applied sciences

Article Undrained Pore Pressure Development on Cohesive Soil in Triaxial Cyclic Loading

Andrzej Głuchowski 1,* , Emil Soból 2 , Alojzy Szyma ´nski 2 and Wojciech Sas 1

1 Water Centre-Laboratory, Faculty of Civil and Environmental Engineering, Warsaw University of Life Sciences-SGGW, 02787 Warsaw, Poland 2 Department of Geotechnical Engineering, Faculty of Civil and Environmental Engineering, Warsaw University of Life Sciences-SGGW, 02787 Warsaw, Poland * Correspondence: [email protected]; Tel.: +48-225-935-405



Received: 5 July 2019; Accepted: 5 September 2019; Published: 12 September 2019


Abstract: Cohesive soils subjected to cyclic loading in undrained conditions respond with pore pressure generation and plastic strain accumulation. The article focus on the pore pressure development of soils tested in isotropic and anisotropic consolidation conditions. Due to the consolidation differences, soil response to cyclic loading is also different. Analysis of the cyclic triaxial test results in terms of pore pressure development produces some indication of the relevant mechanisms at the particulate level. Test results show that the greater susceptibility to accumulate the plastic strain of cohesive soil during cyclic loading is connected with the pore pressure generation pattern. The value of excess pore pressure required to soil sample failure differs as a consequence of different consolidation pressure and anisotropic stress state. Effective stresses and pore pressures are the main factors that govern the soil behavior in undrained conditions. Therefore, the pore pressure generated in the first few cycles plays a key role in the accumulation of plastic strains and constitutes the major amount of excess pore water pressure. Soil samples consolidated in the anisotropic and isotropic stress state behave differently responding differently to cyclic loading. This difference may impact on test results analysis and hence may change the view on soil behavior. The results of tests on isotropically and anisotropically consolidated soil samples are discussed in this paper in order to point out the main features of the cohesive soil behavior.

Keywords: cyclic loading; triaxial test; resilient modulus; undrained conditions; pore pressure; plastic strains

1. Introduction The cyclic loading sources can be distinguished into two categories. The first one is natural sources as ocean waves or earthquake. The second one is the anthropogenic sources. This type of excitation is different because of the loading amplitude and the frequency [1,2]. Cyclic loading can cause rapid failure due to high level repeating stress imposed on the structure or liquefaction when certain soil conditions are met [3,4]. When the load is small enough, the repeating loading can last longer. In that case, the bearing capacity failure will not be reached but excessive settlements can occur [2,5,6]. In this case, post-construction settlements may put out of service further construction. Regarding foundations or road constructions the weakest link is subgrade soils [6]. The traffic loading is a good example of a certain choice, which geotechnical designers need to take [7–9]. When thick embankments are designed, the repeating loading can be transmitted to the subgrade soils, which will result in unknown settlements. The solution to this problem is to increase the embankments thickness and therefore to prevent the cyclic loads to be imposed on the subgrade soils. Nevertheless, this solution generates extra costs to road construction due to longer embankment construction and settlements of subgrade

Appl. Sci. 2019, 9, 3821; doi:10.3390/app9183821 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 3821 2 of 23 soils as a result of static embankment load. What is more, the current practice converts the cyclic and dynamic loads to an equivalent static load, which is combined with the weight of the embankment. The cyclic loading is, therefore, the main reason that impacts the soil respond in such constructions. The traffic engineers have reported long-term cyclic loading settlement effects. The excessive settlements and uneven settlements were the reason for withdrawal from the use of road constructions as well as buildings. Currently, researchers and scholars have focused on road construction problems [2,7–13] as well as on pore pressure development of excess pore water pressure under irregular seismic loading [14,15]. The cyclic loading phenomena were divided into few categories where the attention of researchers is focused. The permanent strain development was studied in order to appoint the threshold stress under which the permanent deformation will stop and the plastic shakedown will occur [2,7,8]. The second main focus subject is pore pressure development during undrained cyclic loading. The pore pressure generation models were developed in order to characterize the soil respond under seismic loading based on the damage concept [15,16]. Extensive studies have been devoted to the coarse-grained soils in unsaturated conditions [17,18] among which most recent studies concentrate on the effect of strain localization on the response of granular materials with geostatistical analysis [19,20]. Last decade brought attention to cohesive soils tested in drained and undrained conditions. The test results have shown non-cohesive soils’ different responses to cyclic loading [21–24]. The cohesive soil loaded by long-term cyclic loading, which will not lead to cyclic failure, will suffer the irrecoverable strains and permanent pore pressure [23,25–27]. The cohesive soil tested with the use of cyclic triaxial test apparatus was mostly the isotropically consolidated one [27–32]. The soil in natural conditions is the anisotropic stress state and therefore, the consolidation should be conducted in the K0 stress state. The soil response is also different when the isotropic and anisotropic condition is applied. The aim of this paper is to capture the difference between cohesive soils consolidated in isotropic and anisotropic stress conditions. Previous studies on the cohesive soil in undrained conditions, which was isotropically consolidated, have shown a rapid increase of pore pressure in the early stage of cyclic loading [33–35]. The long term cyclic loading has shown, that the axial strain tends to stabilize, which gives time to stabilization of pore pressure. The mean effective stress in cyclic loading decreases because of pore pressure development. Nevertheless, when the cyclic loading is low enough the stress path never will reach the critical state line and the failure of the soil is not observed. The development of permanent strain increases nonlinearly but is very similar under different confining pressures and different cyclic deviator stress conditions [36]. The centrifuge tests on a shallow skirted foundation in normally consolidated kaolin clay have shown that two-way cyclic loading in average compression leads to continuous accumulation of the foundation settlement. The mode of failure for a skirted foundation under two-way vertical cyclic loading depends rather on the average vertical stress than on the maximal vertical stress [37]. The K0-consolidated marine natural soft clays were tested by Sun et al. [38]. The conducted cyclic triaxial tests were followed by monotonic loading in undrained conditions. The aim of this work was to study the accumulative behavior, as well as the influence of the frequency of cyclic loading. The results of the tests have shown that under a certain increase of the applied cyclic deviator stress level, the initial excess pore water pressure also increases in the first cycle. The pore pressure will then develop with further cycles and will decrease at failure. The soil response to cyclic loading in regards to plastic strain accumulation shows that under a certain level of loading the deformation of soft clay increases slowly and the plastic strain rate stabilizes after numerous cycles at a small value. The increase of the deviator stress is triggering the failure mechanism, which occurs with extensive plastic strain and the soil collapses abruptly. The authors reported that the reason for such a phenomenon in the great value of stress reversal during cyclic loading. This behavior was not observed in isotropically consolidated samples. The post–cyclic loading of cohesive soils have shown the reduction of soil undrained shear strength in Appl. Sci. 2019, 9, 3821 3 of 23 comparison to monotonic tests. The reduction was between 0.98 to 0.66. The greatest reduction of undrained shear strength was observed in the case of samples, which exhibited the greatest excess pore water pressure increase in relation to initial mean effective stress p00. The conclusion is that the soft clay responds to cyclic loading in a similar manner in terms of plastic strains, which gradually decreases with an increasing number of cycles. The cyclic confining pressure was recognized as a significant factor that affects the permanent strain accumulation. In the case of compacted cohesive soils, their response to cyclic loading should be also analyzed in a matter of specific values such as the cyclic deviator stress level and type, soil type, specific test conditions, and consolidation pressure and consolidation history. The primary objective of this study is to present the differences between isotropic and anisotropic consolidation in response to cyclic loading. The cohesive soil response to cyclic loading is analyzed in terms of excess pore pressure development and permanent strain accumulation.

2. Materials and Methods

2.1. Soil Index Properties The cohesive soil in this study was taken from a road construction site. The cohesive soil tested in this study is typical soil, which represents primary deposits, left behind by a glacier. This type of glacial till is common for the northern and central part of Poland. The clay was recognized as one of the problematic soils due to low permeability and low bearing capacity. The soil has a brown color and is characterized by heterogenic soil diameter distribution with a dominant fraction 0.05–0.1 mm [39]. The soil is normally consolidated and often natural moisture content places it in soft rarely firm consistency. This type of soil has also a low plasticity index (10% < IP < 30%). The soil in the natural state has low to medium strength (undrained strength cu in the range 20 to 60 kPa) based on CPT (Cone Penetration Test) and DMT (Dilatometer Test) tests [40]. The index properties were established including the soil grain composition, Atterberg limits, and optimal moisture content. The results of the tests present in Table1. The cohesive soil was recognized based on the Eurocode 7 [ 41,42] classification as sandy silty clay (sasiCl).

Table 1. Index properties of tested sandy silty clay.

