Advanced Soil Mechanics, Study notes of Soil Mechanics and Foundations

Download Advanced Soil Mechanics and more Study notes Soil Mechanics and Foundations in PDF only on Docsity! Advanced Soil Mechanics Stefan Van Baars © Edited and published by Stefan Van Baars. Edition May 2016 Key words: soil mechanics, foundation engineering, tunnelling 11.2 Old Austrian Tunnelling Method or Old OTM. 11.3 New Austrian Tunnelling Method or NOTM 12 Immersed tunnel 12.1 Construction method 12.2 Chin-nose and jack-leg suppo: 12.3 Advantages and disadvantages. 13 Jacked box tunnel! THT SHALLOW FOUNDATIONS .........cccssscscsssssessececeseterssesseeees OS 14 Types of shallow foundations...........cccsscsssessssessssssssscsssssssssssssssssssssssssssssenesesssssenesees 66 15 Elastic stresses and deformations ..........ccccssesssssssseseeseseseseseseseseseseeeeeeeeeeseeeeeseeeeeee 68 16 17 18 Deformation of layered soil. 19 Bearing capacity of a strip footing. 1 19.1 Lower bound 2 19.2 Upper bound . 84 20 Prandtl & Nesssesersssssssssssssssecssnsssessssesnsesssssssssssssscssssssssssesnsessssessssssnsnsessssssesseensnsessees 86 21 Reissmer & Ng.sesssssssscscssssesssssssnenencasssencncnseseseassneneneeceseasassneneneesesessarsneneneeseeseansneneneeses 89 22 Meeyerhof & Ny ....ssssssssesecesssssssssescececeseseseeeseseseeeeeneeenenenenenenenseseseseseseseaeaeseaeeeeeeeeeeeeeeeees 90 23 Table of the bearing capacity factors .......cssscccssesscscsssescsscsssessessessssesessessssesesceseees 91 24 Correction factors ... 24.1 Inclination factors 24.2 Shape factors s ... 25 CPT, undrained shear strength and Prandtl ............sssssssscscssecesesesescseseeeeeeeeeeeeeeeeeeee 95 TV — PILE FOUNDATIIONG..........cccccsssssssssscsossesssssecesneecessseseeeeee 07 26 Cone Penetration Test (CPT)........ccsessssscsssssscssssssscssscssssssssscssssesssccssssessssessssesssseseees 98 27 Compression piles 27.1 Pile types... 27.2 Bearing capacity... 27.3 CPT, SPT and HDP 27.4 Tip resistance using Meyerhof (Prandtl, Terzaghi or Brinch Hansen) 27.5 Tip resistance using a CPT method (Koppejan) 27.6 Shaft resistance............ seeeeeseseeeeeeeeseseaee 27.7 Settlement of piles 28 Tension piles 28.1 Differences 28.2 Reduction of the cone value g, due to excavation. 120 28.3 Reduction of cone resistance due to tensile pile force 121 28.4 Clump criterion 122 28.5 Edge Piles 123 28.6 MV-pile or Jacket-grouted pile ..........ccccccecececeeeeeeecececscscseseseeeesesssssssssesterererere L23 V UNDERGROUND MEGASTRUCTURES 29 Underground megastructures 30 Sustainable resources VI —_ BUILDING PIT 1.00... eesecssssssssececesnseresssrssesssceeesetesesssreees LST 31 Building pit ..........ccccscsssessesssseessseesesncssesssneesesssncessesesseassnessesnsseeacsneseeassneescaneseeseeneeees 31.1 Introduction + 31.2 Pit collapse .. 31.3 Pit design. VIL WALLS AND LATERAL STRESS .........cccccsssssssssseseeeeeeee 137 32 Walls 32.1 Wall typ 32.2 Soldier pile wall (Berliner wall) . 32.3 Sheet pile wall 32.4 Combi wall .... 32.5 Bored pile wall .. 32.6 Diaphragm wall . 33 Lateral stresses in soils 33.1 Coefficient of lateral earth pressure 33.2 Elastic material .............000 + 33.3 Elastic material under water .......c.cccccsescececesseseesscecscscsesesessessssseseseseseeeerreseseseee 34 Rankine 34.1 Mohr-Coulom| 34.2 Active earth pressure 153 34.3 Passive earth pressure 154 34.4 Neutral earth pressure .. 156 34.5 Menard-penetrometer and CAMKO-pressuremete 156 34.6 Groundwater.. 157 35 Coulomb 35.1 Active earth pressure ... 35.2 Passive earth pressure .. 36 Tables for lateral earth pressure. 36.1 The problem 36.2 Example ...... + 36.3 Tables ......cceccceseceseseeeseeeeesseseseseseseesesssesesececesceecesscscscscsesesensnsnssssavaessseeeerenesesereee 37 Sheet pile walls 37.1 Homogeneous dry soil . 37.2 Pore pressures........... 38 BIUM.......cccsessssensseesecesessensnensnseseseseseseseseseseeeeeeeeseeeseeeeeeeeeeeeenenenensaenensaeeseseseseseseseseees 39 Sheet pile wall in layered soil 39.1 Computer program .. 39.2 Computation of anchor plate 39.3 Horizontal bedding constant 39.4 Finite Element Modelling 39.5 Example quick design...... 40 Sheet pile profiles ...........ssssssssssssssssesesesesessssessseseeeeeseeeeeeeeeeenenenensnenenenseseseseseseseseseaeeee VIIT ANCHORS, STRUTS AND WALES .........cccccccssssseeeoeseees LOT 41 Supports 42 Anchors. 42.1 Anchoring 42.2 Anchor installation 42.3 Soil nailing......... 42.4 Holding capacity of anchor plate 42.5 Holding capacity of a grouted anchor 42.6 Overall stability ........ eee 43 SHruts .....cccccscesececeseseseseseeseseseseseseseseseseseceeseeeneeseeceeeeseneeenenenenenensnenensaseseseseseseseseaeaeeee FA WAIES w...csssecesseseceseseseseseseeesesesesesesesesesesesesesceeeeeeeeeseeeeeeeeeeenenenenenensnenenseseseseseseseseseaeeee 45 Floatation & Archimedes..........csscsesesesssscsenssseseseeeeeeceeeenceeneneneneneneneeseseseseseseseseaeees 214 46 Natural floor & heave ........sesesesesesesesesseceesseesseseeeseeeececeeeceenenenensnenenensnseseseseseseseseaeees 215 47 Unsupported under water concrete fl00r ........csssceeensnesnensnenenesseseseseseseseseseaeeee 216 48 Supported under water concrete floor 48.1 General... ” 48.2 Floatation of the floor 48.3 Transfer of forces to piles & fracture of the pile joint 48.4 Fracture of the floor X GLOBAL STABILITY & FAILURE..........ccccscsssesssseseees 225 49 Failure modes 50 Global translation (sliding) . 51 Global rotation (circular sliding 51.1 Safety factor 51.2 Fellenius 51.3 Bishop... + 51.4 Global failure wo. ceseseesesesesessesescesesesessssscscetesesnssssseseeesesnssnsseseeseseses 234 XI DEWATERING 52 Groundwater flow 52.1 Hydrostatics 10 | Soil improvement il 1 Introduction Soil mechanical engineering is just like other fields of engineering the control of the strength, stiffness or conductivity, which means the control of the stresses, strains and permeability. Sometimes geotechnical tools like piles, anchors, walls and geotextiles can be optimised or even avoided when the soil would has had a higher strength, stiffness, permeability or a combination of these. There are many different ways of improving the strength, stiffness or permeability of the ground. The following chapters will discuss the following options: 1. Aww Mechanical densification Injection techniques Dewatering & drains Ground freezing Geotextiles Ground exchange These techniques will be used when the extra cost of using them is less than the extra cost, which would have to be accepted for extra use of geotechnical tools due to the bad soil conditions. 12 2.2 In-depth compaction At deep compactions, depths of more than about 2 m are compacted, which cannot be reached with the surface compaction techniques mentioned before. For soft soils and deep compaction still very heavy impact slabs can be used: 1) One can drop weights of 15 to 30 tons from 30 m high, with a fixed number of drops. 2) After that the crater is filled with appropriate ground (sandy, not clayey soil) 3) After that the steps 1) and 2) can be repeated. Figure 2-6. In-depth impact compaction. (Picture: Briichner Grundbau) But for sandy soils another technique is used, based on long vibrating needles. These are put in the ground with the help of their own weight, the vibrations, and sometimes also water injection. Most needles are about 30 to 40 cm thick, 3 to 4,5 m long and weigh between 1,5 and 3 tons. The frequencies of the horizontal vibrations are mostly between 30 and 60 Hz. Because of the vibrations, these techniques should not be used near existing buildings. 15 Figure 2-7. Vibration needles, with water injectors at the tip. (Photo: BIUG eotechnik) For sandy soils, this vibration technique, with or without water injection, works fine. For clayey soils, one cannot decrease the amount of pores, but one can increase the strength, stiffness and permeability (for drainage to speed up the consolidation), by vibrating gravel or small stones into the ground. rittler Figure 2-8. Vibrator (Riittler) in sandy soils and gravel (Schotter) injection in clayey soils. 