Order nr : 14284 Location : Rhoon Project : Study on the effectiveness of the TOAD on horizontal stability of lighting poles te RHOON Commisioner : PowerCast b.v. T.a.v. Dhr. E. Raaijmakers Eerschotsestraat 37 5491 AA SINT OEDENRODE NL Author : R.J. Schippers B.Sc. Civ.Eng (+31 1-5 3 246) Report number : R14284-RH_2 Date : 13 januari 215 MOS GRONDMECHANICA B.V. Rhoon Kleidijk 35 Postbus 81 316 AA Rhoon Tel. 1-532 Helmond Kanaaldijk N.O. 14a Postbus 38 57 AA Helmond Tel. 492-535455 Rijssen Kalanderstraat 1a Postbus 153 746 AD Rijssen Tel. 548-512363 Amsterdam Gyroscoopweg 12-142 AZ Amsterdam Tel. 2-7537984 Maastricht Sleperweg 18 Postbus 28 624 AA Bunde Tel. 43-3653153 Suriname Ds Martin Luther Kingweg 15 District Wanica - Suriname Tel. +597-488188
Order nr : 14284 Location : Rhoon Content Pagina 1. INTRODUCTION... 3 2. ELABORATION ON FINITE ELEMENT CALCULATIONS IN SOIL... 4 3. DETERMINATION OF THE PROCEDURE AND SCOPE... 5 4. SOIL AND MATERIAL PROPERTIES... 7 5. SUMMARIZED RESULTS OF FINITE ELEMENT CALCULATIONS... 8 5.1 general... 8 5.2 Summary of results post 12 mm... 8 5.3 Summary of results post 145 mm... 9 5.4 Summary of results post 165 mm... 9 5.5 Summary of results post 2 mm... 1 5.6 Summary of results post 226 mm... 1 5.7 Summary of results post 25 mm... 11 5.8 Analysis of the results... 11 ANNEX A ANNEX B ANNEX C Results Triaxial test on weak soil Copy of table 2B of NEN 9997-1 (Dutch language) Deformed meshes calculations pole 2 mm
- 3-1. INTRODUCTION Commissioned by PowerCast b.v. Mos Grondmechanica b.v. has performed Finite Element calculations to investigate the effectiveness of one of the products of the commisioner, the TOAD. The TOAD is an enhancement to improve horizontal stabilty of lighting poles. Lighting poles are often placed in adverse circumstances and even though the design is specified in Eurocodes (EN 4) there are many known cases of lighting poles that undergo significant horizontal deformation by wind loads. The aim of these calculations is to establish the effectiveness of the TOAD by performing multiple series of standardised calculations under different circumstances. EN 4 gives minimal, average and maximal installation depths for planted lighting columns for different heights. By calculating comparable geometries with and without TOAD the effectiveness can be determined efficiently and reliably. Based on experience, Mos has determined a dataset for Finite Element calculations that should be categorised as 'poor soil'. More details about the soil parameters are given in chapter 4. The commisioner is technically advised by Sapa Pole Products b.v. which was represented by Mr. B. van Boxtel. SAPA has provided us with a matrix of standard dimensions of lighting poles that needed to be investigated. More details of the scope and the specifics of the calculation matrix are given in chapter 3. Pictures of the TOAD are presented in figure 1-1 and 1-2. Figure 1-1 Picture of TOAD Figure 1-2 Drawing of TOAD components (dimensions 1, x 1, x,25m)
- 4-2. ELABORATION ON FINITE ELEMENT CALCULATIONS IN SOIL Soil behaviour, by definition is complicated because of a non lineair behaviour and the geological origin of the material. Stresses and strains in soil are dependant of several factors. Behaviour is strongly influenced by circumstances such as depth and saturation with groundwater. In order to be able to deal with these circumstances software is available in which these conditions are modeled in a proper way. Worldwide the Finite Element program Plaxis is mostly used. In the program several different soil models are available to model different types of soil behaviour. Modelling of consolidation effects for instance ask for a different approach than static loading effects. The program has two main versions, a 2D model and a 3D model. The 2D model is used for plain strain conditions and may be used to calculate i.e. reatining structures in which stress redistribution by arching effects in the soil aren't governing the results. With the 3D version more sophisticated problems in which arching effects have a severe impact on the outcome of the calculations can be investigated. Needless to say that in this case the 3D version is used. The program is also able to model structural elements with lineair elastic behaviour. The structural behaviour of the aluminum lighting posts therefore is also modeled in the correct way. Finally by activating a static horizontal load at half the lighting post height and deactivating it afterwards, the effect of loading and unloading of the post is modelled in a proper way and bending of the post itself is excluded from the comparisson. Soil behaviour in saturated conditions (undrained behaviour) for short term loading is far more complex than now taken into account in the model. Furthermore wind is a dynamic and more or less harmonic load case. For the estimation of the effectiveness of the TOAD this is of less importance at this stage.