Index Properties Value 3 Specific gravity, Gs (g/cm ) 2.67 Optimal moisture content, wopt (%) 12.3 3 Maximal dry density, ρd max (g/cm ) 1.96 Liquid limit, wL (%) 42.0 Plasticity index, IP (%) 18.4 Clay fraction, fCl (%) 19 Silt fraction, fSi (%) 41 Sand fraction, fSa (%) 40

2.2. Monotonic Triaxial Tests Figure1 presents the result of monotonic triaxial tests with di fferent confining pressures. The parameters on the figures are the deviator stress q = σ σ , mean effective stress p = 01 − 03 0 (σ01 + 2σ03)/3, axial vertical strain ε1, and excess pore water pressure ∆u. On Figure1a the e ffective stress paths on the p0–q plane are presented. The slope of the critical state line (CSL) is given as M = 1.33. The monotonic triaxial tests results indicate the typical compacted soil behavior. This type of soil response can be called quasi-overconsolidated due to the reverse curvature of the stress path. The failure points were estimated based on the intersection between the stress path and the CSL. The deviator stress at failure qmax was 46.04, 93.66, and 153.55 kPa for confining pressures of 45, 90, and 135 kPa respectively. The pore pressure presented in Figure1c shows peak values of the pore pressure and therefore indicates the maximum axial strain ε1, max achieved by sample when failure Appl. Sci. 2019, 9, 3821 4 of 23

Appl. Sci. 2019, 9, x 4 of 23 occurredvalue the of ε value1, max was of 1.102%,ε1, max was2.277%, 1.102%, and 3.439% 2.277%, and and the maximal 3.439% andexcess the pore maximal water pressure excess Δ poreu was water pressure27.39,∆ u47.83,was and 27.39, 71.32 47.83, kPa andfor confining 71.32 kPa pressure for confining 45, 90, and pressure 135 kPa 45, respectively. 90, and 135 kPa respectively.

180 180 45 kPa 160 90 kPa 160 140 135 kPa 140

120 120 M = 1.33 100 100 1 80 80

deviator stress q (kPa) q stress deviator 60 60 deviator stress q (kPa) q stress deviator 40 40 45 kPa 90 kPa 20 20 135 kPa 0 0 0 50 100 150 02468 mean effective stress p' (kPa) axial strain ε (%) 1 (a) (b) 80

70 (kPa)

Δu 60

50

40

30

20 excess pore water pressure excess pore water 10 45 kPa 90 kPa 135 kPa 0 02468 ε axial strain 1 (%) (c)

FigureFigure 1. Results 1. Results of theof the static static triaxial triaxial test for for sandy sandy silty silty clay clay under under confining confining pressure pressure of 45 kPa, of 4590 kPa, 90 kPa,kPa, and and 135 135 kPa kPa and and under under thethe isotropicisotropic consolidation: (a ()a The) The deviator deviator stress–mean stress–mean effective effective stress stress relationship,relationship, (b) deviator (b) deviator stress–vertical stress–vertical strain strain relationship, relationship, and and (c ()c )excess excess pore pore water water pressure pressure versus versus verticalvertical strain strain characteristic. characteristic.

2.3. Soil2.3. Sample Soil Sample Properties, Properties, Preparation, Preparation, and and Origin Origin. The soilThe insoil this in studythis study was was taken taken from from a road a road construction construction site site placed placed inin Warsaw.Warsaw. The depth of of soil soil deposition was at 1 m below the ground and the soils were classified as Pleistocene moraine deposition was at 1 m below the ground and the soils were classified as Pleistocene moraine deposits deposits of the Warta Glaciation. of the Warta Glaciation. The soil was stored and dried. The soil past used for sample preparation was in optimal moisture Thecontent soil conditions was stored and and the dried. soil was The then soil pastcompacted used for with sample respect preparation to the Proctor was method in optimal [43]. moistureThe contentenergy conditions of compaction and the was soil wasequal then to 0.59 compacted J/cm3. The with soil respect paste was to the compacted Proctormethod in a scaled [43 ].two-part The energy of compactionaluminum wasmold equal with the to 0.59 dimensions J/cm3. Theof a triaxial soil paste soil wassample compacted (7 cm diameter in a scaled and 14 two-part cm height). aluminum The moldsandy with thesilty dimensions clay sample ofproperties a triaxial in soilthis samplestudy are (7 presented cm diameter in Table and 2. 14 The cm initial height). void Theratio sandye0 was silty clay sampleconstant properties during the inundrained this study cyclic are triaxial presented test and in Tablewas in2 .the The range initial between void ratio0.333 toe0 0.414.was constantThe duringinitial the undraineddensity ρd of cyclic tested triaxial soils was test in and the range was in of the 1.89 range to 2.10 between g/cm3. 0.333 to 0.414. The initial density 3 ρd of tested soils was in the range of 1.89 to 2.10 g/cm . Table 2. The cyclic triaxial test soil sample index properties.

Index PropertiesTable 2. The cyclic 1.1 triaxial1.2 test1.3 soil sample2.1 index2.2 properties.2.3 2.4 2.5 Moisture content, w (%) 14.75 12.62 14.33 12.34 11.14 12.66 6.07 9.38 Index Properties 1.1 1.2 1.3 2.1 2.2 2.3 2.4 2.5 Dry density, ρd (g/cm3) 1.89 1.95 1.89 1.96 1.92 1.94 2.10 1.91 MoistureVoid content, ratio, we0 (%)(−) 14.75 0.414 12.620.345 14.330.412 0.333 12.34 0.399 11.14 0.379 12.66 0.276 6.070.400 9.38 3 Dry density, ρd (g/cm ) 1.89 1.95 1.89 1.96 1.92 1.94 2.10 1.91 Void ratio, e ( ) 0.414 0.345 0.412 0.333 0.399 0.379 0.276 0.400 0 − Appl. Sci. 2019, 9, 3821 5 of 23

2.4. Test Procedure The compacted soil was installed in triaxial apparatus and the saturation process had started. This stage of the triaxial test was performed so full saturation conditions can be achieved. The saturation step was terminated when the Skempton parameter B was equal to 0.95, which has been assumed from a technical point of view and indicates full near saturation conditions. The second stage was consolidation. The consolidation was conducted in isotropic and anisotropic stress (K0-consolidation) conditions. For isotropic consolidation, the stress in cell pressure remained constant and the leakage of pore water pressure was measured. The isotropic consolidation was stopped when the pore water pressure effluent was less than 5 mm3 per five minutes. The anisotropic consolidation set up was designed to achieve pointed effective stress of consolidation σ0k0. The sample was loaded by the deviator stress q and the radial stress during the K0 consolidation was automatically controlled by the triaxial equipment system. The cell pressure compensated the effect of deviator stress loading. After the consolidation step, the cyclic loading test was conducted. The cyclic deviator stress components were the maximal and minimal deviator stress denoted as qmax and qmin respectively and two supplemental values of the cyclic deviator stress: Deviator stress amplitude qa and deviator stress median qm. The cyclic triaxial test program presents Table3. The soil specimens were tested in the constant frequency of loading equal to 1 Hz. The loading wave-form was the semi-sin wave type. The number of cycles was from 10,000 to 50,000 cycles. The tests were conducted in different effective confining pressure levels. The cyclic stress ratio is taken as the ratio of the maximum cyclic deviator stress qmax to the initial effective confining pressure σ03.

Table 3. The cyclic triaxial test program.

Stress Component 1.1 1.2 1.3 2.1 2.2 2.3 2.4 2.5

Maximal deviator stress, qmax (kPa) 43.6 46.0 43.2 117.3 100.9 101.5 169.9 79.6 Minimal deviator stress, qmin (kPa) 35.4 37.0 35.2 96.0 74.0 80.7 138.3 53.1 Deviator stress median, qm (kPa) 39.5 41.5 39.2 106.7 87.5 91.1 154.1 66.4 Deviator stress amplitude, qa (kPa) 4.1 4.5 4.0 10.7 13.5 10.4 15.8 13.3 Effective confining pressure, σ03 (kPa) 45.0 90.0 135.0 65.0 125.0 139.7 94.2 44.9 Cyclic stress ratio, CSR ( ) 0.484 0.256 0.160 0.902 0.403 0.363 0.901 0.886 −

The test equipment was the cyclic triaxial apparatus—an electrodynamical system produced by GDS Instruments. The cyclic load was applied by the servo-loading system. The pressures in this study were applied by the oil pressure system. This kind of triaxial apparatus was equipped with a real-time data acquisition system, which enables long term cyclic loading.

3. Results and Discussion Test results were discussed separately in order to explain the phenomena that occurred during cyclic loading. The discussion concerns the pore pressure behavior, axial strain accumulation, the deviator stress–axial strain characteristics, and the stress paths. The second part of this chapter will discuss the comparison between the isotropic and anisotropically (K0) consolidated samples.

