulations are also used to evaluate the adeptness of the UBCSAND model and its ability to capture the cyclic pore water pressure increase and corresponding cyclic strain response of the studied soil. In order to reproduce the experimental curves, the actual relative density of laterites (DR z 60%) is used to determine the numerical model parameters detailed in Table 3. 2.2.3. Numerical simulation of a cargo hold under the swell effect In order to assess the liquefaction potential of the cargo under the swell effect, the FLAC 2D software is used in plane strain condition. It is based on the finite difference method to solve the full set of dynamic equations of the swell motion to determine the ore stress and strain behavior. The use of numerical modeling was chosen to gain an understanding of the overall cargo behavior, in a single hold, subject to certain conditions and accelerations observed on typical voyages.
Table 2 Correlations proposed by Michael H. Beaty (2011) to determine the UBCSAND model parameters. Parameter
Determination Formula
(N1)60 KeG KeB KpG 4p Rf
(DR/15)2 21:7 20 ðN1Þ0:333 60 KeG 0.7 2 e KG ðN1Þ60 0:003 þ 100 4cv þ ðN1Þ260 =10 ð0:15Þ 1:1 ðN1Þ60
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Fig. 2. Cyclic shear test numerical simulation.
Table 3 UBCSAND model input parameters. Parameter
Input value
(N1)60 KeG KeB KpG 4p Rf
16 1083 758 932 36.6 0.73
In order to fully characterize the cargo behavior during maritime transportation, much information such as bulk carrier motion, wave motions and swell height are required. Indeed, such information constitutes critical input for establishing the force and boundary conditions applied to the hold in numerical modeling. 2.2.3.1. Definition of the model geometry. It is assumed that the hold is in the Full Load condition as defined in the IACS (1997). The waterline of the ship is approximately at the peak of the loaded cargo. The cargo shape and properties used for the numerical modeling and illustrated in Fig. 3 are based on actual measurements and governed by three factors: The shape of the ship's hull. The ore volume in the hold. The ore natural angle of repose. The numerical calculations are performed on a 2D cross-section of a cargo hold. A cargo geometry having a 25 m width and a 5 m height at side and a 10 m height in middle is used to approximate the Nickel ore pile after loading. Fig. 4 shows the numerical grid and meshing modeled on FLAC. In this analysis, the hold was modeled by a structural element, the slope surfaces were assumed to be seepage boundaries, and the bottom of the heap was assumed to be impervious boundaries. Interface elements, allowing slip and separation were placed between the ore pile and the cargo hold. 2.2.3.2. Definition of the applied motion. Understanding and describing the motion and vibrations experienced by the ship (ultimately affecting the behavior of the cargo), across the possible range of sea encountered conditions, constitute critical input for establishing the boundary conditions in the numerical modeling.
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Fig. 3. Modeled cargo shape in a Nickel ore carrier hold.
Fig. 4. The numerical grid modeled on FLAC.
In reality, a ship (and therefore the cargo in the hold) experiences six degrees of motion during a sea voyage: roll, pitch, yaw, surge, sway and heave. From the marine studies work [15] it was concluded that the roll is the most dangerous motion that a cargo can undergo. It is also assumed that contributions from engine vibrations are negligible. Taking these considerations into account, a simple numerical model is designed to apply a roll movement at the hold center of rotation as illustrated in Fig. 5. The swell motion simulated by a sinusoidal velocity is applied along the nodes of the structural element in order to rotate the cargo hold as indicated in Fig. 6. The algorithm developed to simulate this motion is based on rotation equations with respect to the rolling center O (xO,yO) of the hold with a given roll amplitude a. The new coordinates M0 (x’,y’) of a given point M (x,y) are determined by the following equations:
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Fig. 5. Cargo rolling with respect to the hold center of rotation O.