- 5-3. DETERMINATION OF THE PROCEDURE AND SCOPE In order to produce a complete series of calculations a general soil volume of 12 x 8 x 5 m was defined. The properties of this soil volume are constant in all calculations. The program is able to define a general watertable at different depths, so no significant model changes need to made for saturated and unsaturated conditions. The exact dimensions of the TOAD of 1, x 1, x,25 m (including the 45mm hole and a ring shaped volume for the filling material Gneiss 8/4) have been determined in the model and by giving these volumes soil properties or lineair elastic properties the TOAD can be active, or not. An general impression of the model is given in figure 3-1. A picture of the modelling of the TOAD and pole (with the surrounding soil made invisible) is given in figure 3.2. Figure 3-1 General impression soil model Figure 3-2 Model with TOAD and pole (soil made invisible)
- 6 - There are 6 standard dimensions for the lighting poles given by SAPA, varying from 12 mm up to 25 mm. Standard wall thickness for the different diameters is also given. Based on En 4 (part 2) the planting depth is determined for average conditions, which is commonly used by most manufacturers. Furthermore, the height of the columns for each diameter is given. Finally, the ultimate structural resistance (Mu) for each column is given. The load is imposed on the poles at half the lighting height. The poles are loaded up to their structural capacity in three equal increasing loading stages. At 1% F hor the imposed horizontal load equals the ultimate bending capacity of the pole material. This information is summarised in table 3-1. Table 3-1 Summary of information of Poles Diameter Thickness Mu Height Depth F hor (at half height) 33% 67% 1% [mm] [mm] [knm] [m] [m] [kn] [kn] [kn] 12 3, 6,77 6, 1,,75 1,5 2,26 145 3, 9,32 8, 1,2,78 1,55 2,33 165 3,3 13,1 1, 1,5,87 1,75 2,62 2 3,3 18,1 12, 1,7 1,1 2,1 3,2 226 3,3 22,26 14, 2, 1,6 2,12 3,18 25 4, 34,2 15, 2, 1,51 3,2 4,54 All pole diameters have been calculated in dry and saturated conditions. In dry conditions, the groundwatertable is placed at 4 m below the surface and in saturated conditions the watertable is placed at,25 m below the surface (at the bottomlevel of the TOAD). All pole diameters are calculated with and without the presence of the TOAD, so the effectiveness of the TOAD can be evaluated. Since the TOAD proved to be quite efficient, more calculations were performed in which the planting depth of the pole is reduced. The planting depth has been decreased with succesively 15%, 3% and 45%. These calculations (obviously all of them with TOAD) have been performed for dry and saturated conditions. In total for each diameter 1 calculations have been performed. The calculations have been named in a certain structure, starting with the diameter of the pole, followed bij an index A through J. Finally, a calculation with sand is performed for the dry and saturated situation without TOAD for reference, because this is probably the most common environment for current poles in the field.. The meaning of the used indices used is given below: A clay, dry conditions without TOAD full planting depth B clay, dry conditions with TOAD full planting depth C clay, saturated conditions without TOAD full planting depth D clay, saturated conditions with TOAD full planting depth E clay, dry conditions with TOAD planting depth 15% F clay, dry conditions with TOAD planting depth 3% G clay, dry conditions with TOAD planting depth - - 45% H clay, saturated conditions with TOAD planting depth 15% I clay, saturated conditions with TOAD planting depth 3% J clay, saturated conditions with TOAD planting depth 45% K sand, dry conditions without TOAD full planting depth L sand, saturated conditions without TOAD full planting depth