16 3 Injection techniques Injection techniques are techniques in which mixtures of materials are injected under pressure in the pores and other open spaces of the underground in order to decrease the permeability or to increase the strength and/or stiffness. One needs large injection pipes and large machines for this. Figure 3-1. Injection pipes and machinery. There are several grouting techniques: a) Permeation grouting: a very fluid liquid grout (water and cement) is injected in the pores (of mostly sand) to make it more impermeable and stronger. b) Jet-grouting: Soil is mixed with a powerful grout beam. The beam is rotated to make columns or walls. c) Fracture-grouting: a very fluid liquid grout (water and cement) is injected with high pressure in order to create horizontal cracks (unfortunately mostly vertical cracks appear). The horizontal cracks are made for compensating settlements.. d) Compaction Grouting: Very stiff grout is blown up like a balloon in order to compensate settlements. Figure 3-2. Grouting techniques. 17 There is a risk in jet-grouting. The grouting tubes are never installed exactly at where the design requires. Also these tubes are never installed fully perpendicular. Due to this, the centres of the columns are never as designed. Also the radiuses of the columns are never exactly as designed. This can cause small leaks in the grouted floor, which are very difficult to locate and to repair. A famous case is the tunnel under the Big Market Street in Den Hague in the Netherlands, where this problem caused major problems. The final, very time and money consuming method, was to install air-locks and seal off the whole tunnel, pushing out the ground water and repairing the leaks, all under air-pressure. Figure 3-8. Designed (left) and constructed (right) grout floor with leak. 3.3. Fracture grouting Fracture grouting is mainly used for lifting buildings, which have settled too much. This mostly happens due to insufficient deep constructed shallow foundations and settlements caused by excavations like building pits and tunnels. The grout pressure should be far more than the vertical pressure at that particular level in the ground. Figure 3-9. Fracture grouting (Pictures Hayward Baker, USA). 20 3.4 Compaction grouting The technique of compaction grouting is, just as fracture grouting, mostly used for improving shallow foundations. Figure 3-10. Compaction grouting (Picture Hayward Baker, USA). Both the fracture grouting and the compaction grouting can be seen as a way of compensation grouting. This can be done vertically through the house floor, diagonally under a house foundation or horizontally from a pit over a longer distance. This last option is very expensive and is mostly used for the construction of bored tunnels in soft soils near foundations of buildings, in order to compensate the settlements of several nearby houses. err Figure 3-11. Horizontal compensation grouting from pit (Photo Keller Grundbau). 21 4 Dewatering & drains 4.1 Introduction The consolidation and dewatering reduces the amount of pores in cohesive and low- permeable soils (clay and peat). In this way, it increases the stiffness and strength. This is the same as the effect of the mechanical compaction for the non-cohesive and high-permeable soils (sand and gravel). The low-permeable soils however need far more time to consolidate and to creep. Installing vertical drains, improves the dewatering and therefore also the consolidation process. Vertical drains are often used to excel the consolidation process, because the excess groundwater pressure can first flow horizontally to the drain and then vertically to the surface. If the drainage distance reduces from 5 m to only | m, then the consolidation time reduces 25 times; or sometimes from 6 years to only 3 months. Figure 4-1. Plastic vertical drains. The best way to speed up the consolidation process is to use a combination of vertical drains, horizontal drains and a temporarily fill to increase the pressure temporarily. Figure 4-2. Combination of vertical drains, horizontal drains and a temporarily fill. 22 5 Ground freezing 5.1 Introduction Ground freezing is a construction technique that has been used for over one hundred years to provide temporary earth support and groundwater control. Applications are found in the underground civil, mining and environmental remediation industries. The ground freezing process uses a series of drilled freeze pipes and large refrigeration plants to convert existing pore water in the soil to ice, creating a strong, water-tight frozen earth material similar to rock or concrete. The frozen ground acts as an excavation support system requiring no bracing, tiebacks or additional shoring. It has been used extensively for shafts extending over several tens of metres deep. Its impermeable characteristic eliminates the need for dewatering, making the technique practical for large groundwater barriers. These barriers can be used to reduce or eliminate flow into excavations and contain contaminants or restrict the flow of contaminated plumes. Ground freezing may be used in any soil or rock formation regardless of structure, grain size or permeability. However, it is best suited for soft ground rather than rock conditions. Freezing may be used for any size, shape or depth of excavation and the same cooling plant can be used from job to job. As the impervious frozen earth barrier is constructed prior to excavation, it generally eliminates the need for compressed air, dewatering, or the concern for ground collapse during dewatering or excavation. Figure 5-1. Pit only supported by frozen ground, CERN, Switzerland. Freezing is normally used to provide for a stronger foundation, a temporary support for an excavation or to prevent ground water to flow into an excavated area. Successful freezing of permeable water-bearing ground provides simultaneously for a seal against water and a substantial strengthening of incoherent ground. No extraneous materials need to be injected and apart from the contingency of frost heave, the ground normally reverts to its normal state. It is applicable to a wide range of soils, but it takes considerable time to establish a substantial ice wall and the freeze must be maintained by continued refrigeration as long as required. This leads to the differences between the two different freezing techniques. 25 5.2 Brine freezing (indirect cooling) In an indirect cooling system, a primary refrigeration plant is used to abstract the heat froma secondary coolant circulating through pipes driven into the ground. The primary refrigerant most commonly used will typically be some alternative to Freon, which, due to its ozone- depleting characteristics, had to be phased before 1996. Other primary refrigerants are ammonia, NH4 (—33.3°C) and carbon dioxide, CO2, which is not commonly used. The secondary coolant, circulated through the network of tubes in the ground is usually a solution of Calcium Chloride. With a concentration of 30% such as brine, this has a freezing point well below that of the primary coolant. The primary refrigeration process is basically the Carnot cycle of compression and expansion reversed. The time required to freeze the ground will obviously depend on the capacity of the freezing plant in relation to the volume of ground to be frozen and on the spacing and size of freezing tubes and water content in the grounds. The advantage of this calcium-chloride solution (brine) technique is that it is cheap to cool, but the disadvantage is that one has to invest first in installing the whole equipment. Figure 5-2. The brine freezing system (schematic diagram). 