Fig. 6. Velocities applied at each cargo node to reproduce the rolling motion.
x’- xO ¼ (x-xO) cos (a) e (y-yO) sin (a) y’- yO ¼ (x-xO) sin (a) þ (y-yO) cos (a)
(1)
Roll amplitude and period are deduced from real world observations of bulk carriers under similar conditions. In fact, previous ore carriers instrumentations (based on various RAOs and response spectra) reported that the ship roll typically occurs at frequencies in the order of magnitude of 0.14 Hz (i.e. 7s period) [15]. 2.2.3.3. Calculation phases. The calculation phases simulated in the performed FLAC algorithm are detailed below. In this study, initial static stresses are computed from simple gravity. Firstly, a static analysis considering the gravity effect with the Mohr-Coulomb elastic perfectly plastic constitutive model is performed to establish the in-situ stresses before applying the dynamic loading. Afterwards, the water flow is activated during the static solutions. Once initial stress state is established and the soil model is changed to a pore pressure generation constitutive model (UBCSAND model), the effective stress dynamic analysis is started. During these computations, excess pore water pressures are allowed to be generated and their dissipation is modeled. The dynamic calculations are performed in large strain mode.
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The model simulations are undertaken based upon material parameters derived from the results of fully saturated and undrained cyclic triaxial tests, prior to the calibration of the Finite Element Model by Plaxis software as above mentioned. 2.2.3.4. Liquefaction assessment. To distinguish between liquefiable and non-liquefiable zones, the parameter ru is introduced to the FLAC code by a Fish function (an embedded scripting language that enables the user to define new variables and functions as needed). The pore water pressure ratio ru, presented by equation (2), is equal to the pore water pressure divided by the initial effective stress:
. ru ¼ u s0
(2)
ini
This parameter allows identifying the liquefied zones when it exceeds or equals 1. 2.2.3.5. Parametric study. A sensitivity study is carried out to investigate the variation effect of the relative density (DR) of the loaded ore on the soil behavior towards liquefaction (i.e. ru variation) to develop useful insights. Three conditions characterizing the soil density are investigated, as shown in Table 4. 3. Results 3.1. Numerical calibration of experimental cyclic triaxial shear tests results The UBCSAND model parameters listed in Table 3 are adjusted until the numerical model liquefies at the same number of cycles as deduced from the experimental test. When considering Sample S1 results, it is noted from Fig. 7 that the obtained numerical results of the excess pore water pressure evolution are in very good agreement with the experimental ones. Yet, at the onset of liquefaction (after 36 cycles), the experimental curve displays a smoother increase towards a fully liquefied state compared to the numerical predictions.
Table 4 Different density conditions. DR (%)
Density
30 60 90
Loose Moderately dense Very dense
Fig. 7. Excess pore water pressure evolution of sample S1.
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Fig. 8. Axial deformation evolution of sample S1.
Regarding the axial strain evolution illustrated in Fig. 8, the peak-to-peak amplitude remains fairly constant and relatively low (around 0.5%), while there is a rapid and significant compressive axial strain accumulation, reaching high values after 60 cycles. The experimental curve shows a smooth increase of the axial strain. However, for the numerical data, the accumulated deformation remains very small during the first phase of the test (Nc < 36). When approaching the triggering of liquefaction, the axial strain rapidly increases until reaching 4% after 60 cycles. Fig. 9 illustrating the effective stress path for this test shows a densification when the effective mean stress migrates toward the origin and tends to become null. The experimental and obtained numerical results are quite similar. These cyclic shear test results illustrate that the form of this cyclic failure (fully saturated in undrained condition) is rather a cyclic mobility rather than flow liquefaction. This type of behavior is usually witnessed in the case of medium dense to dense soils when subjected to relatively low to intermediate effective confining stresses [16,17]. Actually, during the initial cycles of undrained loading, excess pore water pressures develop and the soil softens and may liquefy in terms of developing excess pore water pressures close to the applied effective confining stresses. However, as the soil deforms in undrained shear, it seems to be able to sustain the applied cyclic stress levels by generating negative excess pore pressures while undergoing axial strains. The second type of response in terms of excess pore pressure, observed on sample S2, is an accommodation behavior due to anisotropic initial stress state. As a matter of fact, Fig. 10 shows that the pore water pressure evolution is limited, stabilizes around 50 kPa and does not reach the initial consolidation stress (failure criteria). Furthermore, an accumulation of the compressive axial strain is observed as illustrated in Fig. 11 (εa >5%). Indeed, the test was stopped after the application of 128 cycles but the axial strain was not yet stabilized, still increasing over 10%, which practically corresponds