- 7-4. SOIL AND MATERIAL PROPERTIES Based on experience we have determined a parameterset for soil that can be categorised as 'poor'. The Netherlands are famous for their weak soil conditions. This obviously has to do with the fact that we are in Delta environment in which many geological formations have been formed by sedimentation of rivers that flow through our country. Furthermore many geological formations were formed by natural materials, such as leaves and cane. Most weak soils have a high percentage of organic material (humus), which makes it rather compressible and gives low strentgh properties. We have taken a sample from a laboratory investigation where a triaxial test was performed on a weak soil sample and taken the finite element parameters from this test. This type of soil is very common, especially at low depths beneath the surface and therefore is found alongside many roads throughout the country. It is therefore (to our opinion) representative for adverse soil conditions or 'poor soil'. The results of the triaxial test are given in Annex A. The finite element parameters that were used are given in table 4-1. Table 4-1: Finite element parameters Layer Model type Grondslag γ dry /γ sat [kn/m³] E' [KN/m 2 ] E oed [KN/m 2 ] c' [KN/m 2 ] ϕ' [ ] 1 MC Organic Clay 14/14 3, e3 3,33 e3 3, 22,5 2 MC Gneiss 21/21 1, e5 1,11 e5, 35, 3 LE Concrete 23/23 3,85 e7 n/a n/a n/a 4 MC Sand 18/19 1, e4 1,11 e4,1 3, MC Mohr Coulomb model LE Lineair Elastic model The dutch version of the Eurocode (NEN 9997-1) gives directives on soil parameters to be used for geotechnical engineering purposes. Table 2B is used for situations where no extensive soil investigation is available. These are relatively conservative parameters. In order to place the used parameters in the range of specific soil conditions that are present in NL a copy of Table 2B is given in Annex B. Volumetric weight, E-modulus, cohesion and friction angle are given in this table. Soil parameters for specific locations are normally established by performing cone penetration tests in situ and using correlations for deducing Finite Element parameters. This can also be done by taking undisturbed soil samples from a borehole which are tested in a geotechnical laboratory, but this is more time consuming and expensive. The posts are modelled by creating circular plates with the actual wall thickness that was provided by SAPA and strength properties of Aluminum (weight 27,5 kn/m 3, Elastic modulus 7, e 7 kn/m 2 ). NOTE: In order to prevent stuctural collapse of the post under maximum loading a 1 times higher Elastic modulus (7, e 8 kn/m 2 ) is used in the calculations as discussed and agreed with the commisioner. This has some influence on the elastic behaviour of the pole, while loaded, but a minor impact on the interaction between the soil and the post (or the post and the TOAD) after unloading. This has been verified by a calibration calculation.
