Andrzej GŁUCHOWSKI* Szkoła Główna Gospodarstwa Wiejskiego

PLASTIC STRAIN DEVELOPMENT DURING CYCLIC UNIAXIAL LOADING OF COHESIVE SOIL

1. Introduction Cyclic loading of soil is a subject of intensive studies [1, 2, 3]. During the last decade, a number of soil models simulating the occurrence of a strain caused by cyclic loads were presented. Cyclic loading in these studies is treated as a “quasi static” phenomenon. It means that in opposite to dynamic excitation, quasi static load does not possess a moment of inertia whose source is soil mass. To create such loads, frequency of cyclic loading should be less than 5Hz [2, 3]. In order to analyse cyclic loading in non-cohesive soils, such as sands, triaxial tests are performed. In case of cohesive soils, time constrains caused by consolidation time, limits number of tests. However, cohesive soils can be tested in unconfined manner in opposite to non-cohesive soils. Unconfined Cyclic Tests (UCT), during which confining pressure is equal σ3=0kPa, could help to understand cohesive soils behaviour during construction phase. Road sub-grade or even foundation sub-grade could be excited by repeated loading numerous times, before the proper structure will be constructed [4]. Standard unconfined compressive strength tests are performed mostly in order to obtain maximal deviator stress for Coulomb-Mohr failure criterion or simply for estimation of the cohesion parameter in case of clayey soils [5]. Cyclic loading in unconfined conditions does not lead to failure of soil specimen, but the repetition of constant stress ratio in numerous cycles. Stress ratio varies for each test in order to find differences in the behaviour of soil. Cyclic loading phenomenon is usually described by resilient modulus Mr, which describes ratio of deviator stress Δσ and recoverable stress εr:

* Promotor: prof. dr hab. inż. Alojzy Szymański; promotor pomocniczy: dr inż. Wojciech Sas

A. Głuchowski

84 Mr 



r

(1)

Resilient modulus is a key parameter in Polish Standard PN-EN13286-7, which is going to replace Young modulus E in mechanistic-empirical design of road structures. Repeated loading of soil leads to a possibility of dividing the strain into two components: recoverable or resilient strain εr and permanent or irrecoverable strain εp. Sum of these two components constitutes strain in one cycle. Fig. 1 presents the scheme of the abovementioned relations.

Fig. 1. A graphical interpretation of resilient modulus and strains in one cycle [1] Rys. 1. Graficzna interpretacja cyklicznego modułu sprężystości i odkształceń w jednym cyklu

Except the resilient modulus, it is important to obtain from UCT test information about permanent strain. The phenomenon of plastic strain increment during cyclic loading still need to be clarified. Studies on non-cohesive soils lead to the discovery of the shakedown and abation phenomena, during which irrecoverable strain dissipates to a small constant value or can even vanish completely [2]. Cohesive soils also exhibit the same behaviour. Shakedown was recognised during cCBR tests and next triaxial studies confirm such a phenomenon. During the UCT, shakedown occurs even when confining pressure is equal to zero. This fact is caused by cohesion properties of fine grained soils. Nevertheless, this test can be performed until constant, for tested material, deviatoric stress, which is a slightly greater than apparent cohesion value caused by negative pore pressure. It is possible to say that in such conditions, the cyclic loading mobilizes the response of soil skeleton in the form of cohesion forces rather than friction forces. Plastic strain development is usually present as total strain value during tests or as plot of plastic strain increment in time or number of performed cycles. Value of plastic strains during an individual cycle can be calculated as difference between total and

Plastic strain development during cyclic uniaxial loading of cohesive soil. elastic strain in one cycle. Presentation of the cyclic triaxial test results in the above mentioned plot, leading to the establishment of the permanent deformation behaviour, depending on stress level [6]. Plastic strain occurs when the stress value crosses a yield stress point. In case of cyclic loading it is a point, in which stress in loading phase crosses the previous stress value during the unloading phase, at the same strain. Fig. 2 presents this relationship.