5.3. Nitrogen freezing (direct cooling) With this method a large portable refrigeration plant is not necessary, and the temperature is much lower, so this freezing method is therefore quicker in application. The nitrogen gas (Nz) boils at -196°C at normal pressure. It provides in this way the required cooling. It is brought to, and stored on site under moderate pressure in insulated containers as a liquid. There is a particular advantage for emergency use, i.e quick-freezing without elaborate fixed plant and equipment. This may be doubly advantageous on sites remote from power supplies. In such conditions the nitrogen can be discharged directly through tubes driven into the ground, and allowed to escape to the atmosphere. Precautions for adequate ventilation must be observed. When there is time for preparation, an array of freezing tubes is installed for the nitrogen circulation, including return pipes exhausting to the atmosphere. The speed of ground freezing with N2 is much quicker than with other methods, days rather than weeks, but liquid nitrogen is costly. Therefore the method is particularly appropriate for a short period of freezing of up to about 3 weeks. It may be used in conjunction with the other processes with the same array of freezing tubes and network of insulated distribution pipes, in which liquid nitrogen is first used to establish the freeze quickly and is followed by 26 ordinary refrigeration to maintain the condition while work is executed. This can be of particular help when a natural flow of ground water makes initial freezing difficult. The advantages are that it is rather cheap to install and the ground freezes quickly. The disadvantage is that the nitrogen is expensive to use for a long time, so then the brine system becomes cheaper. Figure 5-4. Examples of freezing: left complex building pit connection; right: complex safety tunnel lateral to main tube of Western Scheld Tunnel. 5.4 Thermic Design The targets for the design of a freeze are: ¢ Calculation of the location of the freezing tubes ¢ Calculation of the required energy ¢ Calculation of the required freezing time ¢ Selection of the freezing system Sometimes the freeze should be retained within certain limits in order to prevent damage of nearby structures (foundations of buildings, building pits, underground stations or tunnels). For these cases, a combination of freezing tubes and heating tubes has to be used. 27 Figure 6-3. Erosion protection. Figure 6-4. Erosion protection. Figure 6-5. Erosion protection. 30 Figure 6-7. Combination of reinforcing & separating. 6.2 Reinforced soil / Terre armée (Some part of the text in this section is from Terre Armée, France). Soil reinforcement is a technique based on the formation of a composite material through the association of compacted frictional fill and linear soil reinforcement. The soil reinforcement may be either metallic (like the high adherence galvanised steel strips) or synthetic (like the high tenacity polyester-based strips). Reinforced earth provides: ¢ Strength: the resistance and stability of the composite structure provides significant load-bearing capacity. ¢ Cost effectiveness: the ease and speed of construction are significant advantages in reducing overall cost. ¢ Reliability: the durability of the materials used is well documented and the safety of the structures is high. e Adaptability: the technology provides solutions to complex cases and often proves to be the best answer to circumstances such as restricted right-of-way, unstable natural slopes, marginal foundation conditions and large settlements. e Aesthetic appearance: the variety of facings can meet all architectural requirements. 31 i aS -_ = t Figure 6-8. Terre armée construction. A big advantage is that the terre armée elements can be prefabricated and brought to places where it is difficult and time consuming to produce and construct large concrete retaining structures. = 4 Figure 6-9. Terre armée at complex places. One can combine the terre armée wall with the construction of a steep slope by using several layers (sandwiches) of soil and geogrids, see Figure 6-10. Anchor element Foundation of (length = 1m) frame structure Fence), Geogrid Lt RC facing. Reinforcemen for CU cu Drainage Construction joint (CJ) 30° ‘Gabions filled with gravel Figure 6-10. Cross section of combined terre armée wall with slope for Shinkan-sen train yard at Biwajima, Nagoya (Tatsuoka et al.,1992). 32 Metal plates can help the transport on soft ground, if the ground is even softer; mostly the ground water table is high and maybe dredging becomes a better solution. Figure 7-3. Plates spread the load. Dredging and shipping is by far the cheapest solution per cubic metre of ground exchange and transport, of course only when there is water (sea, lake, river or canal) nearby. Figure 7-4. Dredging techniques are the best solution for large sand supplying near water. To optimise the costs, one has to find the right equipment for both the ground type and project size. Figure 7-5. Small tools for small project and large tools for large projects. 35 7.2. Artificial heavy or light products Sometimes it is better not to use natural soils as a replacement. There are cases in which very light or very heavy materials are much better. Heavy products Heavy materials are used in geotechnical engineering when there are buoyancy problems (see Chapters 45 and 46), for example in the case of a bored tunnel which is coming too near the surface at both ends and the amount of ground on the tunnel ends is too light. Another solution to make the whole tunnel deeper, is especially expensive for both entrances, because these will then become much longer and deeper. This can be avoided by exchanging the existing soil above the tunnel ends by slag. Slag is a by-product of smelting ore in the furnaces of a steel mill, to separate the metal fraction from the unwanted fraction. It can usually be considered to be a mixture of metal oxides and silicon dioxide. This waste product is very heavy (up to 40 kN/m*) and cheap. Slag is also often used for the foundation of roads, becomes it becomes very strong and stiff after a while. Light Materials Light Materials are mostly used in combination with soft soils in order to reduce the settlements. EPS (Expanded Polystyrene) foam is extremely light, only 0.15 KN/m* to 0.35 kN/m*, but also strong enough to make roads and even complete bridge abutments (in Figure 7-6. Left: Expanded Polystyrene Foam blocks on both sides of a train line at Alphen at the Rhine, the Netherlands. Picture from M. Duskov, InfraDelft by. Right: Argex Norway) on it. In Japan it is often used, because it is also strong enough to resist earthquakes. Another well-known light weight material is Argex, an expanded clay product with a weight of only 3.7 kN/m’ to 6.5 kN/m’. It is also rather strong and fire resistant. It is often used to reduce the settlements or in combination with sheet pile walls or terre armée walls in order to reduce the active pressure on the wall. 36 Tunnelling 37 9 Cut & cover tunnel 9.1 Open building pit Cut-and-cover is a simple and relatively cheap method of construction for shallow tunnels where a trench is excavated and roofed over with an overhead support system that is strong enough to carry the load of what is to be built above the tunnel. By far the cheapest method to make a tunnel is to make a simple building pit with slopes. This is also only possible when there are no groundwater problems, or when for the duration of the tunnel construction, dewatering (pumping) is allowed. In urban areas this is often not allowed (especially when there are wooden pile foundations or shallow foundations on soft soils, subject to settlements). When it is allowed, it is often only allowed for a year, which is mostly insufficient. Figure 9-2. Open pit tunnelling (Tunnel Route du Nord, Walferdange, Luxembourg). 