Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 111 (2015) 612 – 618
XXIV R-S-P seminar, Theoretical Foundation of Civil Engineering (24RSP) (TFoCE 2015)
Effect of different values of soils shear strength parameters on the size of spread foundation Lucia Orininováa*, Giang Nguyenb a
Lucia Orininová, Department of Geotechnics, Faculty of Civil Engineering, University of Žilina, Univerzitná 8215/1, 010 26 Žilina b Giang Nguyen, Department of Geotechnics, Faculty of Civil Engineering, University of Žilina, Univerzitná 8215/1, 010 26 Žilina
Abstract Shear strength parameters have significant effect on size of spread foundation. When designing spread foundation, the parameters necessary to calculate the bearing capacity of foundation soil are angle of internal friction and cohesion. In this paper the effect of guiding standardized minimal, intermediate and maximal values of shear strength parameters introduced in the old Slovak Technical Standard STN 731001 as so as shear strength parameters vales obtained from geotechnical investigation report on the size of spread foundation is compared. The analysis of design of spread foundation, placed on homogeneous and inhomogeneous subsoil is also made. © 2015 The Authors. Published by Elsevier B.V. © 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of organizing committee of the XXIV R-S-P seminar, Theoretical Foundation of Civil (http://creativecommons.org/licenses/by-nc-nd/4.0/). Engineering (24RSP) under responsibility of organizing committee of the XXIV R-S-P seminar, Theoretical Foundation of Civil Engineering (24RSP) Peer-review Keywords: Spread foundation; Shear strength parameters; Internal angle of friction; Cohesion; Homogeneous and inhomogeneous subsoil.
1. Introduction Design of spread foundation can be made according to various design methods. The choice of used design methods effects bearing capacity of foundation soils and sizes of the foundation. Main factors, which influence on the size of foundation are angle of the internal friction and cohesion. The values angle of the internal friction can be obtained from laboratory tests, for example: direct shear test (DST), or from standardized values introduced in the Slovak Technical Standard.
* Corresponding author. Tel.: Tel.: +421-41-513-5763. E-mail address:
[email protected]
1877-7058 © 2015 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 organizing committee of the XXIV R-S-P seminar, Theoretical Foundation of Civil Engineering (24RSP)
doi:10.1016/j.proeng.2015.07.054
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The design of spread foundation is usually realized according to different standard specifications. In this paper are compared 3 Design Approaches (DAs) Eurocode 7 (EC7) and design flow for geotechnical practice in Slovakia according to the Slovak Technical Standard STN 73 1001:1987 ( in following text we will use the abbreviation “old STN” for it) and the Slovak Technical Standard STN 73 1001: 2010 (abbreviation “new STN” for it). [3] Minimal, intermediate and maximal values of shear strength parameters and cohesion of homogeneous subsoil (F4) introduced in the old Slovak Technical Standard STN 73 1001 had been used to design model spread foundation. Next this paper deals precise calculate bearing capacity base on slip surface. 2. Design spread foundation according to various standard specifications Bearing resistance failure, which is a GEO ultimate limit state, is the relevant ultimate limit state to be considered for the design of the spread foundation in this example. When design for this ultimate limit state, the following inequality needs to be satisfied
Vd d Rd
(1)
where, Vd [kN] is the design vertical load and Rd [kPa] is the design bearing resistance.[1] By the EC7, the designed bearing capacity of the foundation soils for drained condition can be calculated by the formula [2]:
Rd
cc .N .s .b .i qc.N .s .d .i d
c c
c c
q
q
q q
0,5.J c.B.NJ .sJ .bJ .iJ / J R,v
(2)
By the new STN, the designed bearing capacity of the foundation soils for drained condition can be calculated by the formula:[3] Rd
B § ¨ cdc .Nc .sc .dc .ic . jc qc.N q .sq .d q .iq . jq J c. 2 .NJ .s J .dJ .iJ . jJ ©
· ¸ / J R ,v ¹
(3)
The vertical design bearing capacity of subsoil Rd [kPa] is calculated according by “old STN” as.[5] Rd
cd .Nc .sc .dc .ic J 1.d.Nd .sd .dd .id J 2 .bef / 2.Nb .sb .db .ib
where: Rd [kPa] is a design bearing capacity; cd´[kPa] is a design value of effective cohesion, cd´= ck´/γc´; ck´ [kPa] is a characteristic value of effective cohesion; γc´ [-] is a partial factor for cohesion; φd´ [°] is a design value of angle of friction, φd´= φk´/γφ´, φk´ [°] is a characteristic value of angle of friction; γφ´ [-] is a partial factor for an angle of friction; q´ [kPa] is a design effective overloading above foundation base; γ´ [kN.m-3] is an effective unit weight of the soil under foundation base; γR,v [-] is a partial factor for the resistance (bearing capacity); Nc, Nq, Nγ are bearing capacity factors, depending on design angle of internal friction φ d; sc, sq, sγ are foundation shape factors; dc, dq, dγ are factors of foundation depth ; ic, iq, iγ are factor of load inclination; jc, jq, jγ are factors of terrene slope.