to a static failure in compression. It is noted that the same maximum value is reached both for the numerical and experimental cases. Yet, the same difference with sample S1 at the liquefaction triggering point is noticed. The corresponding stress path, observed in Fig. 12, also shows a stabilization of the stress state in the (q, p’) plane without crossing boundary of the failure line. This result confirms the accommodation type of response of this sample. Comparison between the results obtained for samples S1 and S2 clearly shows that the existence of an anisotropic state of consolidation stabilizes the material with respect to the cyclic mobility phenomenon and the development of large strains. According to the previous analyses, it is concluded that the UBCSAND model can fairly predict the experimental results of a cyclic triaxial shear test. The major limitations that need to be mentioned of this model are the irregular evolutions of axial strain and effective stresses when the soil approaches the liquefied state. Indeed, Fig. 11 shows that the numerical prediction underestimates the axial deformation under 60 cycles but still reaches the same value at the final equilibrium state. Fig. 12 shows that the predicted range of effective mean stresses are quite different from the experimental ones, however the deviatoric stress is the same. In this regard, the numerical predictions may be affected marginally.
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Fig. 9. Effective stress path of sample S1 (Left: Numerical results, Right: Experimental results).
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Fig. 10. Excess pore water pressure evolution of Sample S2.
Fig. 11. Axial deformation evolution of Sample S2.
Besides, it should be mentioned that typical 2D analysis only considers a single horizontal and vertical direction of loading. Yet, the obtained experimental results of triaxial cyclic tests are affected by loading in three component directions. Therefore, these small differences are expected to occur between laboratory and numerical results. 3.2. Numerical simulation of a cargo hold under the swell effect To examine the modeling exactness, several iso-values are defined to score the variations of soil parameters during swell motion. The results of these simulations are presented and discussed below.
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Fig. 12. Effective stress path of Sample S2 (Left: Numerical results, Right: Experimental results).
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Fig. 13. Deformed mesh (T ¼ 4.25 s/inclination 10 /Quasi-static Initial state).
Fig. 14. Deformed mesh for a loose ore (T ¼ 2098.25 s (~300 cycles)).
Fig. 15. Deformed mesh for a medium dense ore (T ¼ 2098.25 s (~300 cycles)).
3.2.1. Deformed geometry According to the obtained deformed meshes presented in Fig. 14, Fig. 15 and Fig. 16, it is observed that generally local slip failures occur during transport at the edges of the pile precisely at the corners of the slopes, where there is no confinement from the ship bulkheads or side plates. Indeed, comparing the deformed mesh after 300 cycles to the initial cargo's geometry given in Fig. 13, it is noted that the pile slopes which were initially at the ore angle of repose (35 ) gradually flatten. Furthermore, the pile surface settles along the journey under the solicitations generated by the swell on the hold.
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Fig. 16. Deformed mesh for a very dense ore (T ¼ 2098.25 s (~300 cycles)).
It is also worth mentioning that the deformations of the slopes depend on the ore state. When comparing the obtained figures, it is noticed that the ore pile geometry deforms in a more remarkable way when the loaded cargo is looser. It is deduced that the denser the loaded ore is, the less likely to deform it is and thus less prone to plastic failure. 3.2.2. Plastic points Significant plastic shear strains are observed from Fig. 17, Fig. 18 and Fig. 19 at the pile surface and mainly around the slopes. The large amount of plasticity in these zones is not surprising, as the cargo slopes are close to the natural angle of repose of the material and the cargo cohesion is low. Hence, even the slightest roll angle or lateral acceleration would lead to slope failure after exceeding of Mohr-Coulomb criteria (Quasi-static failure). Since the distribution of plastic points is closely dependent on the cargo state, the same conclusions are made. In fact, it can be deduced that the denser the ore is, the less plastic points it develops. 3.2.3. Pore-water pressure evolution The development of the pore pressure depends on the possibility for the air and water in the voids to escape through the grain skeleton. The aptitude of the air and water to escape is governed by the permeability of the loaded material and the distance from zones with higher pore pressures toward drainage zones. In fact, the dissipation starts as soon as inter-granular volume approaches the water volume. Yet, after the generation of the excess pore pressures the dissipation mechanism continues until the pore pressures reach a static equilibrium. According to the pore water pressure evolution graph obtained from the numerical simulation, depicted in Fig. 20, it is witnessed that the curves present two major parts. The first one is characterized by an acute slope traducing the abrupt build-
Fig. 17. Distribution of plastic points for a loose ore (T ¼ 2098.25 s (~300 cycles)).