40 9.2 Classical cut & cover Two basic forms of cut-and-cover tunnelling are available: 1. Classical cut & cover (Bottom-up method): A trench is excavated, with ground support as necessary, and the tunnel is constructed in it. The tunnel may be of in situ concrete, precast concrete, precast arches, or corrugated steel arches; in early days brickwork was used. The trench is then carefully back-filled and the surface is reinstated. Wall-Roof method (Top-down method): First side support walls and capping beams are constructed from ground level by such methods as diaphragm walling, slurry walling, or contiguous bored piling. Then a shallow excavation will be made for the making of the tunnel roof. This will be made of precast beams or in situ concrete. The surface is then reinstated except for access openings. This allows early reinstatement of roadways, services and other surface features. Excavation then takes place under the permanent tunnel roof, and the base slab is constructed. Shallow tunnels are often of the cut-and-cover type (if under water, of the immersed-tube type), while deep tunnels are excavated, often using a tunnelling shield. For intermediate levels, both methods are possible. Large cut-and-cover boxes are often used for underground metro stations, such as Canary Wharf tube station in London. This construction form generally has two levels, which allows economical arrangements for ticket hall, station platforms, passenger access and emergency egress, ventilation and smoke control, staff rooms, and equipment rooms. The interior of Canary Wharf station has been likened to an underground cathedral, owing to the sheer size of the excavation. This contrasts with most traditional stations of the London Underground, where bored tunnels were used for stations and passenger access. Step Step 2 Step 3 Step 4 temporary support valle: Figure 9-3. Schematisation of the Classical Cut & Cover method. 41 Figure 9-4. Cut & cover tunnelling for the entrances of a submersed tunnel. 9.3 Aqueduct An aqueduct is a special type of tunnel which is built in a similar way to the classical cut & cover method. In this method the canal is temporarily led aside, the building pit is made, the aqueduct is made in the dry building pit and finally the water is led back over the aqueduct. Sometimes an aqueduct is created by making one side first and then the other side, in order to maintain the water connection, although temporarily smaller, in order not to block the shipping. Nice examples for an aqueduct are the Gouwe Aqueduct and the Aqueduct Ring-canal Haarlemmer Lake in the Netherlands. coe Gouwe Aqueduct, Gouda, the Netherlands. Figure 9-5. 42 Figure 9-10. Station Ceintuurbaan in Amsterdam is made with the Wall-Roof method. 45 10 Tunnel Boring Machine (TBM) (Most text and some pictures in this section are from Trem de Alta Velocidade Brasil, Misistério dos Transportes) A tunnel boring machine (TBM) is a machine used to excavate tunnels with a circular cross section through a variety of soil and rock strata. They can bore through anything, from hard rock to sand and clay. Tunnel diameters can range from a metre (done with micro-TBMs) to almost 20 metres. Tunnels of less than a metre or so in diameter are typically done using trenchless construction methods or horizontal directional drilling rather than TBMs. Tunnel boring machines are used as an alternative to drilling and blasting (D&B) methods in rock and conventional "hand mining" in soil. TBMs have the advantages of limiting the disturbance to the surrounding ground and producing a smooth tunnel wall. This significantly reduces the cost of lining the tunnel, and makes them suitable to use in heavily urbanized areas. The major disadvantage is the upfront cost. TBMs are expensive to construct, and can be difficult to transport. However, as modern tunnels become longer, the cost of tunnel boring machines versus drill and blast is actually less—this is because tunnelling with TBMs is much more efficient and results in a shorter project. The bore process contains two stages. The first stage contains the excavation with a cutting wheel and at the same time the advance of the shield with hydraulic jacks and also the grouting for the tail void. The second stage is the temporarily withdrawal of some jacks and the erection of precast concrete lining segments, to build a new ring of segments. After this the first stage is repeated. oo tail seal 4 lr 1 ‘ i segments :_4_Heopoli 1. excavation * hydraulic jacks ZL i 7 Cm f 0 2. advance of shield _, tail seal hydraulic jacks x] 4, erection of segments segments C70 3. grouting for tail void Figure 10-1. Bore process with TBM. Modern TBMs typically consist of the rotating cutting wheel, called a cutter head, followed by a main bearing, a thrust system and trailing support mechanisms. The type of machine used depends on the particular geology of the project, the amount of ground water present and other factors. 46 Figure 10-2. Transport of the precast concrete lining. In soft ground, there are three main types of TBMs: open-face TBM’s, Slurry Shield (SS) and Earth Pressure Balance Machines (EPB). 10.1 Open face TBM Open face TBMs in soft ground rely on the fact that the face of the ground being excavated will stand up with no support for a short period of time - this makes them suitable for use in rock types with a strength of up to 1OMPa or so, and with low water inflows. Face sizes in excess of 10 metres can be excavated in this manner. The face is excavated using a cutter head. The shield is jacked forwards and cutters on the front of the shield cut the remaining ground to the same circular shape. Ground support is provided by use of precast concrete, or segments that are bolted or supported until a full ring of support has been erected. A final segment, called the key, is wedge-shaped, and expands the ring until it is tight against the circular cut of the ground left behind by cutters on the TBM shield. Many variations of this type of TBM exist. Figure 10-3. Open face TBM. 10.2 Hydro shield or slurry shield (SS) TBM. The basic principle of this TBM is to maintain the face pressure during the excavation phase by filling the working chamber, located behind the cutter head, with (bentonite) slurry. In soft ground with very high water pressure and large amounts of ground water, Slurry Shield 47 : Figure 10-7. Hard rock TBM. 10.5 Support pressure All TBMs have to create a horizontal support pressure with the shield or with the slurry in order to stabilise the effective earth pressure and also the groundwater pressure. The maximum pressure of the slurry or shield is the vertical total ground stress at the top of the tunnel, because then a blowout can occur: the uplifting of the ground, creating a leak. The minimum pressure is the groundwater pressure at the bottom of the tunnel, in order to avoid the water to flow into the tunnel. In fact, even a little more pressure is needed to support the 3D arch of ground around the bore front. Failure in this way is sometimes called blowin. Figure 10-8. Blowout. Figure 10-9. Blowin. 50 10.6 Pneumatic caisson Sometimes a pneumatic caisson is used to make a part of the tunnel, for example having a starting point for the tunnel boring machine (TBM). The technique originates from the making of a pillar of a bridge in a river with a caisson. In the example below, the caisson in front of the central station of Amsterdam, there were even two functions; a starting point for a TBM and a foundation for a future bridge. The caisson is sunken down by pneumatic sinking with hydraulic ejectors and pumps, which pump out the sand/water mixture. This technique is mostly used when there is a sandy sub soil (easy excavation) and little space (otherwise a building pit would be cheaper) or a bridge pillar in a river. waste wareniee —"courgesseo ai @ | eee nee sous sn Pressine || owen bt ll Wise marenay ruse eomevens ruse, | CTA eee H SCM TT 4 : Ses 5 uareessine Fla N = Gd Figure 10-11. Pneumatic sinking with hydraulic ejectors and pumps. 10.7 Settlements The volume of ground loss experienced during tunnelling can be related to the volume of settlement expected at the ground surface (Peck, 1969). For a single tunnel in soft ground conditions, it is typically assumed the volume of surface settlement is equal to the volume of lost ground. However, the relationship between the volume of lost ground and the volume of surface settlement is complex. Volume change due to bulking or compression is typically not estimated or included in the calculations. Ground loss will produce a settlement trough at the ground surface where it can potentially impact the settlement behaviour of any overlying or adjacent bridge foundations, building structures, or buried utilities transverse or parallel to the alignment of the proposed tunnel excavation. Empirical data suggests the shape of the settlement trough typically approximates the shape of an inverse Gaussian curve. 