3.1. Isotropically and K0 Consolidated Samples Test Results On Figure2 the undrained cyclic triaxial test results for sample 1.1 are presented. The isotropic confining pressure was equal to 45 kPa. The soil sample was loaded with the deviator stress q, which their components were as follows qm = 39.5 kPa and qa = 4.1 kPa. The soil response to such a loading program could be divided into three stages. The first one is the first loading cycle. In this stage, the soil is accumulating a high amount of permanent strain, which is accompanied by a high generation of excess pore water pressure. The stress path (Figure2e) rises to planned deviator stress level and mean effective stress p0 starts to move towards the deviator stress axis, which indicates a decrease of radial stress due to the mobilization of excess pore water pressure. Appl. Sci. 2019, 9, 3821 6 of 23 Appl. Sci. 2019, 9, x 6 of 23

(a) (b)

(c) (d)

(e) Figure 2.FigureResults 2. Results of the ofcyclic the cyclic triaxial triaxial test test for forsandy sandy silty silty clay clay under under a confining a confining pressure pressure of 45 kPa of 45 kPa and under the isotropic consolidation, initial void ratio e0 = 0.414—sample 1.1: (a) Excess pore water and under the isotropic consolidation, initial void ratio e0 = 0.414—sample 1.1: (a) Excess pore water pressurepressure versus verticalversus vertical strain characteristic,strain characteristic, (b) excess (b) excess pore pore water water pressure pressure characteristic characteristic versus versus number number of cycles, (c) vertical strain characteristic versus number of cycles, (d) deviator stress–vertical of cycles, (c) vertical strain characteristic versus number of cycles, (d) deviator stress–vertical strain strain relationship, and (e) the deviator stress–mean effective stress relationship (red color—last 10 relationship,cycles; andarrow (e color—violet:) the deviator Saturati stress–meanon phase, green: effective Consolidation stress relationship phase, orange: (red First color—last cycle of cyclic 10 cycles; arrow color—violet:loading, blue: Cyclic Saturation loading phase, program). green: Consolidation phase, orange: First cycle of cyclic loading, blue: Cyclic loading program). After the first cycle, the second type of soil response began. The pore pressure rose to a local Aftermaximal the first value cycle, equal theto around second 17 kPa type in ofthe soil 4th responsecycle (Figure began. 1a) and The then poredropped pressure to 15 kPa rose in the to a local maximal11th value cycle. equal After tothis around circumstance, 17 kPa the in pore the pressu 4th cyclere rose (Figure with decreasing1a) and thenincrement. dropped During to this 15 kPa in phase, the permanent strains were also accumulated. This phase ended around the 350th cycle. In the the 11th cycle. After this circumstance, the pore pressure rose with decreasing increment. During first cycle phase and in the second one, most of the permanent strains occurred. The excess pore this phase,pressure the permanentreached most strainsof its value were in these also accumulated.two stages. This phase ended around the 350th cycle. In the first cycleThe second phase phase and in characterized the second with one, decreasing most of the strain permanent and excess strains pore water occurred. pressure The value excess pore pressureincrement. reached mostNevertheless, of its value permanent in these strain two accumu stages.lation and the pore pressure build-up process Thedependence second phase are more characterized complex and needs with to decreasing be investigated strain further. and This excess can be pore easily water noticed pressure by the value increment.Figure Nevertheless, 2b,c analysis. Strain permanent accumulation strain lasted accumulation longer than andthe pore the pressure pore pressure build up build-upor the pore process dependence are more complex and needs to be investigated further. This can be easily noticed by the Figure2b,c analysis. Strain accumulation lasted longer than the pore pressure build up or the pore pressure increment slowed down faster than permanent strain accumulation. On Figure2a after the local minimum, stabilization of the pore pressure increase was observed to a certain point. When axial Appl. Sci. 2019, 9, 3821 7 of 23

strain reachedAppl. Sci. a value2019, 9, xof approximately 0.5% (about the 350th cycle), the pore pressure7 increment of 23 had a constant value when related to the axial strain. pressure increment slowed down faster than permanent strain accumulation. On Figure 2a after the The lastlocal phase minimum, was stabilization the long term of the loading pore pressure phase. increase In this was stage, observed the to pore a certain pressure, point. When as well as the permanentaxial strain, strain rose reached with a constant value of increment.approximately The 0.5% soil (about reached the 350th a stable cycle), response the pore topressure cyclic loading. In this study,increment 20,000 had cycles a constant were value applied. when related The excess to the axial pore strain. water pressure was rising slightly between The last phase was the long term loading phase. In this stage, the pore pressure, as well as the cycle 350 and the last cycle. permanent strain, rose with constant increment. The soil reached a stable response to cyclic loading. The cyclicIn this study, triaxial 20,000 test cycles results werein applied. isotropic The excess consolidation pore water pr conditionsessure was rising where slightly eff betweenective confining pressure wascycleequal 350 and to the 90 last kPa cycle. present in Figure3. The soil in this test had initially the void ratio equal to 0.345,The which cyclic represents triaxial test aresults more in compacted isotropic consolidation sample in conditions comparison where to effective the previous confining test sample. pressure was equal to 90 kPa present in Figure 3. The soil in this test had initially the void ratio equal The cyclic loading performed as well as in the previous test high pore pressure and permanent strain to 0.345, which represents a more compacted sample in comparison to the previous test sample. The accumulationcyclic in loading the first performed cycle. as Nevertheless, well as in the previous excess test pore high water pore pressure pressure andreached permanent roughly strain 11 kPa (17 kPa inaccumulation the previous in the test). first Unlike cycle. Nevertheless, the previous excess test pore the water axial pressure strain reached increment roughly was 11 kPa greater (17 than in the previouskPa stepin the (0.65% previous in test). test Unlike 1.2 and the previous 0.16% in test test the 1.1).axial strain This increment difference was was greater clearly than in caused the by the previous step (0.65% in test 1.2 and 0.16% in test 1.1). This difference was clearly caused by the difference between the initial void ratio and in the radial effective confining pressure. In the second difference between the initial void ratio and in the radial effective confining pressure. In the second stage of loading,stage of loading, the pore the pressure pore pressure rose rose in ain greatera greater amountamount than than in the in theprevious previous test. test.

(a) (b)

(c) (d)

(e)

Figure 3. Results of the cyclic triaxial test for sandy silty clay under a confining pressure of 90 kPa

and under the isotropic consolidation, initial void ratio e0 = 0.345—sample 1.2: (a) Excess pore water pressure versus vertical strain characteristic, (b) excess pore water pressure characteristic versus number of cycles, (c) vertical strain characteristic versus number of cycle, (d) deviator stress–vertical strain relationship, and (e) the deviator stress–mean effective stress relationship (red color—last 10 cycles; arrow color—violet: Saturation phase, green: Consolidation phase, orange: First cycle of cyclic loading, blue: Cyclic loading program). Appl. Sci. 2019, 9, x 8 of 23

Figure 3. Results of the cyclic triaxial test for sandy silty clay under a confining pressure of 90 kPa and under the isotropic consolidation, initial void ratio e0 = 0.345—sample 1.2: (a) Excess pore water pressure versus vertical strain characteristic, (b) excess pore water pressure characteristic versus number of cycles, (c) vertical strain characteristic versus number of cycle, (d) deviator stress–vertical strain relationship, and (e) the deviator stress–mean effective stress relationship (red color—last 10

Appl. Sci.cycles;2019 ,arrow9, 3821 color—violet: Saturation phase, green: Consolidation phase, orange: First cycle of cyclic8 of 23 loading, blue: Cyclic loading program).

FigureFigure4 4 presents presents test results for for the the soil soil sample sample under under a confining a confining pressure pressure equal equal to 135 to 135 kPa kPa and andan initial an initial void voidratio ratioe0 equale0 equal to 0.412. to 0.412. In the Infirst the cycle first stage, cycle stage,the soil the response soil response was stiffer was stithanffer in than test in1.2 test but 1.2pore but pressure pore pressure rose to 11.5 rose kPa, to 11.5 which kPa, was which close was to the close response to the responseobserved observedin test 1.2. inThe test same 1.2. Theconclusion same conclusion could be formed, could be when formed, the whenexcess the pore excess water pore pressure water pressureversus axial versus strain axial plots strain (Figures plots (Figures3a and 4a)3a andwere4a) compared. were compared.

(a) (b)

(c) (d)

(e)

FigureFigure 4. ResultsResults of of the the cyclic cyclic triaxial triaxial test test for for sandy sandy silty silty clay clay under under confining confining pressure pressure of 135 of 135kPa kPaand

andunder under the theisotropic isotropic consolidation, consolidation, initial initial void void ratio ratio e0e 0= =0.412—sample0.412—sample 1.3: 1.3: (a (a) )Excess Excess pore waterwater pressurepressure versusversus vertical vertical strain strain characteristic, characteristic, (b) excess(b) excess pore waterpore water pressure pressure characteristic characteristic versus number versus ofnumber cycles, of (c cycles,) vertical (c) strainvertical characteristic strain characteristic versus numberversus number of cycle, of ( dcycle,) deviator (d) deviator stress–vertical stress–vertical strain relationship, and (e) the deviator stress–mean effective stress relationship (red color—last 10 cycles; arrow color—violet: Saturation phase, green: Consolidation phase, orange: First cycle of cyclic loading, blue: Cyclic loading program).