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Fig. 18. Distribution of plastic points for a medium dense ore (T ¼ 2098.25 s (~300 cycles)).
Fig. 19. Distribution of plastic points for a very dense ore (T ¼ 2098.25 s (~300 cycles)).
up of pore pressures, whereas the second part is rather horizontal due to pore pressures' tendency to stabilize after a number of cycles (250 cycles). These results show that the pore water pressure at the ore pile center increases without reaching the liquefaction threshold (initial effective mean stress). Thus, it can be deduced that the pile core is not prone to liquefy even in the case of a very loose ore. 3.2.4. Pore-water pressure ratio According to the obtained simulation results at different dynamic times, it is noted that the distribution of the non-zero values and the maximum reached pore water pressure ratio increase with the number of applied cycles. Therefore, a large number of cycles is needed to generate liquefied zones (ru > 1), which are essentially located under the slopes and at the bottom of the pile. Therefore, it should be concluded that the cargo liquefaction remains localized and does not affect the whole cargo. Fig. 21, Fig. 22 and Fig. 23 show that the distribution of liquefied zones is as important as the cargo is looser. It is thus deduced that a denser ore cargo is less prone to liquefaction than a looser one.
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Fig. 20. Pore water pressure evolution at the center of the hold for a very dense ore (T ¼ 2098.25 s (~300 cycles)).
Fig. 21. Pore-water pressure ratio distribution for a loose ore (T ¼ 2098.25 s (~300 cycles)).
4. Conclusions The present research studied numerically the assessment of cargo liquefaction potential that can result from the swell effect. The following points are concluded from the obtained results: Cyclic shear test results illustrate that the form of cyclic failure of the sample S1 (fully saturated in undrained condition) is a cyclic mobility rather than flow liquefaction. In fact, the material seems to be able to sustain the applied cyclic stress levels by generating negative excess pore pressures while undergoing axial strains. The existence of an anisotropic state of consolidation stabilizes the material with respect to the cyclic mobility phenomenon and the development of large strains as observed on Sample S2.
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Fig. 22. Pore-water pressure ratio distribution for a medium dense ore (T ¼ 2098.25 s (~300 cycles)).
Fig. 23. Pore-water pressure ratio distribution for a very dense ore (T ¼ 2098.25 s (~300 cycles)).
The UBCSAND model can fairly predict the experimental results of a cyclic triaxial test. The major limitation of this model is the irregular evolution of excess pore water pressure or axial strain when the soil approaches the liquefied state. The UBCSAND model showed good agreements with experimental data when used to simulate an anisotropically consolidated test. Regarding the cargo simulation results, it is noted that before the nearly complete loss of strength associated with liquefaction, the strength of the cargo abruptly reduces. This latter result in a tendency to slide, in particular in the remaining slopes of the cargo surface after loading due to plastic failure. Indeed, surface slope failure events occur at the surface where Cyclic Shear Ratios should be high and the angle of repose is reached. These incremental movements may traduce a cyclic mobility phenomenon occurred at the periphery of the cargo where the confining pressures are low. Similar observations were witnessed in the case of the maritime transport of iron ore fines [14]. The central part of the cargo decreases slightly in height but is not subject of any significant horizontal movement. The settlement of the ore pile depends on the number of cycles as well as the amplitude of applied load.