51 factor of settlement settlement [%] settlement due to relatively instantaneous movement (54.4 %): - excessive removal of soil 273 volume of tail void 24.2 - deformation of segmental ring 29 settlement due to consolidation (45.6 %): - regional ground settlement Md - consolidation caused by drainage, groundwater lowering or 34.5 reduction of compressed air pressure total settlement: 100 Figure 10-12. Overview reasons for settlement ground level. k Settlement Trough Width Ground Level Settlement Profile Figure 10-13. Settlement trough. The shape and magnitude of the settlement trough is a function of excavation techniques, tunnel depth, tunnel diameter, and soil conditions. In the case of parallel adjacent tunnels, surface settlement is generally assumed to be additive. The shape of the curve can be expressed by the following mathematical relationships (Schmidt, 1974): Settlement trough on ground level, Gauss curve S(x) and Decrease in volume AV: (10.1) AV =S,,,iN20 in which: S(x)_ settlement of the ground level; Smax Maximum ground level settlement; x horizontal distance to the axis of the tunnel; z depth of the tunnel axis. 52 There are different ways to make drill & blast rock tunnels. The most well-known in Europe are: e The German method, © The old OTM (Old Austrian Tunnelling Method) and © The NOTM (New Austrian Tunnelling Method). 11.1 German Method or Core Method The Core Method (Kernbauweise), also called the German Method was first used in France. First the area around the core (Kern) is broken away (Ulme and Kalotte) and are inspected. Then the core is broken away. Finally the base (Sohle) is closed. This method limits the settlements of the tunnel. Figure 11-2. German Method or Core Method. 11.2 Old Austrian Tunnelling Method or Old OTM The old OTM (Alte Ostereichische Tunnel Methode) uses a method that can be seen in the figure below. The first excavation is at the base. Thi so used for inspection. It is possible to dig at several places at the same time; therefore this is a very fast method. @OO Figure 11-3. The Old OTM (Austrian Tunnelling Method). 11.3 New Austrian Tunnelling Method or NOTM There is no exact definition of this method. It is an improved method of the Old OTM. There is a patent of Rabcewicz from 1948 and his dissertation of 1950 that explain this method. The first idea is that stresses and settlements are limited by using an optimum of shapes and 55 blasting steps. The second is that deformations are measured to control the whole process; which decides when each following step will start. First the left and right drift walls (left and right ellipses in Figure 11-4 and Figure 11-5) are excavated or drilled, starting at the crown and the bench and base at the end. ay Figure 11-4, The NOTM (New Austrian Tunnelling Method). Figure 11-6. Drilling. 56 Figure 11-7. Explosives injection. Figure 11-8. Reinforcement and shotcrete. 57 Figure 12-5. Left: covered tunnel; right: entrance of tunnel. 12.2 Chin-nose and jack-leg support Every time a new element is placed, the new element will hang with its “nose” on the “chin” of the previous element. Figure 12-6. Chin-nose construction between the two end sides (bulk heads). At the end of each element (at the nose side) the segment will rest on two legs, controlled by jacks to optimise the position of the tunnel. After installation, sand is injected under the segment. From then on, the chin-nose support and the two jack leg supports are out of function. 60 Figure 12-7. Jack leg. 12.3 Advantages and disadvantages The main advantage of an immersed tunnel is that it can be considerably more cost effective than the alternative option; a bored tunnel beneath the water. Other advantages relative to these alternatives include: The speed of construction Minimal disruption to the river/channel, if crossing a shipping route (but boring is even better) Resistance to seismic activity (earthquakes) Safety of construction (for example, work in a dry dock as opposed to boring beneath a river) Flexibility of profile Disadvantages include: The tunnel is rather shallow, so rather exposed (usually with some rock armour and natural siltation) on the river/sea bed, risking a sunken ship/anchor strike Direct contact with water necessitates careful waterproofing design around the joints (same for bored tunnel) and round the jack legs. 61 62 The segmental approach requires careful design of the connections, where longitudinal effects and forces must be transferred across (think of the chin nose structure and the jack legs). Ill Shallow foundations 65 14 Types of shallow foundations There are two types of foundations; shallow foundations and pile foundations. Shallow foundations are used when the upper layer is both strong and stiff enough to carry the load of the structure. If not, pile foundations have to be used in order to transfer the load of the structure to deeper layers which are more strong and stiff. There are four types of shallow foundations: 1. Plate foundation (or single foundation) 2. Strip foundation 3. Grid foundation 4. Slab foundation The choice of the type of shallow foundation depends mostly on the structure and corresponding load. A pillar is founded, for example, usually on a single plate foundation. A wall is usually founded on strip foundation, a large floor usually on a grid foundation or slab foundation. wall or pillar slab foundation Figure 14-1. Types of shallow foundations. Over time the used construction materials for foundations have changed a lot. The oldest foundations were simply made of well stacked dry stones. Later, dry stone-concrete mixtures were used, brick structures and in more contemporary times, concrete without reinforcement. In many countries nowadays only reinforced concrete is used. For renovations and for new structures built near to older buildings, it is still important to understand the behaviour of the old foundations. 66 concrete-stone-mixture dry stone foundation 6 stones only \ in center brick structure e iH K & i LN Sie I s ¥ | f 1 | reinforced concrete reinforced concrete | Figure 14-2. Materials used in shallow foundations. For the design of the settlement of a shallow foundation, see chapter 15-18. For the design of the bearing capacity of a shallow foundation, see chapter 19-22. 16 Boussinesq In 1885 the French scientist Boussinesq obtained a solution for the stresses and strains in a homogeneous isotropic linear elastic half space, loaded by a vertical point force on the surface, see Figure 16-1. Figure 16-1. Point load on half space. A derivation of this solution is given in Appendix B, see also any textbook on the theory of elasticity (for instance S.P. Timoshenko, Theory of Elasticity, paragraph 123). The stresses are found to be ooh = oe RP (16.1) P 3rz 1 =— —(1-2v)——], es ( RRs! (16.2) o - Pie, Rs) on RR+2 R’ (16.3) o = 2p 2 oe Re (16.4) In these equations r is the cylindrical coordinate, r= fery, (16.5) and R is the spherical coordinate, RaVerty tz. (16.6) The solution for the displacements is Paty) Pe Zz Sapp pr w-h (16.7) uy =0, (16.8) _POHY) De W.