In the second stage of the soil response, the pore pressure rose as well as the axial strain in the same pattern. The permanent strain accumulation to ∆u characteristics was almost linear in both cases, Appl. Sci. 2019, 9, 3821 9 of 23 which means, that for the same amount of pore pressure increment, the same amount of accumulated plastic strain was observed. Nevertheless, the magnitude of this phenomenon was different in each stage. In both cases, the limit between the second and third stage of the soil response could not be distinguished. The excess pore water pressure level and its increment rise with initial effective confining pressure growth. The stress paths in all cases moved towards the deviator stress axis, which indicates undrained conditions. On Figures5–9, results of the cyclic triaxial test in K0 consolidation conditions are presented. The soil response to cyclic loading differed when compared to previous tests. The excess pore water pressure in test 2.1 rose rapidly, which was accompanied by moderate axial strain accumulation. When the ∆u increment started to decrease, the permanent axial strain began to develop. That process of the soil reaction to cyclic loading indicates that the pore pressure triggered plastic strain accumulation. This was true since the excess pore pressure decreased the effective stress in the soil skeleton and therefore is weakening the soil contacts. During test 2.1 excess pore water pressure reached a maximum value equal to 35 kPa after around 2500 cycles of loading and then slowly decreased to 33 kPa after 3000 cycles. The excess pore water pressure remained after the previous event at a constant level and equaled 32 kPa up to 33 kPa. The soil response can be divided into two stages, the pre-maximal excess pore water pressure stage, where rapid pore pressure generation and permanent strain accumulation was observed, and the second stage—the post-maximal pore pressure stage where permanent axial strains suddenly stopped and pore pressure decreased to a constant level. It is clear that the decrease of pore pressure would result in an increase of effective mean stress and therefore would increase the soil stiffness and the permanent strain accumulation would rapidly decrease. The reason for this phenomenon is the critical soil state, which was achieved during the first part of cyclic loading. The soil accumulated 4% of axial permanent strain during the first 2500 cycles of loading. The pore water pressure development has led to soil failure. After the failure, the pore pressure dropped and therefore, the soil was able to sustain further loading. Furthermore, almost a constant high level of pore water pressure was observed, which was accompanied by a slight permanent strain accumulation. Figure5e presents the abovementioned behavior. The stress paths moved towards the deviator stress axis and when the stress state reached the soil critical state, pore pressure decreased, and the stress path turned around. On Figure6 triaxial test results on the K0 consolidated sandy silty clay sample is presented. The K0 stress state was equal to 0.71, which was close to the previous K0 stress state for sample 2.1, which was equal to 0.67. The initial void ratio in the case of sample 2.2 was around 0.07 greater than in the case of the 2.1 sample and was equal to 0.399. The type of loading in this study was a sin wave as in previous cases but it was performed in another manner. The soil was loaded with the deviator stress, which was oscillating around the point where the consolidation phase was terminated (qm was on the deviator stress level reached after K0 consolidation). For example, the 2.1 test was performed in such a manner where the minimum deviator stress qmin was on the deviator stress level after consolidation. In the first cycles, negative excess pore water pressure was observed. After 10,000 cycles the excess pore pressure had raised to 30 kPa. The pore water pressure was building up with a decrease of its increment. This type of soil response caused almost no plastic strains (0.134% after 10,000 cycles). It seems that the type of loading has a great impact on the K0 consolidation samples response. The soil in which the negative pressure occurred would suffer much lesser plastic strains. This was a result of another pore pressure generation model. In the previous tests of isotropically consolidated samples, the pore pressure rose rapidly in the first few cycles, this was accompanied by plastic strain accumulation. Sample 2.1. also generated excess pore water pressure but was much faster than in the case of sample 2.2, which was the reason why the plastic strains were accumulated with a much slower rate. Appl. Sci. 2019, 9, x 10 of 23 case of sample 2.2, which was the reason why the plastic strains were accumulated with a much Appl. Sci. 2019, 9, 3821 10 of 23 slower rate.

(a) (b)

(c) (d)

(e)

Figure 5. Results ofof thethe cycliccyclic triaxial triaxial test test for for sandy sandy silty silty clay clay under under a confining a confining pressure pressure of 65 of kPa 65 andkPa underand under the K the0 consolidation, K0 consolidation, initial initial void void ratio ratioe0 = e00.333, = 0.333,K 0K=0 =0.67—sample 0.67—sample 2.1: 2.1: ((aa)) ExcessExcess pore water pressure versusversus vertical vertical strain strain characteristic, characteristic, (b) excess(b) excess pore waterpore water pressure pressure characteristic characteristic versus number versus ofnumber cycles, of ( ccycles,) vertical (c) vertical strain characteristic strain characteristic versus numberversus number of cycle, of ( dcycle,) deviator (d) deviator stress–vertical stress–vertical strain relationship,strain relationship, and (e )and the ( deviatore) the deviator stress–mean stress–mean effective effective stress relationshipstress relationship (red color—last (red color—last 10 cycles; 10 arrowcycles; color—violet:arrow color—violet: Saturation Satura phase,tion green: phase, Consolidation green: Consolidatio phase, blue:n phase, Cyclic blue: loading Cyclic program). loading program). A similar response to cyclic loading can be observed in test 2.5 where the sample was consolidated to σ0A3 equalsimilar to response 44.9 kPa. to The cyclic soil loading was loaded can withbe observed 13.3 kPa in deviator test 2.5 stress where amplitude the sample and was the excessconsolidated plastic to strain σ’3 equal was to observed. 44.9 kPa.The The poresoil was pressure, loaded in with this 13.3 case, kPa had deviator not reached stress maximal amplitude value, and whichthe excess indicates plastic nostrain failure was inobserved. this test. The The pore soil pres tendedsure, in to this stabilize case, had its not response reached to maximal cyclic loading. value, Thewhich pore indicates pressure no after failure 5000 in cyclesthis test. increased The soil at tend a slowered to ratestabilize and plasticits response strain to as cyclic well accumulatedloading. The withpore apressure decreasing after rate. 5000 The cycles excess increased pore water at a slower pressure rate had and greater plastic amplitude strain as well than accumulated in test 2.1 but with this phenomenona decreasing wasrate. caused The excess by greater pore deviatorwater pressure stress amplitude had greaterqa. Samplesamplitude 2.3 than and 2.4in (testFigures 2.1 7but and this8 ) σ werephenomenon consolidated was incaused K0 stress by greater conditions deviator and withstress a confiningamplitude pressure qa. Samples03 equal 2.3 and to 139.72.4 (Figures and 94.2 7 and kPa respectively. The pore pressure response to cyclic loading in the case of sample 2.3 (qa equal to 10.4 kPa) Appl. Sci. 2019, 9, x 11 of 23

Appl. Sci. 2019, 9, 3821 11 of 23 8) were consolidated in K0 stress conditions and with a confining pressure σ’3 equal to 139.7 and 94.2 kPa respectively. The pore pressure response to cyclic loading in the case of sample 2.3 (qa equal to was10.4 higherkPa) was than higher in the casethan ofin sample the case 2.4 of (qa sampleequal to 2.4 15.8 (q kPa).a equal The to cause 15.8 ofkPa). this The phenomenon cause of wasthis thephenomenon lower initial was void the lower ratio einitial0 in the void case ratio of samplee0 in the 2.4case (e of0 = sample0.276) 2.4 than (e0 in= 0.276) sample than 2.3 in (e sample0 = 0.379). 2.3 The(e0 = greater 0.379). density The greater of sample density 2.4 resulted of sample in lower 2.4 poreresulted pressure in lower generation. pore pressure Nevertheless, generation. plastic strainNevertheless, accumulated plastic in strain sample accumulated 2.4 with a higher in sample rate 2.4 than with in sample a higher 2.3. rate In than sample in sample 2.2 (on 2.3. Figure In sample6 with e2.20 = (on0.399 Figureσ03 = 6 125.0with kPa,e0 = 0.399 and qσa’3= =13.5 125.0 kPa), kPa, the and plastic qa = 13.5 strain kPa), accumulation the plastic strain was close accumulation to what could was beclose observed to what in could the case be observed of sample in 2.3. the case of sample 2.3.

