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Procedia Engineering 165 ( 2016 ) 845 – 852

15th International scientific conference “Underground Urbanisation as a Prerequisite for Sustainable Development” OCR and POP parameters in Plaxis-based numerical analysis of loaded over consolidated soils

Roman Melnikov a, Juriy Zazulya a, Maxim Stepanov a, Oleg Ashikhmin a,*, Tatyana Maltseva a

aIndustrial University of Tyumen, Volodarskogo str. 38, Tyumen, 625001, Russia bNorthern Trans-Ural State Agricultural University, Respubliki str. 7, Tyumen, 625003, Russia

Abstract

The paper discusses deformation of over consolidated soils in Hardening Soil Model in terms of their initial stress state. When carrying out numerical analysis in Plaxis, it has been stated that Hardening Soil Model “remembers” the history of previous loadings. In forming the initial stress state of over consolidated soils with the pre-overburden pressure POP, there occurs the more reliable description of the soil deformation process than with the over consolidation ratio OCR. These findings are valid for odometer conditions and for real geotechnical calculations. © 20162016 The The Authors. Authors. Published Published by Elsevierby Elsevier Ltd. ThisLtd. is an open access article under the CC BY-NC-ND license (Peerhttp://creativecommons.org/licenses/by-nc-nd/4.0/-review under responsibility of the scientific). committee of the 15th International scientific conference “Underground Peer-reviewUrbanisation under as a responsibility Prerequisite offor the Sustainable scientific committee Development of the. 15th International scientific conference “Underground Urbanisation as a Prerequisite for Sustainable Development Keywords: plaxis, oedometer tests, hardening soil model, overconsolidation ratio – OCR, pre-overburden pressure – POP, numerical analysis.

1. Introduction

Software systems with a wide range of soil models such as Plaxis, Abaqus, ZSOIL, ANSYS, etc. are a popular and more accessible tool for conducting geotechnical calculations. In here, according to the European Geotechnical Community [1], the users of the software systems have some difficulties when dealing with them, the main ones are: selection of the most adequate soil model; indication of the soil model parameters; initialization; analysis of the

* Corresponding author. Tel.:+7-3452-29-01-03 E-mail address: [email protected]

1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 15th International scientific conference “Underground Urbanisation as a Prerequisite for Sustainable Development doi: 10.1016/j.proeng.2016.11.783 846 Roman Melnikov et al. / Procedia Engineering 165 ( 2016 ) 845 – 852

calculation results obtained. To overcome each difficulty it is required to study and analyze them carefully, as their total solution can improve trouble-free long life and economic justifiability of designing and erecting buildings and structures. In many works devoted to problem-solving in carrying out numerical analysis of geotechnical problems, there exists a common approach [2, 3, 4]. This approach stems from the fact that if pre-consolidated soils occur in the ground bed simulated with a numerical problem, then the overconsolidation ratio OCR is used to describe the initial stress state and the performance of the soils under the loads. However, Plaxis allows the pre-overburden pressure – POP to be used for these purposes. The task of identifying specific use of OCR and POP during the numerical analysis has not been solved. The paper investigates the differences in developing the initial stress state of overconsolidated soils when using OCR and POP parameters. Hardening Soil Model being a part of Plaxis software system is used as a soil model; it has gained popularity in geotechnical calculations due to its adequacy [5-8]. The paper aims at identifying the differences when using the overconsolidation ratio OCR and pre-overburden pressure POP involved in developing the initial stress state of overconsolidated soils and their deformation under loading.

2. Initial Stress State

The initial stress state of the ground bed depends not only on the vertical and horizontal stresses of soil dead weight, but the pre-consolidation pressure σ'p [9] - maximum vertical pressure that the soil had in the past; it could be created by a glacier or sedimentary rocks that are not available any more or by a technological process [10, 11]. The soil suffers from the vertical pressure of its own weight σ'yy; this pressure is called natural or domestic pressure. If the pre-consolidation pressure σ'p is greater than the domestic pressure σ'yy, the soil is overconsolidated, and the horizontal stresses σ'xx exceed the vertical ones σ'yy in the initial stress state. If the pre-consolidation pressure is missing, the soil is normally consolidated and the vertical stresses exceed the horizontal ones. To determine the pre-consolidation pressure σ'p data processing operations of oedometer tests are carried out. A number of methods for determining the pressure σ'p has been created, but the method of Casagrande is preferable [12]. One can use the direct method, when the characteristic fracture on the oedometer curve ε = f (σ) indicates the pre-consolidation pressure σ'p. Plaxis allows calculation of the initial stress state to be carried out automatically using the coefficient of earth pressure Ko = σ'xx / σ'yy. By default it is believed that the simulated soil is normally consolidated, so the coefficient NC of earth pressure in normal consolidation Ko is used; it depends on the angle of internal friction and is NC automatically evaluated by the formula after Jaky [13, 14]: Ko = 1-sinφ. If the soil is overconsolidated, adjustment of the coefficient of earth pressure Ko is required specifying the value of the overconsolidation ratio OCR and pre-overburden pressure POP. OCR is evaluated by the formula: OCR = σ'p / σ'yy. If OCR≤1, the soil is considered to be normally consolidated, when OCR> 1 - it is overconsolidated. POP is evaluated by the formula: POP =|σ'p-σ'yy| and is not used in the classification of soils (Fig. 1).