= SR (2d Y)+o5h (16.9) 70 The vertical displacement of the surface is particularly interesting. This is 1 a Pd=v?) z=0 = (16.10) For r-—>0 this tends to infinity. At the point of application of the point load, the displacement is infinitely large. This singular behaviour is a consequence of the singularity in the surface load, and as in the origin, the stress is infinitely large. The fact that the displacement in that point is also infinitely large may not be so surprising. Another interesting quantity is the distribution of the stresses as a function of depth, just below the point load, i.e. for y=0. This is found to be Figure 16-2. Vertical normal stress ©... r=0 2 oe OP : Ime’ (16.11) P r=0 : Onn = Fog =U 2) (16.12) These stresses decrease with depth, of course. In engineering practice, it is sometimes assumed, as a first approximation, that at a certain depth, the stresses are spread over an area that can be found by drawing a line from the load under an angle of about 45°. That would mean that the vertical normal stress at a depth z would be Plaz , homogeneously over a circle of radius z. That appears to be incorrect (the error is 50 % if r=0), but the trend is correct, as the stresses indeed decrease with / z’. In Figure 16-2 the distribution of the vertical normal stress o., is represented as a function of the cylindrical coordinate r, for two values of the depth z. 71 Figure 16-3. Uniform load over circular area. The assumption of linear elastic material behaviour means that the entire problem is linear, as the equations of equilibrium and compatibility are also linear. This implies that the principle of superposition of solutions can be applied. Boussinesq’s solution can be used as the starting point of more general types of loading, such as a system of point loads, or a uniform load over a certain given area. As an example, consider the case of a uniform load of magnitude p over a circular area, of radius a. The solution for this case can be found by integration over a circular area (S.P. Timoshenko, Theory of Elasticity, paragraph 124), see Figure 16-3. The stresses along the axis r =0, i.e. just below the load, are found to be 3 0: a, = p-*). (16.13) r 3 Z 4, 2 On = I+ VF 3 0- (16.14) Il So in which b= iz" +a° . The displacement of the origin is 2, pa =0,2=0 : = 20-7). r=0,z u, = 2( we (16.15) This solution will be used as the basis of a more general case in the next chapter. Another important problem, which was already solved by Boussinesq (see also Timoshenko) is the problem of a half space loaded by a vertical force on a rigid plate. The force is represented by P= za’ p, see Figure 16-4. The distribution of the normal stresses below the plate is found to be z=0,0<r<a: (16.16) 72 Oo, = L216, — @,)—sin@, cos@, + sin, cos @,], (17.5) 0 o,, = feos? 4, -cos’ 6]. (17.6) 7 In the centre of the plane, for *= 0, 9, =—6,. Then the stresses are x=0 : o, = P16, +sin4 cos6| (17.7) 7 Cxx/P z/a Figure 17-3. Stresses for x=0. 2p . x=0: Fu == 14, —sin8, cos 6,1, (17.8) x=0: o,, =0. (17.9) That the shear stress o,, =0 for x=0 is a consequence of the symmetry of this case. The stresses o,, and ©. are shown in Figure 17-3, as functions of the depth z. Both stresses tend towards zero for z 00, of course, but the horizontal normal stress appears to tend towards zero much faster than the vertical normal stress. It also appears that at the surface the horizontal stress is equal to the vertical stress. At the surface this vertical stress is equal to the load p, of course, because that is a boundary condition of the problem. Actually, in every point of the surface below the strip load the normal stresses are 0, =0,, = p- 75 2 Figure 17-4. Strip load next to a smooth rigid wall. It may be interesting to further explore the result that the shear stress o,, =0 along the axis of symmetry x=0 in the case of a strip load, see Figure 17-2. It can be expected that this symmetry also holds for the horizontal displacement, so that u,=0 along the axis x=0. This means that this solution can also be used as the solution of the problem that is obtained by considering the right half of the strip problem only, see Figure 17-4. In this problem the quarter plane x>0, x>0 is supposed to be loaded by a strip load of width a on the surface z=0, and the boundary conditions on the boundary x=0 are that the displacement u, = 0 and the shear stress o,. =0, representing a perfectly smooth and rigid vertical wall. The wall is supposed to extend to an infinite depth, which is impractical. For a smooth rigid wall of finite depth the solution may be considered as a first approximation. The formulas (17.7) and (17.8) can also be written as 2p a az x=0: o., = —[arctan(—) + ; 2 [ © Fie! (17.10) x=0 : o, =P tarctan(4)-— 42 | : a > geet (17.11) Integration of the horizontal stress 0, from z=0 to z=h gives the total force on a wall of height h, 2 a = — pharctan(—). Q a? ( D (17.12) For a very deep wall (1 > a) this becomes, because arctan(a/h) © a/h, hoo: Q=~ pa=0.637 pa. (17.13) 1 The quantity pa is the total vertical load F (per unit length perpendicular to the plane of the drawing). It appears that the horizontal reaction in an elastic material is 0.637 F. For a very shallow wall (h«a) the total lateral force will be, because then arctan(a/h) © 7/2, h>0: Q= ph. (17.14) 76 P Figure 17-5. Line load next to a smooth rigid wall. This is in agreement with the observation made earlier that the value of the horizontal stress at the surface, just below the load, is o,, = p. For a very short wall the horizontal force will be that horizontal stress, multiplied by the length of the wall. Another interesting application of Flamant’s solution is shown in Figure 17-5. In the case of a surface load by two parallel line loads it can be expected that at the axis of symmetry (.x=0) the horizontal displacement and the shear stress will be zero, because of symmetry. This means that the solution of that problem can also be used as the solution of the problem of a line load at a certain distance from a smooth rigid wall, because the boundary conditions along the wall are that u, =0 and o,,=0 for x=0. By the symmetry of the problem shown in the left half of Figure 17-5, these conditions are satisfied by the solution of that problem. The horizontal stresses against the wall are given by equation (17.2) for Flamant’s basic problem, multiplied by 2, because there are two line loads and each gives the same stress. In this formula the value of x should be taken as x=a, where a is the distance of the force to the wall. The horizontal stress against the wall in this case is _4° Fa’z a(a+ey xx (17.15) The distribution of the horizontal stresses against the wall is also shown in Figure 17-5. The maximum value occurs for z= 0.577a, and that maximum stress is One max =04135~, a The total force on a wall of depth / can be found again by integration of the horizontal stress over the depth of the wall. This gives 2 =#F gina] (17.16) If a=0 this is Q=0.637F . If a increases the value of Q will gradually become smaller. A force at a larger distance from the wall will give smaller stresses against the wall. It should be kept in mind that only the extra forces and stresses resulting from the loads are mentioned. The weight of the soil itself also causes stresses, both in vertical and horizontal direction. 77 column. These are the final effective stresses. The seventh and eight columns contain the actual computation of the deformations of each layer, using Terzaghi’s logarithmic formula, and the value C,, =50. By adding the deformations of the layers the total settlement of the reservoir is obtained, which is found to be 0.10 m. That is quite large, and it may mean that the construction of the reservoir on such a soft soil is not feasible. The procedure described above can easily be extended. It is, for instance, simple to account for different properties in each layer, by using a variable compressibility. The method is also not restricted to circular loads. The method can easily be combined with Newmark’s method to calculate the stresses below a load of arbitrary magnitude on an area of arbitrary shape. It is also possible to incorporate creep by adding the formula of Koppejan in the calculation. The method can also be elaborated with little difficulty to a computer program. Such a program may use a numerical form of Newmark’s method to determine the stresses, and then calculate the settlements of the loaded area by the method illustrated above. The formula to compute the deformation of each layer may be Terzaghi’s formula, but it may also include a time dependent term, to account for creep and consolidation. 