Fig. 2. A graphical interpretation of yield stress during cyclic loading Rys. 2. Graficzna interpretacja granicy sprężystości podczas obciążenia cyklicznego

2. Material and methods The tests were conducted on soil taken from 1.5m-deep earthwork construction site. On the basis of conducted sieve tests and analysis [PKN-CEN ISO/TS 178924:2009], the sieve curve was estimated. The material was classified as silty clay (siCl), in accordance with PN-EN ISO 14688:2006. Test result is presented in Fig. 3. The UCT tests were performed on specimens prepared in accordance with existing Polish code procedures. Compaction was performed with the use of Proctors method. Compaction of specimens for tests was conducted to obtain 0.59J/cm3 compaction energy in optimal moisture content. Physical properties of silty clay are presented in Table 1.

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Fig. 3. Particle size distribution of tested soil Rys. 3. Krzywa uziarnienia badanego gruntu

Table 1 Physical properties of silty clay/Właściwości fizyczne iłu pylastego. Properties Symbol Value Skeleton density

ρs (g∙cm-3)

2.55

Volume density

-3

ρd (g∙cm )

2.13

Optimum moisture content

wopt (%)

14.0

Liquid limit

LL (%)

27.4

Plasticity limit

PL (%)

12.3

Plasticity index

PI (%)

11.3

After marking material physical properties and preparing the samples, UCT tests were performed. Cylindrical sample used in this study was 14cm high and 7cm in diameter. Samples were loaded to 8kPa and than unloaded to 0.8kPa. Average stress σavg was equal 4.4kPa. The cyclic loading was repeated 200 times with frequency equal 0.1Hz. Sample was prepared in optimal moisture content conditions. Cyclic loading was performed in a one-way manner, which means that the loading phase consisted only of compression. Results were stored in digital form and contain data about applied force and displacement in the load direction.

Plastic strain development during cyclic uniaxial loading of cohesive soil.

3. Results Results of test were presented in Fig. 4 and 5. In Figure 4 plot of stress strain relationship is presented. Black dots represent yield stress during the loading phase. As we can see, with the increase in the yield stress, the increment of plastic strain decreases. Fig. 5 presents a more detailed view of plastic strain development during cyclic loading. .

Fig. 4. Stress-strain relationship obtained from the UCT Rys. 4. Wykres naprężenia do odkształcenia z badania UCT

Increase of accumulated plastic strain seemed to reach constant value around 50th cycle and was equal to εp=0,002% in each cycle. Yield stress also reached steady value around this amount of cycles. As a result of obtaining the data about plastic and elastic strain value in each cycle, the method yield stress point calculation was proposed. In selected cycles, elastic strain was added to a strain at beginning of corresponded cycle. Right yield stress value was later noted and results are presented in Fig. 6 as calculated yield stress and plotted against points of yielding which was presented in Fig. 4. Goal of this comparison is to denote that yield point occur after crossing of criterion presented on Fig.2. Yield stress obtained from calculation is in this case lower than yielding point estimated from test. However, in both cases with the increase of cycle numbers, stress calculated by using elastic strain also increases.

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By assumption that after yielding only plastic strain occurs during loading phase, elastic modulus in loading phase E, plastic modulus in loading phase K and elastic

strain/odkształcenie ε1 [-]

modulus in unloading phase Mr can be distinguished for each cycle. 0,034 0,032 0,03 0,028 0,026 0,024 0,022 0,02

0

1000

2000 time/czas [s]

3000

4000

Fig. 5. Strain-time relationship obtained from the UCT Rys. 5. Zależność odkształcenia i czasu z badania UCT

stress/naprężenie [kPa]

8 7 6 5 4

calculated yield stress/obliczona granica spręzystości

3

estimated yield stress/określona granica sprężystości

2 1 1

10 log of no. of cycle/logarytm z numeru cyklu N[-]

100

Fig. 6. Relationship of yield stress in next cycles estimated and calculated from UCT Rys. 6. Granica sprężystości obliczona i zbadana z badania UCT w kolejnych cyklach

Modulus of elasticity E was calculated as E   Y  r where ΔσY is yield stress and εr is elastic strain obtained as difference between the strain at the end of loading phase and the strain at end of the unloading phase. Modulus of plasticity K was calculated as K   P  p where ΔσP is difference between yield stress and maximal stress in cycle, εp is plastic strain. Mr value is calculated by equation (1). Results of modulus calculations are presented in Fig. 7. All modules increase during subsequent cycles. Resilient modulus at 200th cycle was equal 6.84MPa. Plasticity modulus increase was caused by decreasing of plastic strain and constant value of estimated yield stress.