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The obtained deformed meshes and distributions of plastic point show that the swell motion may cause some instability to the peripheral slopes of the cargo but it does not lead to large scale cargo shift required to cause ship instability. The pore water pressure ratio iso-values indicate that the liquefied zones are localized and concentrated in the bottom of the hold. This statement is confirmed by the pore water pressure evolution at the ore pile center which increases without reaching the liquefaction limit. Thus, it is deduced that the pile core liquefaction requires large number of cycles and high solicitation. Finally conforming to the cyclic triaxial test results, the ore may temporarily liquefy and/or dilate under the cyclic rolling. In fact, this corresponds to cyclic mobility/softening where the ore loses its strength but recovers cyclically associated with the rolling of the ship. It should be mentioned that under more severe voyage conditions (i.e. rough seas and bad weather forecast), the cargo is susceptible to liquefy more rapidly. Moreover, a cargo that does not get liquefied after a short voyage may get liquefied after a long one since the duration of loading affects enormously the cargo shear resistance. The conducted parametric study allows assuming that the looser a cargo is, the more prone to slope sliding and pile deformation it is. Therefore, a dense cargo is less susceptible to liquefaction under the swell motion than a loose one. On the basis of simulation results, it is recommended to take account of the cargo density since it appears to be a key parameter in affecting the liquefaction occurrence. Typically, a loaded cargo is denser at the lower part of the pile than the upper part due to confinement and compaction. Thus, it would be more appropriate to define a mean cargo density which corresponds to the upper pile part (3 first meters) to conduct the laboratory tests. It is worth mentioning that the laboratory tests are not enough accurate since they do not precisely reproduce the cargo state (stress distribution, load condition, applied solicitation …) and the obtained results are generally overestimated owing to conservative assumptions. It is recommended for upcoming researches to conduct triaxial tests on unsaturated cargo samples with pore water pressure measurements and simulate these features in a dynamic numerical model of a cargo hold under the swell effect.
Acknowledgements This work was supported by the CNRT (Centre National de Recherche Technique "Nickel et son Environnement") and SEM (Syndicat des Producteurs-Exportateurs et Exportateurs de Minerai de Nickel de NC) in the scope of Rheolat I and II projects 2011e2016. We thank them both for providing insight and expertise that greatly assisted this research. We would also like to show our gratitude to the CERMES-Navier laboratories who are part of this project and conducted the physical characterization and the Cyclic Triaxial tests. Appendix 1
Monotonic shear test set up Consolidated undrained tests (CU tests) with measure of pore water pressure u are carried out on saturated samples. The specimens are prepared initially dry and then saturated. In order to easily reconstitute the samples, the dry density selected is about 0.9rd,opt. The specimens are reconstituted layer by layer and compacted manually. A confining pressure of 50 kPa is applied to the sample. The saturation phase is then carried out by first circulating carbon dioxide under a pressure of 15 kPa for 15 min, then by flowing de-aired water through the specimen under a hydrostatic head of about 10 kPa. A minimum back-pressure u0 equal to 200 kPa is applied and the Skempton coefficient B is measured to ensure a good level of saturation (B > 0.98). The specimen is finally isotropically consolidated to the selected consolidation pressure, during a period of 16 h. Shearing is then performed under undrained conditions, at controlled strain-rate according to standard NF P [94-074] (0.05% axial strain per minute). For a given ore, three tests are carried out for three different consolidation pressures, which allows to determine the parameters of the Mohr-Coulomb criterion (angle of internal friction 40 and apparent cohesion c’), and undrained shear strength cu. Cyclic shear test set up In order to evaluate the liquefaction properties of the nickel ores under cyclic loading, cyclic triaxial tests are conducted to determine the shear resistance of a specimen. The corresponding tests are usually carried out on servo controlled triaxial setups allowing to run stress-controlled cyclic tests with measurement of pore water pressure. The experimental setup used to perform cyclic tests is composed of self-contained triaxial cell, electronic test control unit and data acquisition computer (see Fig. 24). The triaxial cell possesses an upper piston driven by a pneumatic servo-controlled system which allows applying force-controlled or displacement-controlled cyclic deviatoric loadings to the specimen. The specimens have a diameter of 70 mm and a height of 140 mm.