80 19 Bearing capacity of a strip footing The biggest problem for a shallow foundation, just as any other type of foundation, is a failure due to an overestimation of the bearing capacity. This means the correct prediction of the bearing capacity of the shallow foundation is often the most important part of the design of a civil structure. Figure 19-1. Overloaded shallow foundation of a row of silos I. Kk N NUS cA WUT YS Figure 19-2, Overloaded shallow foundation of a row of silos II. One of the simplest problems for which lower limits and upper limits can be determined is the case of an infinitely long strip load on a layer of homogeneous cohesive material ( ¢ = 0), see Figure 19-3. 81 P Figure 19-3. Strip footing. The weight of the material will be disregarded, at least in this chapter. This means that it is assumed that y=0. The problem is a first schematisation of the shallow foundation of a structure, using a long strip foundation, made of concrete, for instance. It will first be attempted to obtain a lower bound for the failure load, using an equilibrium system. Such a system should consist of a field of stre: that satisfies the conditions of equilibrium in all points of the field, that agrees with the given stress distribution on the soil surface, and that does not violate the yield condition in any point. 19.1 Lower bound An elementary solution of the conditions of equilibrium in a certain region is that the stresses in that region are constant, because then all conditions are indeed satisfied. In a two-dimensional field these equilibrium conditions are, in the absence of gravity, (19.1) (19.2) (19.3) Ss The main difficulty is to satisfy the boundary condition, because the normal stress o., discontinuous along the surface, see Figure 19-3. This difficulty can be surmounted by noting that in a statically admissible field of stresses (an equilibrium system), not all stresses need be continuous Formally this can be recognized by inspection of the equations of equilibrium, eqs. (19.1) — (19.3). All partial derivatives in these equations must exist, which means that the stresses must at least be continuous in the directions in which they have to be differentiated. It follows that the shear stress o,, must be continuous in both directions, that the normal stress o,,. must be continuous in x-direction, and the normal stress o., must be continuous in z- direction. However, two of the partial derivatives, Oo,,,/Oz and 00, /Ax, do not appear in the equations of equilibrium, and therefore no conditions have to be imposed on the continuity of these two normal stresses in these directions. This means that o,, may be discontinuous in z-direction, and that o., may be discontinuous in x-direction. Such a discontinuity is shown, for the vertical direction, in Figure 19-4. 82 equilibrium. If the circle rotates, a shear stress occurs at the periphery. If the shear stress is assumed to be maximal, so t=c, the moment with respect to the axis of rotation of the internal friction stresses at the periphery of the circle equals 2 mca , because the length of the circular are is 7a. The eccentricity of the external load is +a, so the exerted moment becomes tpa. Equating these two moments gives p=2ac. This is an upper bound for the failure load p., PD, < 6.28c. (19.5) A somewhat lower upper bound can be found by choosing the centre of the circle somewhat higher, see Figure 19-8. : Figure 19-8, Mechanism 2. If the angle at the top is 2a, it follows 2cR°a = 4 pa’, and because a= Rsina, in which R is the radius of the circle and a the width of the load, 4ca sin?a For @= 7 the previous upper bound is recovered. The smallest value is obtained for a = 1.165562, or a@ = 66.78°. The centre of the circle then is located at a height 0.429a. The corresponding value of p is 5.52c. This is an upper bound, hence PD, <5.52c. (19.6) It can be concluded at this stage that it has been shown that 4c < p, <5.52e. (19.7) In the next chapter the failure load will be approximated even closer. 85 20 Prandtl & N, The first step in solving the bearing capacity of a strip of infinite length, on weightless soil, was made by Ludwig Prandtl. He published in 1920 an analytical solution for the problem of a strip load on a half plane, see Figure 20-1 and Figure 20-2, on the basis of the assumption that in a certain region at the soil surface, the stresses satisfy the equilibrium conditions and the Mohr-Coulomb failure criterion. In this entire region the soil then is on the verge of yielding. G B A TI oh # Cx q D> Sa ; 20, 7D SULLSLSE i Figure 20-1. Prandtl’s schematisation (original drawing). This solution is both statically admissible and kinematically admissible, and must therefore give the true failure load. The lower bound part of Prandtl’s solution, with an equilibrium system of stresses, will be presented in this chapter. The proof that this solution is also kinematically admissible, which is much more difficult, will be omitted here. A complete proof can be found in textbooks on the theory of plasticity. The analytical solution gives the maximum foundation pressure or bearing capacity of the soil under a limit pressure, p, causing kinematic failure of the weightless infinite half-space underneath. The strength of the half-space is given by the angle of internal friction, ¢, and the cohesion, c. The sliding soil part is subdivided into three zones: 1. Zone 1: A triangular zone below the strip load with a width B=2-b,. Since there is no friction on the ground surface, the directions of the principal stresses are horizontal and vertical; the largest principal stress is in the vertical direction. 2. Zone 2: A wedge (Prandtl’s wedge) with the shape of a logarithmic spiral, where the principal stresses rotate through 90° from Zone | to Zone 3. The pitch of the sliding surface equals the angle of internal friction ¢, creating a smooth transition between Zone 1 and Zone 3 and also creating a zero frictional moment on this wedge (see Equation 13). 3. Zone 3: A triangular zone adjacent to the strip load. Since there is no friction on the surface of the ground, the directions of principal stress are horizontal and vertical with the vertical component having the smallest amplitude. 86 Figure 20-2. Strip foundation with failure mechanism. The interesting part of the solution is that all three zones are fully failing internally according to the Mohr-Coulomb failure criterion, while the outer surfaces are simultaneously fully sliding according to the Coulomb failure criterion. Only the latter criterion exists in the case of a Bishop slope stability calculation. The Prandtl-wedge failure mechanism can be confirmed by laboratory tests, see Figure 20-3. Figure 20-3. Prandtl-wedge failure planes in sand. Prandtl published an analytical solution for the bearing capacity of this three-zone problem considering the soil to be weightless (7 = 0) and without a surcharge (q = 0): p=cN., (20.1) in which: . 1+ sing N,=(N,-Wecot¢, with N, = K,exp(ztang) and K,= Tosing . (20.2) In the case of a frictionless soil (¢ = 0), this becomes: p=(m+2)ce=5.14c. (20.3) If we check the solution of Prandtl of the cohesion bearing capacity factor N. with finite element calculations, then we see that for lower friction angles (¢ <25°) this solution is rather accurate, see Figure 20-4, but for higher friction angles, another failure mechanism start to appear, see Figure 20-5. Therefore the solution of Prandtl is a bit unsafe. FEM calculations made by the author, both displacement and stress controlled, show it would be more correct to apply a cohesion bearing capacity factor of, see Figure 20-6: N.