- 8-5. SUMMARIZED RESULTS OF FINITE ELEMENT CALCULATIONS 5.1 general The loading of the different post diameters actually seems to fit the circumstances quite well. In most calculations an acceptable amount of horizontal deformation occurs without causing collapse of the soil body. The program iterates through a numer of calculation steps untill stress redistribution reaches an equilibrium. In most cases equilibrium is reached in the predetermined number (1) of steps. In some cases the predfined number of load steps (1 steps) is insufficient to reach equilibrium and (too) large deformations already have occured. The most significant results of the calculations are presented for each diameter in the next paragraphs. The maximum deflection at half the lighting point height is determined and based on this the slope of the deflection is determined. Calculations that did not reach equilibrium are indicated in a red box in stead of a green box. In Annex C the deformed meshes for one complete series of calculations for one pole diameter are presented for further reference. 5.2 Summary of results post 12 mm D = 12 mm F = 2,26 kn L = 6, m ID DEFLECTION,33 F,67 F 1, F [deg] [deg] [deg] 14284 12 A,5 5,2 29, 14284 12 B,1,3,8 14284 12 C,7 7,9-14284 12 D,1,4 1,1 14284 12 E,3 1,4 3,8 14284 12 F,6 3,1-14284 12 G 3,4 - - 14284 12 H,4 1,9 5,3 14284 12 I,8 4, - 14284 12 J 3,8 - - 14284 12 K,4 3, 17,1 14284 12 L,6 5,9 31,8
- 9-5.3 Summary of results post 145 mm D = 145 mm F = 2,33 kn L = 8, m ID DEFLECTION,33 F,67 F 1, F [deg] [deg] [deg] 14284 145 A,5 5,5 35,7 14284 145 B,1,3,8 14284 145 C,8 9,3-14284 145 D,1,5 1,2 14284 145 E,1,7 2,1 14284 145 F,4 2,1-14284 145 G,5 2,6-14284 145 H,2 1,1 3,2 14284 145 I,5 3, - 14284 145 J,7 3,4-14284 145 K,3 2,9 15,1 14284 145 L,5 5,9-5.4 Summary of results post 165 mm D = 165 mm F = 2,62kN L = 1, m ID DEFLECTION,33 F,67 F 1, F [deg] [deg] [deg] 14284 165 A,2 1,6 7,3 14284 165 B,,1,3 14284 165 C,3 2,9 16, 14284 165 D,1,2,6 14284 165 E,1,2,7 14284 165 F,1,4 1, 14284 165 G,2 1,1 3,4 14284 165 H,1,4 1,2 14284 165 I,1,6 1,6 14284 165 J,3 1,6-14284 165 K,1,7 3, 14284 165 L,2 1,5 8,5
- 1-5.5 Summary of results post 2 mm D = 2 mm F = 3,2 kn L = 12, m ID DEFLECTION,33 F,67 F 1, F [deg] [deg] [deg] 14284 2 A,1,9 3,5 14284 2 B,,1,2 14284 2 C,2 1,7 7,3 14284 2 D,,2,4 14284 2 E,,2,6 14284 2 F,1,5 1,7 14284 2 G,4 2,6-14284 2 H,1,4 1,1 14284 2 I,2,9 3,1 14284 2 J,6 4,5-14284 2 K,1,4 1,3 14284 2 L,1,7 2,5 5.6 Summary of results post 226 mm D = 226 mm F = 3,18 kn L = 14, m ID DEFLECTION,33 F,67 F 1, F [deg] [deg] [deg] 14284 226 A,,4 1,4 14284 226 B,,1,1 14284 226 C,1,8 3,1 14284 226 D,,1,3 14284 226 E,,1,3 14284 226 F,1,2,9 14284 226 G,1,5-14284 226 H,,2,6 14284 226 I,1,5 1,7 14284 226 J,2,9-14284 226 K,,2,5 14284 226 L,,3 1,
- 11-5.7 Summary of results post 25 mm D = 25 mm F = 6,49 kn L = 15, m ID DEFLECTION,33 F,67 F 1, F [deg] [deg] [deg] 14284 25 A,1 1,3 6,2 14284 25 B,,1,5 14284 25 C,3 3, - 14284 25 D,1,3 1,1 14284 25 E,1,3 1,4 14284 25 F,1 1, 7,2 14284 25 G,6 13,5-14284 25 H,1,6 3,8 14284 25 I,2 2, - 14284 25 J 1, - - 14284 25 K,1,5 1,9 14284 25 L,1 1,2 5,5 5.8 Analysis of the results From the calculation results it is quite clear that the TOAD has a profound impact in the lateral behaviour of the lighting pole. In the calculation the most adverse soil conditions suitable for lightpole foundations have been modelled. In all cases the deformation of the lighting poles that are statically loaded up to their structural capacity significant raking of the poles occurs. In order to establish the effectiveness of the TOAD, Mos has suggested to perform Finite Element Calculations with the program Plaxis 3D. Plaxis is known all over the world and utilised daily for advanced modeling of geotechnical issues. Based on the experience of Mos Grondmechanica soil properties of weak soil (as can be found in the Netherlands) have been established. With this set of soil parameters the behaviour of a range of pole diameters with heights varying from 6 to 15 m have been analysed. This was done systematically by creating multiple models in which the conditions vary. In the calculations the actual measurements and strength behaviour of the Aluminum posts is