Roman Melnikov et al. / Procedia Engineering 165 ( 2016 ) 845 – 852 847

Fig. 1. Evaluation of OCR and POP.

3. Initial Stress State

To achieve the objectives of the work, numerical analysis simulating oedometer tests were carried out using the technique [15]. Previously, [15] the parameters of Hardening Soil Model had been determined for soil undisturbed 3 3 ref ref ref samples: γunsat = 17.55 kN/m ; γsat = 18.31 kN/m ; e = 0.957; E50 = Eoed = 3100 kPa; Eur = 21700 kPa; m = 0.9; 0 0 ref с' = 41 kPa; φ' = 16 ; ψ = 0 ; νur, p – default entry. The soil sample was normally consolidated if the coefficient of NC earth pressure was Ko = 0.7244. The error in the description of the experimental dependency diagram of the setting from the load was less than 5% in ε> 0.04. Hardening Soil Model takes into account the history of ground bed loading. In proof of this, the soil was pre- consolidated directly by application of the external load for the first numerical calculation. In this regard, the pressure p1 = 300 kPa was applied to a normally consolidated soil sample, thus, pre- consolidation pressure was created. Then the soil sample was unloaded with nullification of deformation values. The repeated loading p2 = 600 kPa with subsequent unloading was created at the next stage of calculation. Simultaneously, independent calculation was conducted when the pressure p2 = 600 kPa with subsequent unloading was immediately applied to the normally consolidated soil sample. The analyzed results of calculations (Fig. 2) make it possible to establish that the curves of primary loading of both calculations are the same up to the pressure of 300 kPa on the diagrams of oedometer tests uy = f (σ). In the soil sample subjected to pre-consolidation, reloading gives the characteristic fracture of the oedometer curve at the value close to p1 = 300 kPa. When the pressure on the sample exceeds p1, the slope of the oedometer curve agrees with the curve of primary loading. Thus, Hardening Soil Model takes into account the history of ground bed loading; in here, there is the fracture on the oedometer curve indicating the pre-consolidation pressure. The inverse problem was solved when the pre-consolidation pressure σ'p was directly determined for the numerically obtained oedometer curve ε = f (σ) [16] (Fig. 3). It has been found out that the pre-consolidation pressure σ'p - 271.2 kPa is less than the pressure that creates consolidation p1 = 300 kPa. This is due to the fact that soil consolidation occurs only under plastic deformation; at consolidation pressure p1 deformation is partly elastic.

848 Roman Melnikov et al. / Procedia Engineering 165 ( 2016 ) 845 – 852

pressure, kPa log(σ), kPa 0 300 600 1 10 100 1000 0,0 0,0

-0,5 -0,2 σ'p = 271,2 kPa -1,0 -0,4

-1,5 -0,6

-2,0 -0,8

vertical deformation, mm deformation, vertical -1,0 -2,5 -1,2 -3,0 vertical deformation, mm -1,4 -3,5 Первичноеp1=600 kPa нагружение 600 кПа -1,6 Первичноеp1=300 kPa нагружение 300 кПа

Повторноеσp=300 kPa, нагружение p2=600 kPa 600 кПа -1,8

Fig. 2. Oedometer curves uy=f(σ) of the first calculation. Fig. 3. Pre-consolidation pressure diagram.