(4)
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3. Design spread foundation, when inhomogeneity of subsoil consist of layered bedrock If the soil bellow the footing bottom is inhomogeneous then the inputted profile is transformed into a homogeneous soil based on the Prandtl slip surface, which represents the type and location of failure of the foundation. To determine the value of the design bearing capacity R d are used average value of the parameters of subsoil layers. The average value of the angle of friction φ and the cohesion c is determined with respect to the length of the slip surface in different layers subsoil. The average unit weight γ is determined as to areas limited slip surfaces in different layers subsoil. The course of slip surfaces shall be established for the average value of the angle of friction φpr soil in the subsoil. You can use the following formulas: For angle:
D
45q
E
45q
I pr 2
I pr 2
,
(5)
,
(6)
Z 90q . The length of the initial line logarithmic spiral r0
b .sin D . sin(90q M pr )
(7)
The length of individual line logarithmic spiral ri
Z .tgM pr
r0 .cos M pr .e
.
(8)
Depth slip surface below footing bottom zs
D .tgM pr
r0 .cos M pr .e
.
(9)
Horizontal range slip surface
ls
2.rn .cos E .
(10)
Formulas for calculation average values will be a form: for angle of friction
tgM
6li .tgMi 6li
(11)
for cohesion
c
6li .ci 6li
(12)
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for unit weight
J
6Ai .J i . 6Ai
(13)
When φi is angle of friction of soil layer ci is cohesion of soil layer, γi is an effective unit weight of soil layer, li is length slip surface of soil layer, Ai is area delimited by slip surface of soil layer. The resulting characteristics are obtained with iterative procedures. b
Fig. 1. Form of slip surface below footing bottom.
4. Analysis of specific foundation For analysis of differences between various specific standard we will deal with foundation of square shape, vertical action (permanent and transient load) for drained conditional of homogeneous subsoil and drained conditional of inhomogeneous subsoil. The water level is one meter below the surface. At the Fig.X is illustrated model example for the spread foundation design. Subsoil consist of layered bedrock. Bearing capacity of spread foundation is calculated for homogeneous subsoil (for soil F4 and F6). This calculation is compared with bearing capacity for layered bedrock. Layered bedrock included the effect slip surface.
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Fig. 2. Model example for the comparison of spread foundation design.
In this paper, differences between size of foundation according to various design procedures were compared. As we can see at Fig.1, design by various design procedures has significant effect on size of foundation. At Fig. we can comparison influence various values angle of friction and cohesion. Analysis was made based on minimum, intermediate and maximum values angle of friction and cohesion and this is with geotechnical investigation report compared. Design procedures for homogeneous and inhomogeneous are various, we can see differences at fig. 2.
Fig. 3. Size of foundation by various design procedures. Tab.1. Size of foundation by various design procedures and various shear strengh parameters.
report
min.
interm.
max.