modeled. The stiffness behaviour is increased by a factor 1 as stated earlier. The commisioner has provided us with a matrix of diameters, pole heights and planting depth, based on the directives of EN 4. Furthermore this matrix gives the ultimate structural capacity (Mu) of the different pole diameters. The TOAD itself (including the Gneiss) is geometrically modeled in the calculation by creating a volume with the actual size of the TOAD. In each calculation the properties of this volume can be chosen as soil (to calculate without TOAD) or the actual properties of the concrete block (to calculate with TOAD). In each calculation a horizontal static load is imposed on the pole at half the lighting column height in three equal loadstages. The ultimate horizontal load equals the ultimate structural capacity of the
- 12 - pole. After each loading step the load is removed to determine the residual deformation of the pole, thereby excluding the bending of the pole. By calculating the same geometry in 4 different conditions (unsaturated soil, saturated soil, without TOAD and with TOAD). the results enable a very good insight in the effectiveness of the TOAD. Finally additional calculations have been performed to establish the behaviour for a combination of utilising the TOAD with less planting depth by decreasing planting depth with 15%, 3% and 45%. The calculations indicate that for each pole from 6 to 15 m, even in very weak soil conditions the effectiveness of the TOAD is very high. In the most adverse soil conditions suitable for lightpole foundations (weak, saturated clayey soil) the installation of a TOAD reduces horizontal deformation of a pole by at least a factor of 5 to 6. That means installation of a TOAD will reduce horizontal deformation with at least 8%. For all calculated poles the installation in saturated clay with a TOAD is more stable then normal planted poles in dry clay or even in sand (without TOAD). The calculations show that the planting depth according to EN 4 for the poles with a small diameter is not ideally suited for each diameter post. If an overall safety factor on the loading is assumed, each pole should perform well up to 67% of the structural capacity of the post. In some cases this load already leads to a raking of more than 3 degrees (12 mm and 145 mm) and in some cases not (165, 2, 226 and 25 mm). When a TOAD is placed the raking reduces, mostly resulting in a raking of less than 1 degree. We assume 3 degrees should be a maximum allowed visual situation for a lighting column. As an example the results for a comparable situation with and without TOAD the results after unloading from the highest loading stage of pole 226 mm are shown in figure 5-1 and 5-2. Figure 5-1 unload from 1,F Figure 5-2 unload from 1,F Pole 226 mm without TOAD Pole 226 mm with TOAD Without TOAD the pole has a maximum horizontal displacement of 37,9 cm. With TOAD the horizontal displacement is reduced to 3,3 cm, which means a reduction of approximately 9 % of the original displacement.
- 13 - The calculated deformations of the TOAD itself at the end of the loading stage that corresponds with figure 5-2 is shown in figure 5-3. Figure 5-3 displacements TOAD The calculations show also that the deformations of the TOAD itself are very small and that the components of the TOAD are able to cope with the stresses that are imposed by static loads up to the structural capacity of the posts. The vertical deformation of the TOAD is negligable. Because the TOAD is placed just below the surface the extra weight (that may cause vertical consolidation settlement) is merely the difference between the weight of the original soil and the weight of the TOAD. We have performed additional calculations for a situation with better soil conditions, namely in sand. The results of the calculation is a comparable, if not even higher improvement of the stability of the lighting poles. Since these calculations were not part of the original scope of this study, the graphic results are not shown in Annex C. The results only appear in the summary of results (see ch. 5.2 5.7). R.J. Schippers B.Sc. Civ.Eng (+31 1-5 3 246) Rhoon, 13 januari 215 Mos Grondmechanica B.V. Contr. : g.s.