=(N,—Vcot¢, with N, =cos¢-K,, -exp(z tan ¢). (20.4) 87 22 Meyerhof & N, In this chapter the case of a strip footing on cohesive material, considered in chapters 19 and 20, is extended to a general type of shallow foundation, on a soil characterised by its cohesion c, friction angle ¢ and volumetric weight v. The soil is assumed to be completely homogeneous. Although the formulas were originally intended to be applied to foundation strips of buildings, at a shallow depth below the soil surface, they are also applied to large caisson foundations used in offshore engineering for the foundation of huge oil production platforms. In 1940, equation (21.1) of Prandtl and Reissner has been extended by Keverling Buisman for the soil weight, y . It was Von Terzaghi (1943) who first wrote this extension as: p=cN,+qN,+357BN,, (22.1) where B is the total width of the loaded strip, and y is the volumetric weight of the soil. For the coefficient N, various suggestions have been made by Keverling Buisman (1940), Von Terzaghi (1943), Meyerhof (1951; 1953; 1963), Caquot and Kérisel (1953), Brinch Hansen (1970), Vesic (1973) and Chen (1975), on the basis of theoretical analysis or experimental evidence. The equation by Brinch Hansen, for the soil weight bearing capacity coefficient, was based on calculations of Lundgren-Mortensen and also of Odgaard and Christensen. The Chen equation for the soil weight-bearing capacity coefficient became the currently used equation: N, = 2(N, ~I)tang. (22.2) In 2015, Van Baars showed, based on finite element calculations, that also this solution is unsafe and proposed a more accurate and safer solution: N,= 7 tang- 7"? (22.3) Later the formula (22.1) has been further extended with various correction coefficients, in order to take into account the shape of the loaded area, the inclination of the load, a possible inclined soil surface, and a possible inclined loading area. Most of these effects were assembled into a single formula for the vertical bearing capacity by Meyerhof (1963) and later Jorgen Brinch Hansen (1970), P, =1,5.CN, +1,8,gN, +i,8, 7/BN,. (22.4) In this equation the coefficients i, and i, are correction factors for a possible inclination of the load (inclination factors), and s, and sq are correction factors for the shape of the loaded area (shape factors). Some other factors may be used (for a sloping soil surface, or a sloping foundation foot), but these are not considered in this book. 90 23 Table of the bearing capacity factors In Table 23-1 the values of N., Ng and N, are given, based on the finite element calculations, (eqs: 20.4, 21.4 and 22.3), as a function of the friction angle ¢. In the limiting case ¢ =0 the value of N. = 2+, as found in Chapter 20. If c = 0 and ¢=0 the bearing capacity must be equal to the surcharge, i.e. p=q. Even a layer of mud can support a certain load, provided that it is the same all over its surface. This is expressed by the value N, =1 for g=0. ¢] N,N, N, ¢] N. N, N, 0 | 5.142 1.000 0.000 20 | 12.778 5.651 3.588 1 | 5.360 1.094 0.058 21 | 13.449 6.163 4.028 2 | 5.590 1.195 0.122 22} 14.166 6.724 = 4.517 3 | 5.831 1.306 0.194 23 | 14.933 7.339 5.060 4 | 6.085 1.426 0.274 24] 15.755 8.015 5.665 5 | 6.353 1.556 0.362 25 | 16.637 8.758 6.339 6 | 6.634 1.697 0.459 26 | 17.584 9.576 7.092 7 | 6.931 1.851 0.567 27 | 18.603 10.479 7.934 8 | 7.244 2.018 0.687 28 | 19.702 11476 8.877 9 | 7.574 2.200 0.818 29 | 20.888 12.578 9.935 10| 7.922 2.397 0.964 30 | 22.172 13.801 11.125 M1] 8.291 2.612 1.125 31 | 23.563 15.158 12.466 12] 8.680 2.845 1.302 32 | 25.075 16.668 13.980 13] 9.092 3.099 1.498 33 | 26.720 18.352 15.693 14] 9.528 3.376 L714 34 | 28.516 20.234 17.637 15] 9.991 3.677 1.953 35 | 30.480 22.342 19.848 16 | 10.482 4.006 2.218 36 | 32.633 24.709 22.371 17] 11.004 4,364 2.510 37 | 35.001 27.375 25.258 18] 11.558 4.756 2.833 38 | 37.612 30.386 28.571 19] 12.149 5.183 3.191 39 | 40.499 33.796 32.387 20| 12.778 5.651 3.588 40 | 43.703 37.671 36.797 Table 23-1: Commonly used bearing capacity factors (Prandtl, Reissner and Chen). The Eurocode does not recommend which equations have to be used for the calculation of the bearing capacity; in fact this can be found in the country annex, which means that every country selects its own equations. The problem of these annexes is that no explanation is given as to why a certain equation has been selected; even references to authors or publications are never given. Besides this, equations other than the equations of Meyerhof and Brinch Hansen are used and sometimes the inclination and shape factors of Brinch Hansen are often used, although they are incorrect. 91 24 Correction factors 24.1 Inclination factors i In the case of an inclined load, i.e. loading by a vertical force and a horizontal load at the same time, the horizontal component of the load is limited at the foundation surface, due to the Coulomb shear failure, P, Sct p, tang. (24.1) But also the vertical bearing capacity is considerably reduced by the additional horizontal load. In 1953 Meyerhof published his results of laboratory experiments on inclined loading on “purely cohesion materials “ and “cohesionless materials”, for cases in which the horizontal component of the load is smaller than its maximum possible value. The correction factors for the inclination of the load were in 1963 expressed by him as: i, =i, -(-S). ,-[-2) » for: a<¢. (24.2) In 1970 Brinch Hansen proposed other inclination factors: i,=1- Pror , i= 2, c+Pp,,,, tang (24.3) vert Although these inclination factors are often used, they are however a disallowed mixture of the Coulomb failure criterion, which should only be applied at the interface, and the Mohr- Coulomb bearing capacity failure of the half-space below the interface. A clear indication of the incorrectness of his solution is the fact that the surcharge inclination factor, i, , depends here on the cohesion, c_, while the factor N, for any inclination, and therefore also i, . should not depend on the cohesion, c. The same even applies for the cohesion inclination factor, i, . This indicates that these inclination factors should not be used. Based on the Prandtl wedge, one can assume that there is a failure mechanism for inclined loads as in Figure 24-1. ¥ Figure 24-1. Failure mechanism for an inclined load. 92 25 CPT, undrained shear strength and Prandtl In the Netherlands the cone penetration test is mainly used as a model test for pile foundations. In the Western parts of the Netherlands the soil usually consists of 10 — 20 metres of very soft soil layers (clay and peat), over a rather stiff sand layer. This soil structure is very well suited for wooden or concrete piles of about 20 cm — 45 cm diameter, reaching just into the sand. The weight of the soft soil acts as a surcharge on the sand, which has a considerable cone resistance. The allowable stress on the sand depends upon its friction angle @, its cohesion c (usually very small, or zero), and the surcharge g. The dimensions of the foundation pile have very little influence, because this parameter appears only in the third term of Meyerhof’s formula, which is a small term if the width is less than, say, 1 metre. This means that the maximum pressure for a large pile and the thin pile of a cone penetrometer will be practically the same, so that the allowable pressure on a pile can be determined by simply measuring the cone resistance. This will be elaborated in Chapter 26. The cone penetration test can also be used to determine physical parameters of the soil, especially the shear strength. It can be postulated, for instance, that in clays the cone resistance will be determined mainly by the undrained shear strength of the soil (s,). In agreement with the analysis of Meyerhof the relation will be of the form q.-F,=NS,5 (25.1) where ©, is the local vertical stress caused by the surcharge, and N, is a dimensionless factor. For a circular cone in a cohesive material a cone factor N, of the order of magnitude 15 — 18 is usually assumed, on the basis of plasticity calculations for the insertion of a cone into a cohesive material of infinite extent. By measuring the cone resistance gq. the undrained shear strength s,, can be determined. The results are not very accurate, because of theoretical shortcomings and practical difficulties, but the measurement has the great advantage of being done in situ, in the least disturbed soil. The alternative would be taking a sample, bringing it to a laboratory, and then doing a laboratory test. This process includes many possible sources of disturbance, which can be avoided by doing a test in situ. 95 96 IV Pile foundations 97