Plastic strain development during cyclic uniaxial loading of cohesive soil.

89

modulus value/wartość modułu [MPa]

8 7 6 5 4

Mr

3 2

K

1

E

0 1

10 100 log of no. of cycle/logarytm z numeru cyklu N[-]

1000

Fig. 6. Relationship of yield stress in subsequent cycles estimated and calculated from UCT Rys. 6. Granica sprężystości obliczona i zbadana z badania UCT w kolejnych cyklach

4. Conclusions In this article, cyclic uniaxial test results on cohesive soil, silty clay, were presented. Soil sample was loaded 200 times with constant amplitude 7.2kPa and average stress σavg=4.4kPa. Obtained data about strains and stress lead to the following conclusions: 1. Unconfined tests are fast in comparison to triaxial tests, where time needed to obtain fully saturated conditions is much greater. 2. Unconfined tests can be a proper tool for preliminary recognition of soil properties and for testing behaviour of soil in various loading conditions. Obtained data can be used later to program triaxial tests for more sophisticated stress conditions. 3. In this article, yield stress during cyclic loading was examined. Theoretical yield stress points are similar to those obtained by calculation based on experimental results. 4. Plastic modulus of material can be later utilized in a more complex model of plastic strain development during cyclic loading, where function of plastic strain, with a varying number of cycles be replaced by a function of plastic strain with a varying degree of stress or above mentioned modulus K. 5. In the future, the author will perform cyclic triaxial tests on the basis of the UCT results, which could lead to the establishment of interesting relationships with the application of shakedown theory.

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90 BIBLIOGRAPHY

1. Araya A.A.: Characterization of Unbound Granular Materials for Pavements. Doctoral thesis, TU Delft, 2011. 2. Wichtmann, T.: Explicit accumulation model for non-cohesive soils under cyclic loading. Doctoral thesis, Ruhr University Bochum, 2005. 3. Karg, Ch.: Modelling of Strain Accumulation Due to Low Level Vibrations in Granular Soils. Doctoral thesis, Gent University, 2007. 4. Putri, E.E., Rao, N.S.V.K., Mannan, M.A.: Evaluation of the Modulus of Elasticity and Resilient Modulus for Highway Subgrades. Elactronic Journal of Geotechnical Engineering, 15, 1285-1293, 2010. 5. Wiłun, Z.: Zarys Geotechniki. WŁK, Warszawa 2010 6. Werkmeister S.: Permanent deformation behaviour of granular materials and the shakedown theory. Journal of Transportation Research Board nr 1757, 2001,75-81. 7. PN-EN-13286-7:2004 Mieszanki niezwiązane i związane spoiwem hydraulicznym – Część 7: Próba cyklicznego obciążania trójosiowego mieszanek niezwiązanych. 8. PKN-CEN ISO/TS 17892-4:2009 Badania geotechniczne -- Badania laboratoryjne gruntów -- Część 4: Oznaczanie składu granulometrycznego 9. PN-EN ISO 14688: 2a: Projektowanie geotechniczne – Część 1: Rozpoznawanie i badanie podłoża gruntowego. PLASTIC STRAIN DEVELOPMENT DURING CYCLIC UNIAXIAL LOADING OF COHESIVE SOIL Summary In this article, cyclic loading of cohesive soil problem was detailed. Results of the Unconfined Cyclic Test was presented. The aim of article was to present the cyclic loading phenomenon and results of plastic modulus calculation. ROZWÓJ ODKSZTAŁCEŃ PLASYCZNYCH W TRAKCIE CYKLICZNEGO OBCIĄŻANIA GRUNTÓW SPOISTYCH Streszczenie W artykule przedstawiono problem cyklicznego obciążania gruntów spoistych. Zaprezentowano wyniki badania Cyklicznego Jednoosiowego Ściskania. Celem artykułu było zaprezentowanie efektów działania cyklicznego obciążenia na grunt spoisty oraz obliczenie modułu plastyczności na podstawie wyników badań.