ANNEX A Result triaxial test on weak soil
ANNEX B Copy of Table 2B NEN 9997-1
Dit document is door NEN onder licentie verstrekt aan: / This document has been supplied under license by NEN to: MOS Grondmechanica R.Schippers@mosgeo.com 13-1-215 14:52:51 NEN-EN 1997-1+C1:212/NB:212 Tabel 2.b Karakteristieke waarden van grondeigenschappen Grondsoort Karakteristieke waarde a van grondeigenschap Hoofdnaam Bijmengsel Consis- tentie b γ c γsat qc d g Cp g Cs Cc/(1 + e) g C f Csw /(1 + e) g E1 g h ϕ g c cu kn/m 3 kn/m 3 MPa [-] [-] [-] MPa Graden kpa kpa Grind Zwak siltig Los Matig Vast Sterk siltig Los Matig Vast Zand Schoon Los Matig Vast 17 18 19 2 18 19 2 21 17 18 19 2 19 2 21 22 2 21 22 22,5 19 2 21 22 15 25 3 1 15 25 5 15 25 5 1 12 14 4 6 1 15 2 6 1 15,46,23,19,16,58,38,23,15,115,38,23,15,15,8,6,5,19,13,8,5,38,13,8,5 45 75 9 15 3 45 75 11 15 45 75 11 32,5 35, 37,5 4, 3, 32,5 35, 4, 3, 32,5 35, 4, n.v.t. n.v.t. n.v.t. Zwak siltig, kleiig 18 19 2 21 12 45 65,51,35,17,12 35 5 27, 32,5 n.v.t. Sterk siltig, kleiig 18 19 2 21 8 2 4,115,58,38,19 15 3 25, 3, n.v.t. Leem e Zwak zandig Slap Matig Vast 19 2 21 22 19 2 21 22 1 2 3 25 45 7 1 65 13 19 25,92,511,329,23,37,2,13,9,37,17,11,77 Sterk zandig 19 2 19 2 2 45 7 13 2.511,329,2,13,17,11 3 5 27,5 35, 1 5 1 Klei Schoon Slap Matig Vast Zwak zandig Slap Matig Vast 14 17 19 2 15 18 2 21 14 17 19 2 15 18 2 21,5 1, 2,,7 1,5 2,5 7 15 25 3 1 2 3 5 8 16 32 5 11 24 4 6,3286,1533,92,767,23,115,767,46,131,61,37,31,92,46,31,18,195,511,37,256,767,383,256,153 2 3 5 7 1 2 4 1 1,5 3 5 1 27,5 27,5 27,5 3, 32,5 35, 17,5 17,5 17,5 25, 22,5 22,5 22,5 27,5 Sterk zandig - 18 2 18 2 1, 25 14 32 168,92,164,37,7,37,55 2 5 27,5 32,5 1 1 Organisch Slap Matig 13 15 16 13 15 16,2,5 7,5 1 15 3 4 6,367,23,1533,153,115,77,122,767,511 Veen Niet voorbelast Slap 1 12 1 12,1 5 7,5 2 3,46,367,23,153,1533,122,2,5 15, 1 2,5 1 2 Matig voorbelast Matig 12 13 12 13,2 7,5 1 3 4,367,23,153,115,122,767,5 1, 15, 2,5 5 2 3 Variatiecoëfficiënt v,5,25,1,2 Zie vervolg,5 1, 2, 15, 15, 1 2,5 3,8 5 13 15 5 13 15 1 1 5 1 2 3 25 5 1 2 4 8 12 17 1 25 3 29
f Dit document is door NEN onder licentie verstrekt aan: / This document has been supplied under license by NEN to: MOS Grondmechanica R.Schippers@mosgeo.com 13-1-215 14:52:51 NEN-EN 1997-1+C1:212/NB:212 Tabel 2.b (einde) a b De tabel geeft van de desbetreffende grondsoort de lage, respectievelijk de hoge karakteristieke waarde van gemiddelden. Binnen een gebied, gedefinieerd door de rij van het bijmengsel en de kolom van de parameter (een cel), geldt: als een verhoging van de waarde van een van de grondeigenschappen tot een ongunstiger situatie leidt dan de toepassing van de in de tabel