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Fig. 24. Experimental set up of cyclic triaxial shear test.
Two criteria are used to determine if a specimen has reached a state of liquefaction: Criterion n 1: the excess pore water pressure reaches the value of the consolidation stress Du ¼ s0 c. Criterion n 2: the peak-to-peak axial strain within a cycle is equal to εa ¼ 5%. References [1] International Maritime Organization (IMO). Solid bulk cargoes code [IMSB code 268(85)]. IMO publishing; 2012. ISBN: 978-92-801-1535-2. [2] The Swedish Club. Carriage of nickel ore and iron ore fines. Detailed Bulletin. [Available Online and Accessed on March 2016]. 2012. [3] International Association of Classification Societies (IACS). Bulk carriers, guidance and information on bulk cargo loading and discharging to reduce the likelihood of over - stressing the hull structure. IACS publishing; 1997. [4] Zou Y, Shen C, Xi X. Numerical simulations on the capsizing of bulk carriers with nickel ores. J Navig 2013;66:919e30. https://doi.org/10.1017/ S0373463313000349. [5] Ota SM, Ura T, Tanaka M. Study on prevention of nickel of sliding ore in bulk. J Soc Nav Archit Jpn 2000;187:301e7. [6] TWG. Submission for evaluation and verification. Reference Tests [Online]. Available: http://ironorefines-twg.com/report-4-reference-tests/; 2013a. Accessed 20 May 2016.
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[7] Atkinson JH, Taylor RN. Moisture migration and stability of iron ore concentrate cargoes. In: Leung Lee, Tan, editors. Proc int. Conf. Centrifuge 94, Singapore (31st Aug-2nd Sep 1994). Rotterdam: A.A. Balkema; 1994. ISBN: 9054103523. [8] Koromila IA, Spandonidis CC, Spyrou KJ. Experimental investigation of cargo liquefaction and impact on the stability of a bulk - carrier. In: Proceedings of the 13th international ship stability workshop. Pp. 1e7; 2013. [9] Spandonidis CC, Spyrou KJ. Micro-scale modeling of excited granular ship cargos: a numerical approach. Ocean Eng J 2013;74(2013):22e36. [10] CERMES/Navier laboratories, Evaluation of the liquefaction properties of three reference nickel ores, September 2014. [11] Byrne PM, Park SS, Beaty MH, Sharp MK, Gonzalez L, Abdoun T. Numerical modeling of liquefaction and comparison with centrifuge tests. Can Geotech. J 2004;41(2):193e211. [12] Beaty MH, Byrne PM. An effective stress model for predicting liquefaction behavior of sand. In: Dakoulas P, Yegian M, Holtz RD, editors. Geotechnical earthquake engineering and soil dynamics III, ASCE geotechnical special publication No. 75, vol. 1, proceedings of a specialty conference (pp. 766e777); 1998. [13] Shriro M, Bray JD. Seismic assessment of earth structures overlying potentially liquefiable soils. 2011. [14] Beaty MH, Byrne PM. UBCSAND constitutive model version 904aR [Online]Available:http://www.itascaudm.com/media/download/UBCSand/ UBCSAND_UDM_Documentation.pdf. 2011. Accessed May 2015. [15] TWG. Submission for evaluation and verification - marine report [Online]. Available:. 2013. http://ironorefines-twg.com/report-5- Marine Report/. Accessed 20 May 2016. [16] Seed HB. Soil liquefaction and cyclic mobility evaluation for level ground during earthquakes. J Geotech. Eng Div ASCE 1979;105(No. GT2). [17] Seed HB, Idriss IM. Ground motions and soil liquefaction during earthquakes. California: Berkley: Earthquake Engineering Research Institute Publication; 1982. [18] Munro M, Mohajerani A. ‘Liquefaction incidents of mineral cargoes on board bulk carriers’, in Advances in Materials Science and Engineering. ISSN1687-8442. United States: Hindawi Publishing Corporation; 2016. p. 1e19.