(a) (b)

(c) (d)

(e)

Figure 6.6. Results ofof thethe cyclic cyclic triaxial triaxial test test for for sandy sandy silty silty clay clay under under a confining a confining pressure pressure of 125 of kPa125 andkPa underand under the K the0 consolidation, K0 consolidation, initial initial void void ratio ratioe0 = e00.399, = 0.399,K 0K=0 =0.71—sample 0.71—sample 2.2: 2.2: ((aa)) ExcessExcess porepore water pressure versusversus vertical vertical strain strain characteristic, characteristic, (b) excess(b) excess pore waterpore water pressure pressure characteristic characteristic versus number versus ofnumber cycles, of ( ccycles,) vertical (c) strainvertical characteristic strain characteristic versus numberversus number of cycles, of cycles, (d) deviator (d) deviator stress–vertical stress–vertical strain relationship,strain relationship, and (e )and the ( deviatore) the deviator stress–mean stress–mean effective effective stress relationshipstress relationship (red color—last (red color—last 10 cycles; 10 arrowcycles; color—violet:arrow color—violet: Saturation Satura phase,tion green: phase, Consolidation green: Consolidatio phase, blue:n phase, Cyclic blue: loading Cyclic program). loading program). Appl. Sci. 2019, 9, 3821 12 of 23 Appl. Sci. 2019, 9, x 12 of 23

(a) (b)

(c) (d)

(e)

Figure 7. Results of the cyclic triaxial test for sandy s siltyilty clay under a confining confining pressure of 139.7 kPa and under the KK00 consolidation, initialinitial voidvoid ratioratioe e00 == 0.379, K0 == 0.67—sample0.67—sample 2.3: 2.3: ( (aa)) Excess Excess pore pore water water pressure versusversus vertical vertical strain strain characteristic, characteristic, (b) excess(b) excess pore waterpore water pressure pressure characteristic characteristic versus number versus numberof cycles, of ( ccycles,) vertical (c) vertical strain characteristic strain characteristic versus numberversus number of cycles, of cycles, (d) deviator (d) deviator stress–vertical stress–vertical strain strainrelationship, relationship, and (e )and the ( deviatore) the deviator stress–mean stress–mean effective effective stress relationshipstress relationship (red color—last (red color—last 10 cycles; 10 cycles;arrow color—violet:arrow color—violet: Saturation Satura phase,tion green: phase, Consolidation green: Consolidatio phase, blue:n phase, Cyclic blue: loading Cyclic program). loading program). The axial strain, which was measured in this study, could be divided into two categories based on the plasticThe axial strain strain, accumulation which was rate. measured The first in onethis isstudy, steady could exponential be divided growth into two in which, categories the plasticbased onstrain the incrementplastic strain decreases accumulation with each rate. cycle. The first In thisone case,is steady the soilexponential might su growthffer extensive in which, deformation the plastic straindue to increment accumulated decreases plastic with strains each after cycle. numerous In this case, cycles. the soil This might type ofsuffer response extensive was deformation observed in duesamples to accumulated 2.2, 2.3, and 2.4plastic. The strains second after type numerous of plastic straincycles. development This type of representsresponse was samples observed 2.1 and in samples2.5 where 2.2, the 2.3, extensive and 2.4. plastic The second strain wastype accumulatedof plastic strain in thedevelopment first phase represents of cyclic loading samples due 2.1 to and the 2.5imposed where high the extensive value of the plastic deviator strain stress. was accumulate After a fewd thousandsin the first repetitions,phase of cyclic the steadyloading response due to the of imposedthe cohesive high soil value was of observed, the deviator which stress. characterized After a few the thousands lower rate repetitions, of plastic strain the steady accumulation. response of the cohesive soil was observed, which characterized the lower rate of plastic strain accumulation. Appl. Sci. 2019, 9, 3821 13 of 23 Appl. Sci. 2019, 9, x 13 of 23

(a) (b)

(c) (d)

(e)

Figure 8. Results ofof thethe cycliccyclic triaxial triaxial test test for for sandy sandy silty silty clay clay under under a confining a confining pressure pressure of 94.2 of 94.2 kPa kPa and andunder under the Kthe0 consolidation, K0 consolidation, initial initial void void ratio ratioe0 =e0 0.276,= 0.276,K 0K=0 =1.07—sample 1.07—sample2.4: 2.4: ((aa)) ExcessExcess pore water pressure versusversus vertical vertical strain strain characteristic, characteristic, (b) excess(b) excess pore waterpore water pressure pressure characteristic characteristic versus number versus numberof cycles, of ( ccycles,) vertical (c) vertical strain characteristic strain characteristic versus numberversus number of cycles, of cycles, (d) deviator (d) deviator stress–vertical stress–vertical strain strainrelationship, relationship, and (e )and the ( deviatore) the deviator stress–mean stress–mean effective effective stress relationshipstress relationship (red color—last (red color—last 10 cycles; 10 cycles;arrow color—violet:arrow color—violet: Saturation Saturati phase,on green:phase, Consolidation green: Consolidation phase, orange: phase, orange: First cycle First of cycliccycle of loading, cyclic loading,blue: Cyclic blue: loading Cyclic program).loading program).

The pore pressure response to cyclic loading was also influenced influenced by by the the deviator deviator stress stress value. value. The samplessamples thatthat failedfailed or or were were close close to to failing failing (2.1 (2 and.1 and 2.5) 2.5) generated generated higher higher pore pore pressure pressure in the in firstthe first2000 2000 cycles cycles than than the other the other three threeK0-consolidated K0-consolidated samples. samples. Nevertheless, Nevertheless, here here could could be also be also seen seen that thatafter after reaching reaching maximum maximum value value by excess by excess pore waterpore water pressure pressure the increment the increment was much was lower much than lower in thansamples in samples 2.2 to 2.4. 2.2 to 2.4. Appl. Sci. Sci. 20192019,, 99,, x 3821 1414 of of 23 23

(a) (b)

(c) (d)

(e)

FigureFigure 9. ResultsResults of the cycliccyclic triaxialtriaxial test test for for sandy sandy silty silty clay clay under under a confininga confining pressure pressure of 44.9 of 44.9 kPa kPa and andunder under the Kthe0 consolidation, K0 consolidation, initial initial void void ratio ratioe0 =e0 0.400,= 0.400,K 0K0= =1.00—sample 1.00—sample 2.5:2.5: (a) Excess pore pore water water pressure versusversus vertical vertical strain strain characteristic, characteristic, (b) excess(b) excess pore pore water water pressure pressure characteristic characteristic versus numberversus numberof cycles, of ( ccycles,) vertical (c) vertical strain characteristic strain characteristic versus versus number number of cycles, of cycles, (d) deviator (d) deviator stress–vertical stress–vertical strain strainrelationship, relationship, and (e and) the (e deviator) the deviator stress–mean stress–mean effective effective stress relationshipstress relationship (red color—last (red color—last 10 cycles; 10 cycles;arrow color—violet:arrow color—violet: Saturation Satura phase,tion green: phase, Consolidation green: Consolidatio phase, blue:n phase, Cyclic blue: loading Cyclic program). loading program). 3.2. The Effect of Consolidation on the Soil Response to Cyclic Loading 3.2. TheFor Effect the purposeof Consolidation of establishing on the Soil the Response difference to Cyclic between Loading the soil response to cyclic loading for samples consolidated in isotropic and K conditions, the plots of distinct cycles are presented in For the purpose of establishing the difference0 between the soil response to cyclic loading for Figure 10. Figure 10a presents the cycles 1000 and 20,000 where the ∆u–ε characteristic for one cycle samples consolidated in isotropic and K0 conditions, the plots of distinct cycles are presented in of isotropically consolidated sample is presented. The plot shows, that the hysteresis curve had the Figure 10. Figure 10a presents the cycles 1000 and 20,000 where the Δu–ε characteristic for one cycle same shape. The 1000 cycle was characterized by a hysteresis curve in which the area of the hysteresis of isotropically consolidated sample is presented. The plot shows, that the hysteresis curve had the and its inclination changed. The pattern of hysteresis curve evolution was similar for tests 1.1 and 1.3. same shape. The 1000 cycle was characterized by a hysteresis curve in which the area of the hysteresis and its inclination changed. The pattern of hysteresis curve evolution was similar for tests 1.1 and Appl. Sci. 2019, 9, 3821 15 of 23

Appl. Sci. 2019, 9, x 15 of 23 The inclination and the area of the hysteresis curve rose in both cases. The different responses could be 1.3. The inclination and the area of the hysteresis curve rose in both cases. The different responses observed in the case of sample 1.2 wherein cycle 20,000 the inclination, as well as the area, was smaller. could be observed in the case of sample 1.2 wherein cycle 20,000 the inclination, as well as the area, The unloading process in this test showed that sample tended to decrease excess pore water pressure was smaller. The unloading process in this test showed that sample tended to decrease excess pore much faster than the recovering of strain. This difference of the response to cyclic loading was caused water pressure much faster than the recovering of strain. This difference of the response to cyclic by the initial void ratio difference since there was no distinct difference in deviator stress conditions. loading was caused by the initial void ratio difference since there was no distinct difference in The impact of the initial void ratio could be seen in terms of the generated excess pore water pressure deviator stress conditions. The impact of the initial void ratio could be seen in terms of the generated in one cycle. The excess pore water pressure in the case of tests 1.1 and 1.3 had risen up to 1.8 and excess pore water pressure in one cycle. The excess pore water pressure in the case of tests 1.1 and 1.7 kPa. In the case of sample 1.2, the excess pore water pressure built up to 1.1 kPa, which was less 1.3 had risen up to 1.8 and 1.7 kPa. In the case of sample 1.2, the excess pore water pressure built up when comparing the amount of generated pore pressure. On the other hand, the axial strain in one to 1.1 kPa, which was less when comparing the amount of generated pore pressure. On the other cycle caused by cyclic loading seemed to be independent of the initial void ratio. The axial strain hand, the axial strain in one cycle caused by cyclic loading seemed to be independent of the initial in one cycle was equal to 0.0216%, 0.0177%, and 0.0146% respectively for the initial consolidation void ratio. The axial strain in one cycle was equal to 0.0216%, 0.0177%, and 0.0146% respectively for pressure σ03,0 equal to 45 kPa, 90 kPa, and 135 kPa and seemed that the σ03,0 was the governing factor the initial consolidation pressure σ’3,0 equal to 45 kPa, 90 kPa, and 135 kPa and seemed that the σ’3,0 in this phenomena. was the governing factor in this phenomena.