One should distinguish the consolidation pressure p1 and pre-consolidation pressure σ'p obtained after the oedometer tests, in here σ'p = 0.9 • p1. It is important to take into account that only the pre-consolidation pressure σ'p can be determined when testing the real soil sample, i.e. the pressure that soil “remembers”. Then two numerical calculations imitating oedometer tests were done. They aimed at valid description of overconsolidated soil deformation using the overconsolidation ratio - OCR (Fig. 4) and pre-overburden pressure – POP (Fig. 5). After the calibration procedure the predicted oedometer curves uy = f (σ) were compared with the initial curve obtained from the first calculation when preliminary soil consolidation was created directly with the pressure p1. The acceptable level of accuracy for numerical solution was 5%. Thus, OCR is invalid in describing the process of overconsolidated soil deformation. The oedometer curve throughout the whole range of loading does not have the characteristic fracture even with significant overestimation of OCR value (more than 10); besides, deformations are significantly overestimated (over 60%) for all values of OCR <100. The diagrams are not different from the oedometer curve of primary loading (Fig. 2). Roman Melnikov et al. / Procedia Engineering 165 ( 2016 ) 845 – 852 849

pressure, kPa pressure, kPa 0 300 600 0 300 600 0,0

-0,2 -0,2

-0,4 -0,7 -0,6

-0,8 -1,2 -1,0

-1,7 -1,2 vertical deformation, mm deformation, vertical -1,4 vertical deformation, mm deformation, vertical -2,2 -1,6

-1,8 -2,7 POP=270 kPa POP=300 kPa

-3,2 Повторноеσp=300 kPa, нагружение p2=600 kPa 600 кПа

OCR=2 OCR=20 OCR=200 OCR=2000 Повторноеσp=300 kPa, нагружение p2=600 kPa 600 кПа

Fig. 4. Oedometer curves uy=f(σ) of the second calculation with Fig. 5. Oedometer curves uy=f(σ) of the third calculation with changed OCR, POP=0. changed POP, OCR=1.

POP makes it possible to describe the oedometer curve of the overconsolidated soil with a characteristic fracture; in here the required accuracy of the given curve is achieved when consolidating the soil directly if POP = 270 kPa (i.e. equals σ'p) (Fig. 5). Thus, after the oedometer curve analysis the resulting pre-consolidation pressure σ'p gave the possibility of the specified accuracy to be achieved. It has been stated that OCR is invalid in describing the process of overconsolidated soil deformation under loading, while POP is capable of describing the process with a given accuracy; in here POP = 0.9 • p1 = σ'p.

4. Numerical Analysis of Real Calculation Limitations

Oedometer conditions were provided during the numerical experiment when the area of pre-consolidation pressure transmission agreed with the area of reloading. In the next numerical experiment the conditions were close to the actual design – the area of pre-consolidation largely exceeded the area of reloading (Fig. 6). The first calculation was done when pre-consolidating soil with the external load p1 = 100 kPa (Fig. 6a). Then the soil sample was unloaded with nullification of deformation values and reloaded p2 = 270 kPa on a smaller area (Fig. 6b). After that the calculations were done when creating the initial stress state of soil with OCR or POP (Fig. 6c). After the settlement diagrams obtained uy=f(σ) it can be stated that the overconsolidation ratio OCR is invalid in 850 Roman Melnikov et al. / Procedia Engineering 165 ( 2016 ) 845 – 852

describing the process of overconsolidated soil deformation under loading (Fig. 7). The settlement diagram is monotonous with lack of characteristic fracture in overconsolidated soil deformation. When using POP the characteristic fracture (Fig. 8) can be seen on the settlement diagram; in POP = 0.9 • p1 = σ'p = 0.9 • 100 kPa = 90 kPa the error in description of the diagram obtained by preliminary loading does not exceed 5%. It has been found out that under conditions close to the real geotechnical calculation OCR is invalid in describing the process of overconsolidated soil deformation under loading, as opposed to POP; in here the necessary accuracy is achieved with POP = σ'p.

a) b) c)

Fig. 6. Plaxis 2D – based loading diagrams: а – pre-consolidation with external loading р1=100 kPa; b – reloading р2=270 kPa; c – OCR or POP , loading р2=270 kPa.

5. Conclusions

After the research done one can draw the following conclusions on the use of the overconsolidation ratio - OCR and pre-overburden pressure POP in Hardening Soil Model: x For complex soil models such as Hardening Soil it is necessary to take into account the initial stress state, i.e. the history of the previous loadings which soil “remembers”. For overconsoldated soils the history of loadings greatly affects the process of deformation. x It is necessary to determine the pre-consolidation pressure σ'p. The accuracy of σ'p is achieved during kinematic oedometer tests and the use of different techniques for processing the results [13, 14]. x There is a difference between the initial consolidation pressure and pre-consolidation pressure σ'p. It is possible to determine only σ'p in the soil sample i.e. the pressure that soil "remembers". x If OCR is used to describe the initial stress state, it is invalid in characterizing the process of overconsolidated soil deformation under loading. x If POP – equal to the pre-consolidation pressure σ'p - is used to describe the initial stress state, the process of overconsolidated soil deformability can be described with the acceptable level of accuracy of 5%. Roman Melnikov et al. / Procedia Engineering 165 ( 2016 ) 845 – 852 851

pressure, kPa pressure, kPa 0 100 200 300 0 100 200 300 0 -5 -5 -15 -10 -25 -15 -35 -20 -45