gepresenteerde lagere karakteristieke waarde, moet de rechterwaarde op dezelfde regel zijn gebruikt. Is er rechts geen waarde vermeld, dan moet de waarde er rechtonder zijn toegepast; OPMERKING Dit is bijvoorbeeld het geval bij negatieve kleef op een paal waar een hogere waarde van, c en cu ook een hogere waarde van de negatieve kleef oplevert. voor Cc/(1+e), C en Csw/(1+e) zijn in de tabel de hoge karakteristieke gemiddelde waarden vermeld. Los: < Rn <,33 Matig:,33 Rn,67 Vast:,67 < Rn < 1, De γ -waarden zijn van toepassing bij een natuurlijk vochtgehalte. De hier gegeven qc-waarden (conusweerstand) behoren beschouwd te worden als ingang in de tabel en mogen niet in de berekeningen worden gebruikt. De waarden hebben betrekking op verzadigde leem. De C-waarden zijn geldig voor een spanningverhogingstraject van ten hoogste 1 %. c d e g h Voor grind, zand en in beperkte mate ook voor leem en sterk zandige klei zijn qc, E1, ϕ en de samendrukkingsparameters Cp, Cc/(1+e) en Csw/(1+e) genormeerd voor een effectieve verticale grondspanning v van 1 kpa. Om voor de in het terrein gemeten waarden van qc een juiste ingang in de tabel te krijgen, moeten deze waarden zijn geconverteerd naar het niveau van de effectieve verticale grondspanning v van 1 kpa. In dat kader moet de formule qc;tabel = qc;terrein Cqc worden gebruikt, waarbij Cqc moet zijn ontleend aan Cqc = (1/ v),67. Voor de hoek van inwendige wrijving en de cohesie c geldt dat deze afhankelijk zijn van de consistentie van de grond. Dit betekent dat deze conversie ook nodig is voor en c. Als qc;tabel groter wordt dan de in de tabel gegeven waarde geldt de onderste regel voor de desbetreffende grondsoort. 3 De elasticiteitsmodulus bij belastingsherhalingen mag zijn aangenomen als zijnde driemaal de aangeven waarde. VOORBEELD In schoon zand op een diepte van 5 m onder water is gemeten: qc;terrein = 9 MPa en v = 5 kpa. Uit de formule voor Cqc volgt dan Cqc = 2,67 1,6. Volgens de formule voor qc;tabel geldt dan in dit voorbeeld qc;tabel = 9 1,6 = 14,4 MPa. Dit betekent dat E = 45 MPa, ϕ= 32,5 graden, Cp = 6, Cc /(1+e)=,38 en Csw/(1+e) =,13.
ANNEX B Deformed meshes for calculations pole 2 mm
Calculation Results: 14284-2-A Deformed Mesh
Calculation Results: 14284-2-B Deformed Mesh
Calculation Results: 14284-2-C Deformed Mesh
Calculation Results: 14284-2-D Deformed Mesh
Calculation Results: 14284-2-E Deformed Mesh
Calculation Results: 14284-2-F Deformed Mesh
Calculation Results: 14284-2-G Deformed Mesh
Calculation Results: 14284-2-H Deformed Mesh
Calculation Results: 14284-2-I Deformed Mesh
Calculation Results: 14284-2-J Deformed Mesh
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