(a)

(b)

FigureFigure 10. PorePore pressurepressure versus versus the the axial axial strain strain for selected for selected cycles fromcycles the from triaxial the tests: triaxial (a) Isotropically tests: (a) Isotropicallyconsolidated consolidated samples, and samples, (b)K0-consolidated and (b) K0-consolidated samples. samples.

TheThe excessexcess porepore water water pressure pressure in the in case the of Kcase0 consolidated of K0 consolidated samples had samp differentles had characteristics. different characteristics.The ∆u in one cycleThe Δ wasu in greaterone cycle for was test greater 2.2 where for the test deviator 2.2 where stress the parametersdeviator stress were parameters smaller in were terms smallerof the stress in terms median of the and stress greater median in terms and of greater deviator in stressterms amplitude. of deviator Test stress 2.2 amplitude. was characterized Test 2.2 by was the characterizedexcess pore water by the pressure excess pore equal water to 4.5 pressure kPa after equal 10,000 to cycles.4.5 kPa The after same 10,000 excess cycles. pore The water same pressure excess porevalue water was observedpressure value in the was case observed of sample in 2.5. the The case value of sample of ∆u /2.5.qa ratio The wasvalue equal of Δ tou/q 0.257,a ratio0.333, was equal 0.240, to0.190, 0.257, and 0.333, 0.338 0.240, respectively. 0.190, and The 0.338 diff respectively.erence between The thedifference ratios was between caused the by ratios different was initialcaused void by differentratios and initial different void medianratios and levels different of deviator median stress. levels The of impactdeviator of stress.e0 shows The that impact the biggerof e0 shows the initial that thevoid bigger ratio the value initial was void the greater ratio va valuelue was of the the∆ greateru/qa ratio value in one of cyclethe Δu would/qa ratio be. in Although one cycle the would deviator be. Althoughstress amplitude the deviator was greaterstress amplitude in the case was of greater sample in 2.2, the while case theof sampleqm value 2.2, was while otherwise. the qm value Another was otherwise. Another way of loading, in the case of sample 2.2 results in different characteristics of the excess pore water pressure generation. Appl. Sci. 2019, 9, 3821 16 of 23

Appl. Sci. 2019, 9, x 16 of 23 way of loading, in the case of sample 2.2 results in different characteristics of the excess pore water pressureThe excess generation. pore water pressure in cycle 1000 had different characteristics than the cycle observed in cycleThe 20,000 excess or pore 10,000. water The pressure cycle in in the cycle case 1000 of had sample different 2.1 and characteristics 2.3 had a small than thearea cycle and observed greater inclinationin cycle 20,000 than in or the 10,000. last cycle The of cycle loading. in the Sample case of 2.2 sample and 2.5 2.1 were and characterized 2.3 had a small by high area excess and greater pore waterinclination pressure than generation, in the last cyclethe big of loading.area of the Sample hysteresis 2.2 and curve 2.5 were in comparison characterized to previous by high excess tests and pore thewater same pressure inclination generation, after 10,000 the bigcycles area of of loading. the hysteresis The same curve phenomena in comparison can beto seen previous in sample tests 2.4’s and responsethe same to inclination cyclic loading. after The 10,000 lesser cycles pore of water loading. pressure The same value phenomena might be caused can be by seen a low in sampleinitial void 2.4’s ratio.response In Figure to cyclic 11, the loading. comparison The lesser of laws pore cycl watere of pressureloading for value excess might pore be water caused pressure by a low and initial the deviatorvoid ratio. stress In Figure increment 11, the in comparisonone cycle was of lawspresente cycled. of The loading tests foron excessthe isotropically pore water consolidated pressure and samplesthe deviator showed stress that increment for the same in one initial cycle void was ratio, presented. the excess The pore tests water on the pressure isotropically generated consolidated in one cyclesamples had showedthe same that value for for the equal same stress initial conditions. void ratio, Sample the excess 1.2, porewhich water was more pressure compact, generated had lower in one generatedcycle had excess the same pore value water for pressure equal stress in comparison conditions. to Sample deviator 1.2, stress which conditions was more that compact, corresponds had lower to thegenerated previously excess observed pore water phenomena. pressure in comparisonThe Δu/qmax toratio deviator was stressequal conditions to 0.195, that0.122, corresponds and 0.200 to respectively. the previously observed phenomena. The ∆u/qmax ratio was equal to 0.195, 0.122, and 0.200 respectively. The K0-consolidated samples behaved in a similar way. Sample 2.1 with an e0 equal to 0.333 had The K0-consolidated samples behaved in a similar way. Sample 2.1 with an e0 equal to 0.333 had the the Δu/qmax ratio equal to 0.108, which corresponds to sample 1.2 where e0 was equal to 0.345. The ∆u/qmax ratio equal to 0.108, which corresponds to sample 1.2 where e0 was equal to 0.345. The sample 2.2 sample 2.2 with an initial void ratio equal to 0.399 had the Δu/2qa ratio equal to 0.170. This relationship with an initial void ratio equal to 0.399 had the ∆u/2qa ratio equal to 0.170. This relationship was almost waslinear almost for all linear five samples.for all five Based samples. on this Based test on the this conclusion test the conclusion could be formed, could be the formed, excess porethe excess water porepressure water in pressure one cycle in in one long-term cycle in cyclic long-term loading cyclic test dependedloading test on depended the deviator on stress the deviator amplitude stress and amplitudethe initial voidand the ratio. initial This void indicates ratio. that This the indicate consolidations that the type consolidation would not impacttype would on this not characteristic. impact on thisNevertheless, characteristic. the diNevertheless,fferences could the be differences seen in the could inclination be seen of thein the stress–strain inclination and of excessthe stress–strain pore water andpressure–strain excess pore water characteristics. pressure–strain characteristics.

(a)

(b)

FigureFigure 11. 11. ExcessExcess pore pressure andand deviatordeviator stress stress versus versus axial axial strain strain for for the the last last cycle cycle of loading of loading from fromthe triaxial the triaxial tests: tests: (a) Isotropically (a) Isotropically consolidated consolidated samples, samples, and (andb) K (0b-consolidated) K0-consolidated samples. samples.

For K0-consolidated samples’ Δu/qmax ratio had a linear relationship with qm/qa, which indicates that the excess pore water pressure value in one cycle impacted the deviator stress characteristics. Appl. Sci. 2019, 9, 3821 17 of 23

For K0-consolidated samples’ ∆u/qmax ratio had a linear relationship with qm/qa, which indicates that the excess pore water pressure value in one cycle impacted the deviator stress characteristics. Appl.The Sci. inclination 2019, 9, x of the hysteresis loop can be described by the modulus conception. The stress–strain17 of 23 characteristics in cyclic loading are often explained with the resilient modulus definition. The resilient The inclination of the hysteresis loop can be described by the modulus conception. The stress– modulus Mr is a quotient of cyclic stress and resilient strain and for the purpose of this study can be strain characteristics in cyclic loading are often explained with the resilient modulus definition. The defined as: resilient modulus Mr is a quotient of cyclicqmax stressq minand resilient∆q strain2 qa and for the purpose of this study can be defined as: Mr = − = = · . (1) εmax ε εr εr − min ∆ ∙ The deviator stress difference is the𝑀 cyclic = stress in= one= cycle.. Therefore, the cyclic stress can be defined(1) as a double deviator stress amplitude in one cycle. The resilient strain is accordingly the maximum andThe minimum deviator strainstress observeddifference in is one the cycle. cyclic stress in one cycle. Therefore, the cyclic stress can be defined as a double deviator stress amplitude in one cycle. The resilient strain is accordingly the Another type of soil modulus that can help to understand how excess pore water pressure impacts maximum and minimum strain observed in one cycle. on the soil stiffness in one cycle is the excess pore water pressure modulus M , which can be defined Another type of soil modulus that can help to understand how excess∆u pore water pressure as the quotient of excess pore water pressure in one cycle to resilient strain: impacts on the soil stiffness in one cycle is the excess pore water pressure modulus MΔu, which can be defined as the quotient of excess pore water pressure in one cycle to resilient strain: umax umin ∆u M∆u = − = . (2) ε ε ∆ ε 𝑀∆ = max =min . r (2) − TheThe presented presented relationship relationship between between strainstrain andand stre stressss components components can can be be used used for for the the evaluation evaluation ofof the the hysteresis hysteresis curve curve inclination inclination change. change. On FigureFigure 1212 thethe resilient resilient modulus modulus and and excess excess pore pore water water pressurepressure modulus modulus for for isotropically isotropically consolidated consolidated samplessamples are presented. presented. For For the the sample sample consolidated consolidated in inσ0 3σequal’3 equal to to 45 45 kPa, kPa, the the resilient resilient modulusmodulus characteristiccharacteristic was was very very similar similar to to the the excess excess pore pore water water pressurepressure modulus. modulus. TheThe Mr valuevalue first first rose rose and and then then around around cycle cycle 50 reached 50 reached its maximum its maximum value. The value. TheMMΔu ∆valueu value had had a similar a similar characteristic, characteristic, although although the the maximum maximum value value was was achieved achieved around around cycle cycle 40. 40. InIn the the case case of of samples samples 1.2 1.2 and and 1.3, 1.3, the the resilientresilient modulus also also reached reached a ama maximumximum value value around around cycle cycle 5050 and and then then decreased. decreased. The The maximum maximumM Mrr was equal equal to to 45.0 45.0 MPa, MPa, 64.5 64.5 MPa, MPa, and and 70.3 70.3 MPa MPa respectively. respectively.