-55 -25 vertical deformation, vertical deformation, sm -65 sm deformation, vertical -30

-75 -35

-85 -40 OCR=1 OCR=2 OCR=3 OCR=4 POP=80 kPa POP=90 kPa OCR=5 OCR=6 1σp=100 kPa, POP=100 kPa 1σp=100 kPa, p2=270 kPa p2=270 kPa

Fig.7. Setting diagram uy=f(σ) with changed OCR, POP=0. Fig. 8. Setting diagram uy=f(σ) with changed POP, OCR=1.

6. Summary

Accurate numerical analysis of the soil stress-strain state depends not only on the identified mechanical characteristics of the soil, but also on the soil model which describes its performance. Since the mechanical properties of soils depend considerably on the degree of their consolidation, it is necessary to determine the pre-consolidation pressure σ'p of the soil. The complex calculation models of the soil such as Hardening Soil take into account the initial stress state of the overconsolidated soils by means of the overconsolidation ratio-OCR or pre-overburden pressure POP. POP is more preferable than OCR, since it describes the deformability process more accurately. Therefore, further research is needed to determine the limits of OCR and POP applicability. In conclusion let us remember the words of George Box, the famous British mathematician: "All models are wrong, but some are useful." One can agree with him and add that we must learn how to use these models correctly.

References

[1] Report of the Commission on Economic Performance Measurement and Social Progress: Chapter One. Work translation, State Research Institute of System Analysis of the Russian Federation Audit Chamber, Research Institute SP, Moscow, 2010. [2] I.G. Lukmanova, A.G. Korolyov, E.V. Nezhnikova, Project Management, a tutorial, Moscow State Civil Engineering University, Moscow, 2013. [3] N.Y. Yaskova. Investment and Construction Processes Development in the Context of Globalization, International Academy of Investment and Construction Economics, Moscow, 2009. [4] J. Huang, X. Chen, B. Huang, X. Yang, Economic and environmental impacts of foreign direct investment in China: A spatial spillover analysis, Original Research Article. China Economic Review, In Press, Corrected Proof. (2016). [5] A. Teixeira, A. Queirós, Economic growth, human capital and structural change: A dynamic panel data analysis, Research Policy. 45(8) (2016) 1636-1648. 852 Roman Melnikov et al. / Procedia Engineering 165 ( 2016 ) 845 – 852

[6] T. Ciarli, M. Valente, The complex interactions between economic growth and market concentration in a model of structural change, Structural Change and Economic Dynamics, 38 (2016) 38-54. [7] S.B. Sborshchikov, N.V. Lazareva, Ya.V. Zharov, Theoretical Bases of Multidimensional Modeling of Sustainable Development in Investment and Construction Activities, Vestnik MGSU. 6 (2014) 165-171. [8] J.R. Afonso, E. C. Araújo, B. G. Fajardo, The role of fiscal and monetary policies in the Brazilian economy: Understanding recent institutional reforms andeconomic changes, The Quarterly Review of Economics and Finance. 62 (2016) 41-55. [9] D.N. Silka. On priority measures for creating the basis for the development of the russian economy, Life Science Journal. 11(7) (2014) 310- 313. [10] D.N. Silka, I.G. Lukmanova, А.А. Afanasev, М.А. Kasyanov, Synchronization of processes related to economic activity with stages of development of spatially-organized systems, International Journal of Economics and Financial Issues. 5(3) (2015) 121-124. [11] P.G. Grabovyi, I.P. Avilova, A.V. Sharapova, The empiric methodology of evaluating and managing the aggregate risk at implementing large complex building and investment projects abroad, Life Science Journal. 11(12) (2014) 1097. [12] N. Lee, R. Ponton, A.W. Jeffreys, R. Cohnet, Analysis of industry trends for improving undergraduate curriculum in construction management education, ASC Proceedings of the 47th Annual International Conference. (2011). [13] R. Sacks, E. Pikas, Building information modeling education for construction engineering and management, Industry requirements, state of the art, and gap analysis, Journal of Construction Engineering and Management. 139(11) (2013) 196-201. [14] S. Iamsiraroj, The foreign direct investment̢economic growth nexus, International Review of Economics & Finance. 42 (2016) 116-133. [15] F. Amri, The relationship amongst energy consumption, foreign direct investment and output in developed and developing, Countries Review Article, Renewable and Sustainable Energy Reviews. 64 (2016) 694-702.