EN 7: (DA1)/C1
2,01
2,08
1,95
1,62
EN 7: (DA1)/C2
2,14
2,37
2,01
1,72
EN 7:
(DA2)
2,18
2,44
2,04
1,72
EN 7:
(DA3)
2,43
2,69
2,27
1,94
"new" ST N
2,19
2,45
2,15
1,73
"old" ST N
2,36
2,60
2,20
1,89
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Fig.4. Comparison design procedures for homogeneous and inhomogeneous subsoil. Tab.2. Comparison size of foundation according design procedures for homogeneous and inhomogeneous subsoil.
F4
slip surface
F6
EN 7: (DA1)/C1
1,74 (-13,43%)
2,01
2,19 (+8,96%)
EN 7: (DA1)/C2
2,04 (-4,67%)
2,14
2,45 (+14,49%)
EN 7:
(DA2)
2,08 (-4,59%)
2,18
2,65 (+21,56%)
EN 7:
(DA3)
2,32 (-4,53%)
2,43
2,81 (+15,64%)
"new" ST N
2,09 (-4,57%)
2,19
2,26 (+3,2%)
"old" ST N
2,31 (-2,12%)
2,36
2,87 (+21,61)
From the data in Tab.1 and Fig.2 we can see that differences in the size of foundation by design procedures for inhomogeneous subsoil have reached the values from 2,19 m up to 2,36 m (different 7,76%) for values shear strength parameters from geotechnical investigation report and for standardized values of shear strength parameters introduces in the STN 73 100: for minimal values from 2,45 m up to 2,60 m (different 6,12%), for intermediate values from 2,15 m up to 2,20 m (different 2,3%) and for maximal values from 1,73 m up to 1,89 m (different 9,25%). To compare the shear strength parameters, percentual difference between minimal and maximal values for „new“ STN is 41,6%, for EN 7, DA1 (C1) is 28,4%, for EN 7, DA1 (C2) is 37,8%, for EN 7, DA2 is 41,9%, for EN 7, DA3 is 38,7%, for „old“ STN is 37,6%. From comparison of soils with better and worse properties by design procedures we found out percentual difference for „new STN“ 8,1%, for EN 7,DA1 (C1) 25,86%, for EN 7,DA1 (C2) 20,1%, for EN 7, DA2 27,4%, for EN 7, DA3 21,12% and for „old“ STN 24,24%. In table 3 we can see comparison of design procedures for homogeneous subsoil and design procedures for layered subsoil. By design procedures for layered subsoil is size of the foundation around 5% larger in comparison with design procedures for homogeneous subsoil and for this case. We can see comparison size of foundation for homogeneous subsoil and layered subsoil. 5. Conclusion The fact, that shear strength parameters have significant effect on size of foundation. Standardized values of shear strength parameters included in the STN 73 1001 have large range and we give significant differences size of
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foundation. Design procedure for inhomogeneous subsoil which including form slip surface is more accurate as design procedures for homogeneous subsoil. Therefore is properly to made geotechnical investigation report to obtain as accurate shear strength parameters as possible, in order to not design an excessive spread foundation, what significantly impact on economic of the structure. References [1] L. Trevor, L. Orr., Model solutions for Eurocode 7 Workshop Examples. Ireland, Trinity Colleg, Dublin University, 2005. [2] STN EN 1997-1: Geotechnical design. Part 1: General rules. (in Slocak language). Bratislava: Slovak Standards Institute, Slovak Republic, 2005. [3] STN 73 1001: Geotechnical structures. Foundation ( in Slovak language). Bratislava: Slovak Standards Institute, Slovak Republic, 2010. [4] J. Frankovská, M. Suľovská, P. Turček, Zakladanie stavieb. Podklady k navrhovaniu, plošné a hĺbkové základy. Vydavateľstvo STU, 2011. [5] STN 73 1001: Foundation of structures. Subsoil under shallow foundation ( in Czech language). Prague: Institute for Standardizations and Measurements, Republic of Czechoslovakia, 1987. [6] G. Nguyen, Designing spread foundation by Slovak Technical Standard STN 73 1001 and Eurocode 7. Teoretical Foundation of Civil Engineering, XX. Polish - Russian – Slovak Seminar, Žilina 2011.