(a)

(b)

Figure 12. Cont. Appl. Sci. 2019, 9, 3821 18 of 23 Appl. Sci. 2019, 9, x 18 of 23

Appl. Sci. 2019, 9, x 18 of 23

(c)

FigureFigure 12. 12.Resilient Resilient modulus modulus and and excess excess pore pore water water(c pressure) pressure modulus modulus change change during during the cyclic the cyclic loading forloadingFigure isotropic 12.for consolidated isotropicResilient consolidatedmodulus samples: and samples: ( aexcess) σ03,0 =pore(a)45 σ ’ kPa,3,0water = 45 (b kPa,pressure) σ03,0 (b=) σ 90modulus’3,0 kPa,= 90 andkPa, change (andc) σ 0( c3,0during) σ=’3,0135 = the135 kPa. kPa.cyclic

loading for isotropic consolidated samples: (a) σ’3,0 = 45 kPa, (b) σ’3,0 = 90 kPa, and (c) σ’3,0 = 135 kPa. TheThe excess excess pore pore water water modulus modulus followedfollowed the same pattern. pattern. After After reaching reaching the the maximal maximal value, value, M∆Mu Δdecreased,u decreased,The excess this this pore characteristic characteristic water modulus waswas followed linear in the the semi-logarithmic semi-logarithmicsame pattern. After after after reaching cycle cycle 100 100the in maximal inall all three three cases.value, cases. r Δu 0 MΔOnu decreased,On Figure Figure 13 13this results results characteristic ofof M r andand was MM linear∆ calculationsu calculations in the semi-logarithmic for forK consolidatedK0 consolidated after samples cycle samples 100 are in presented.all are three presented. cases. The Themodulus modulusOn Figure characteristics characteristics 13 results were of were M differenr and diff MerenttΔ fromu calculations from the characteristics the characteristicsfor K0 consolidated that were that weresamplesobserved observed are in presented.the incase the of case Thethe of thesamplesmodulus samples consolidated characteristics consolidated in anwere in isotropic an differen isotropic manner.t from manner. theBoth characteristics Bothmodulus modulus values that values first were rose firstobserved to rosearound toin aroundthe the case10th the ofcycle the 10th cycleandsamples and then then consolidated started started to decrease. to in decrease. an isotropic When When the manner. local the local minimumBoth minimummodulus was valuesreached was reached first in cyclerose in to 800 cycle around for 800 sample the for 10th sample 2.1 cycle and 2.1 in the 500th cycle for sample 2.2 the soil resilient modulus started to increase. The MΔu followed the andand in thethen 500th started cycle to decrease. for sample When 2.2 thethe soillocal resilient minimum modulus was reached started in to cycle increase. 800 for The sampleM∆u 2.1followed and same pattern but it preceded the Mr value change. This is helpful information when performing the thein same the 500th pattern cycle but for it sample preceded 2.2 the theM soilr value resilient change. modulus This started is helpful to increase. information The M whenΔu followed performing the stiffness change forecasting. The hardening process, which is indicated by the resilient modulus thesame stiffness pattern change but it forecasting. preceded the The Mr hardeningvalue change. process, This is which helpful is information indicated by when the resilient performing modulus the growth, was in both cases going to end. The question was if in example test 2.2 the resilient modulus growth,stiffness was change in both forecasting. cases going The to end.hardening The question process, was which if in is example indicated test by 2.2 the the resilient resilient modulus modulus would decrease again. wouldgrowth, decrease was in again. both cases going to end. The question was if in example test 2.2 the resilient modulus Similar phenomena could be observed in the case of sample 2.5 where after numerous cycles, wouldSimilar decrease phenomena again. could be observed in the case of sample 2.5 where after numerous cycles, the soilSimilar resilient phenomena modulus could was reachingbe observed its lowestin the casevalue of (around sample 2.5cycle where 3000) after and numerous then rose cycles,again. the soil resilient modulus was reaching its lowest value (around cycle 3000) and then rose again. Duringthe soil theresilient test 2.3 modulus the plastic was strain reaching rate wasits lowest the lowest. value Therefore,(around cycle the modulus3000) and characteristic then rose again. was During the test 2.3 the plastic strain rate was the lowest. Therefore, the modulus characteristic was lessDuring obvious the test than 2.3 in thethe plasticpreviously strain mentioned rate was test.the lowest. Nevertheless, Therefore, two thelocal modulus minima characteristicof modulus value was less obvious than in the previously mentioned test. Nevertheless, two local minima of modulus value couldless obvious be observed. than in Test the previously2.4 in which mentioned the CSR value test. wasNevertheless, the highest two shows local that minima the resilient of modulus modulus, value could be observed. Test 2.4 in which the CSR value was the highest shows that the resilient modulus, ascould well be as observed. the excess Test pore 2.4 water in which pressure the CSR modulus, value wasdecreased. the highest The showslocal characteristic that the resilient change modulus, might asbe wellas wellspotted as theas thearound excess excess porecycle pore water5000 water but pressure pressure there was modulus, modulus, no stiffness decreased. decreased. increase The The after local local this characteristic characteristic event. Samples change change with mightmight high be spottedCSRbe spotted value around hadaround cycle a similar cycle 5000 pattern5000 but there but of there responding was was no sti noff toness stiffness cyclic increase loading. increase after after this this event. event. Samples Samples with with high high CSR valueCSR had Wevalue acan similar had see a thatsimilar pattern the pattern M ofΔu responding value of responding started to cyclicto decrease,to cyclic loading. loading. which meant that for the same amount of strainWeWe canthe can pore see see that pressure that the theM growthM∆uΔuvalue value was startedstarted smaller toto decrease,decrease,than in previous which meant meantcycles that thatand for forwhich the the samemeant same amount amountthat the of of straineffectivestrain the the pore stresses pore pressure pressure would growth increase. growth was Thiswas smaller mightsmaller than result than in previous in in another previous cycles phase cycles and of which softeningand which meant or meantmight that the indicatethat eff ectivethe stressesthateffective the would soil stresses achieved increase. would some Thisincrease. state might ofThis equilibrium. result might in anotherresult Ne invertheless, phaseanother of phaseit softening is worth of softening to or note might thator indicatemight the previous indicate that the soilphasethat achieved the of soilsoftening some achieved state and some ofhardening equilibrium. state of took equilibrium. Nevertheless,around 1000Nevertheless, cycles it is worth and it nowis to worth note the thattorepeating note the that previous of the the previous process phase of softeningwouldphase oftake and softening many hardening more and cycles tookhardening aroundto occur. took 1000 around cycles 1000 and cycles now theand repeating now the ofrepeating the process of the would process take manywould more take cycles many to more occur. cycles to occur.

(a)

(a) Figure 13. Cont. Appl. Sci. 2019, 9, 3821 19 of 23 Appl. Sci. 2019, 9, x 19 of 23

(b)

(c)

(d)

(e)

FigureFigure 13. 13.Resilient Resilient modulus modulus and and excess excess pore pore water water pressure pressure modulus modulus change change during during the cyclic the loadingcyclic

forloadingK0 consolidated for K0 consolidated samples: samples: (a) σ03,0 =(a)65.0 σ’3,0 kPa,= 65.0 (b kPa,) σ0 3,0(b)= σ’125.03,0 = 125.0 kPa kPa (c) σ(c03,0) σ’=3,0 139.7= 139.7 kPa, kPa, ( d(d) )σ σ03,0’3,0 = 94.2= kPa,94.2 kPa, and and (e) σ (0e3,0) σ=’3,044.9 = 44.9 kPa. kPa.

TheThe pore pore pressure pressure build-up build-up based based on on stress-controlled stress-controlled cyclic stress stress can can be be analyzed analyzed based based on on the the empiricalempirical models. models. This This model model is is able able to to analyze analyze excessexcess pore water water pressure pressure wi withth the the number number ofof cycles cycles to ato certain a certain event, event, which which in in non-cohesive non-cohesive soils soils isis liquefaction.liquefaction. In In the the case case of of cohesive cohesive soils, soils, the the pore pore pressure analysis can be conducted to maximal pore pressure occurrence. The parameter that governs this analysis is pore pressure ratio, which can be presented as: Appl. Sci. 2019, 9, 3821 20 of 23 pressure analysis can be conducted to maximal pore pressure occurrence. The parameter that governs this analysis is pore pressure ratio, which can be presented as: Appl. Sci. 2019, 9, x 20 of 23 ∆u ru = , (3) ∆∆umax 𝑟 = , (3) ∆ where the ∆umax is the maximum pore pressure in one cycle. The pore pressure empirical models where the Δumax is the maximum pore pressure in one cycle. The pore pressure empirical models were were developed over the years. One of the best known is the pore pressure model developed by developed over the years. One of the best known is the pore pressure model developed by Seed et al. Seed et al. [44], which is defined as follows: [44], which is defined as follows: " 1/β # 1 1 N⁄  = + 𝑟 =ru + 𝑎𝑟𝑐𝑠𝑖𝑛arcsin2 2 −1, 1 ,(4) (4) 2 π NL − where the N/NL is the cycle ratio, β is the empirical parameter, and NL is the last cycle analyzed in this where the N/NL is the cycle ratio, β is the empirical parameter, and NL is the last cycle analyzed in this model. On Figure 14 the results of the calculations are presented for K0-consolidated samples. model. On Figure 14 the results of the calculations are presented for K0-consolidated samples.

Figure 14. Comparison of measured and predicted pore pressure ratios for K -consolidated samples. Figure 14. Comparison of measured and predicted pore pressure ratios for K0-consolidated samples.

The pore pressure ratio for K0-consolidated samples had similar characteristics. The pore pressure The pore pressure ratio for K0-consolidated samples had similar characteristics. The pore ratio rose to 0.7–0.8 of the maximum value in half of the cycle ratio. In comparison to non-cohesive pressure ratio rose to 0.7–0.8 of the maximum value in half of the cycle ratio. In comparison to non- soils, presented characteristics rose rapidly towards ru = 1 when the cycle ratio was higher than 0.9. cohesive soils, presented characteristics rose rapidly towards ru = 1 when the cycle ratio was higher Nevertheless when N/NL value was equal to 0.5 the pore pressure ratio was equal to 0.4–0.6 [38–41]. than 0.9. Nevertheless when N/NL value was equal to 0.5 the pore pressure ratio was equal to 0.4–0.6 An attempt to fit the seed model was made as well, the β parameter, in this case, was equal to 3.0. [38–41]. An attempt to fit the seed model was made as well, the β parameter, in this case, was equal to4. 3.0. Conclusions

4. ConclusionsIn this article, the cyclic loading of the compacted silty sandy clay was performed. The soil samples were consolidated in two different manners. The isotropic and anisotropic (K0) consolidation impacts on In this article, the cyclic loading of the compacted silty sandy clay was performed. The soil soil response to repeated loading. The tested soil stress history was different from the previously tested samples were consolidated in two different manners. The isotropic and anisotropic (K0) consolidation ones due to compaction in optimum moisture content. Conducted tests were in a stress-controlled impacts on soil response to repeated loading. The tested soil stress history was different from the manner and a minimum of 10,000 cycles was performed to capture soil response to cyclic loading in previously tested ones due to compaction in optimum moisture content. Conducted tests were in a undrained conditions. This type of test is preferable when pore pressure characterization is the focus stress-controlled manner and a minimum of 10,000 cycles was performed to capture soil response to of the tests. cyclic loading in undrained conditions. This type of test is preferable when pore pressure Cohesive soil samples consolidated in isotropic test conditions, behaved abruptly to cyclic loading characterization is the focus of the tests. in the first cycle. The deviator stress caused rapid pore pressure generation and permanent strain Cohesive soil samples consolidated in isotropic test conditions, behaved abruptly to cyclic generation. The first cycle showed a more severe impact on isotropically consolidated samples. loading in the first cycle. The deviator stress caused rapid pore pressure generation and permanent The stress-controlled triaxial tests performed by Yasuchara et al. [45] shows that isotropically strain generation. The first cycle showed a more severe impact on isotropically consolidated samples. consolidated samples developed higher pore pressure than anisotropically consolidated samples. The stress-controlled triaxial tests performed by Yasuchara et al. [45] shows that isotropically Nevertheless, the soil in this study was Ariake clay with an IP equal to 58%. The compacted sandy silty consolidated samples developed higher pore pressure than anisotropically consolidated samples. clay soil tested in this study behaved differently. The response to cyclic loading was more dependent Nevertheless, the soil in this study was Ariake clay with an IP equal to 58%. The compacted sandy on the CSR than on the consolidation method. silty clay soil tested in this study behaved differently. The response to cyclic loading was more The cohesive soil response in isotropic consolidation conditions could be divided into three stages. dependent on the CSR than on the consolidation method. The first one is the above mentioned, the first cycle, the second one is the intermediate zone, and the The cohesive soil response in isotropic consolidation conditions could be divided into three stages. The first one is the above mentioned, the first cycle, the second one is the intermediate zone, and the third one is the long term response. This type of behavior was observed in the sample with the highest tested CSR. Samples tested in higher CSR that had a two-step response to cyclic loading were compared to test 1.1, where no intermediate zone was observed. Appl. Sci. 2019, 9, 3821 21 of 23 third one is the long term response. This type of behavior was observed in the sample with the highest tested CSR. Samples tested in higher CSR that had a two-step response to cyclic loading were compared to test 1.1, where no intermediate zone was observed. The intermediate zone is characterized by the decrease of the permanent strain accumulation magnitude as well as by the decrease of pore pressure increment in each cycle. As a result, the excess pore water pressure generation and plastic strain accumulation weaken in each cycle. This behavior is complex and no direct connection between this to phenomena can be established. The third phase is characteristic of the long term cyclic loading. In this phase, the tendency observed in the previous stage is continued. Nevertheless, the changes in pore pressure and sample deformation may not be observed in one cycle but they might occur after several cycles. It means that in one cycle no plastic strain is observed. In this type of soil response, the effect of cyclic loading is fully embraced by the sample. The set conditions were established. The third phase begins in the first 500 cycles. The long term pore pressure response to cyclic loading shows that the soil had reached a steady state in which the excess pore water pressure remains on the same level and changes slightly during loading. The impact of the initial void ratio on pore pressure was recognized. High e0 value caused a higher generation of pore water pressure. The K0 consolidated samples behaved differently to cyclic loading in terms of plastic strain accumulation and pore pressure development. The excess pore water pressure in the test performed with the same loading pattern as in the case of isotropic consolidation it rose rapidly in the first few hundred cycles. When the ∆u characteristic started to decrease, the permanent axial strain began to develop, which could be explained by the fact that the excess pore pressure decreased the effective stress in the soil skeleton and therefore was weakening soil contacts. It was found that the type of loading had a great impact on K0 consolidation samples’ response. The soil in which the negative pressure occurred in the first cycles of loading would suffer much lesser plastic strains. This was the result of another pore pressure generation model. The isotropically consolidated samples generated pore pressure rapidly in the first few cycles, which was accompanied by plastic strain accumulation. The K0 consolidated soil also generated excess pore water pressure but much faster than in the case of K0 consolidated soil loaded with another manner, which was the reason why the plastic strains were accumulated with a much slower rate. To establish the difference between the soil response to cyclic loading for soil consolidated in isotropic and K0 conditions the hysteresis curve analysis for a distinct cycle was performed. The ∆u/qmax ratio was dependent on the initial void ratio in both cases of consolidation techniques. Nevertheless, the differences could be seen in the inclination of the stress–strain and excess pore water pressure–strain characteristics. To describe the inclination change and the resilient modulus value change an excess pore water pressure conception was utilized. It was found that the M∆u follows the same pattern but it precedes the Mr value change. This is helpful information when performing the stiffness change forecasting. The pore pressure ratio ru calculated for samples consolidated in an anisotropic manner indicates that the pore pressure ratio had similar characteristics, which in comparison to non-cohesive soils had a higher value in the half of cycle ratio but had a constant rate between the cycle ratio equal to 0.9–1.0 in opposite to non-cohesive soils.

Author Contributions: A.G. conceived and designed the experiments; A.G., E.S. and W.S. performed the experiments; A.G., wrote the paper; W.S. and A.S. edited and audited the content. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest. Appl. Sci. 2019, 9, 3821 22 of 23

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