Talk:Lateral earth pressure

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[edit] Errors

There are quite a few errors on this page. A reference I have (Kramer 1996) has Rankines equation as: Ka= (1-SIN(phi')/(1+SIN(phi') = TAN^2(45-(phi'/2). This page ascribes this to Coulomb (wrong!) ... I cant be bothered writing the rest, but some of the others arent correct either. I'll try and edit myself. Hopefully I wont make too much of a mess.—Preceding unsigned comment added by GeoEng (talk • contribs) 09:25, April 6, 2007

OK, I've made some changes. More yet to do include adding the references for Caquot & Kerisel, Terzaghi & Peck. "Bells relation" should be moved under "Rankine". More discussion is required for At-rest pressures, compaction pressures etc. A whole section on dynamic earth pressure theory is missing and needs to be added. Usual story... If I have time. Note this page NEEDS figures!!! GeoEng 11:51, 6 April 2007 (UTC)

No, I believe you are wrong. Rankine's equation was the larger one; he also presented the simplified version of it with a horizontal backfill. You can see the larger equation in his original work. As for what exactly Coulomb wrote down, I do not know because I have different sources saying different things (see [1]). The way it is now is fine because it gives a single equation for "Coulomb theory" and does not specify what equation Coulomb originally wrote down. -- Basar (talk · contribs) 21:19, 26 August 2007 (UTC)

Additionally, Ka = TAN^2(45-(phi'/2) is valid in both Coulomb and Rankine theory when the appropriate circumstances are met to simplify the equations. -- Basar (talk · contribs) 23:19, 26 August 2007 (UTC)

[edit] Discussion

I have moved the "discussion" section here because I cannot figure out how to integrate it with the rest of the article, and it is largely of a tone different than what we normally are going for on Wikipedia (WP:BETTER#Information style and tone). -- Basar (talk · contribs) 23:16, 26 August 2007 (UTC)

Imagine a soil deposit with a horizontal surface and with a vertical membrane of zero thickness and infinite stiffness inserted into it without disturbing the soil. The stress on each side of the membrane is called the at-rest lateral stress σ_o. Its value at any depth z is given by K_o.γ.z = K_o.σ_v where σ_v is vertical stress at depth z and K_o is the coefficient of at-rest lateral stress. The value of K_o cannot be calculated as it depends on many factors, including the geological history of the soil. There are some empirical expressions for estimating its value, and attempts can be made to measure it but, of course, the insertion of a measuring instrument into the ground immediately disturbs the soil and the measured value may be greater or less than the actual value. Typically, in a normally-consolidated soil its value may be around 0.5, and in an over-consolidated soil it may be up to 2 or 3. Imagine the membrane being held in place while soil is excavated on one side of it to the base of the membrane over a large horizontal distance. Then imagine the membrane being allowed to move away from the soil it is retaining by rotation about the base of the excavation, or by lateral translation. The lateral stress at any depth will steadily reduce until a certain amount of movement has occurred, when it will remain constant even though further movement of the membrane is allowed. This stress is called the active lateral stress and is equal to K_a.σ_v where K_a is the coefficient of active lateral stress. The amount of movement of the top of the membrane necessary to reduce the lateral stress to the active value is quite small (perhaps less than 0.1% of the excavation depth). The name 'active' is given to this stress because the soil actively follows the membrane as it is moved away. Instead of allowing the membrane to move away from the soil, imagine it being pushed towards the soil, rotating about the base of the excavation or moving laterally. The stress required to move it will increase until a maximum value is reached, which will not increase with further movement. This stress is called the passive lateral stress and is equal to K_p.σ_v where K_p is the coefficient of passive lateral stress. The amount of membrane movement at the ground surface required to reach the passive value is much greater than that needed to reduce the stress to the active value (perhaps 10% of the excavation depth). The name 'passive' is given to this stress because the soil passively resists the membrane as it is pushed towards it. The lateral stress values in the ground can be expressed in terms of total or effective stresses. In the case of a total stress analysis in a saturated, fine-grained soil, K_a = K_p = 1.0. In an effective stress analysis, the effective active lateral stress σ_a' = K_a'.σ_v' and the effective passive lateral stress σ_p' = K_p'.σ_v', where σ_v' is the effective vertical stress at depth z. Typically, the value of K_a' is around 0.3 and the value of K_p' will be similar that that of K_o in heavily-overconsolidated soils i.e. 2 to 3. In design, no safety factor is applied to the active stress. However, a reduction factor is applied to the passive stress because the amount of lateral movement required to generate the full value would be unacceptable in most soil retaining situations. A factor of 3 to 4 is commonly used. Static water in the soil will exert a pressure on the wall that is hydrostatic beneath the water table. Although it might be thought that negative water pressure above the water table in fine-grained soils would result in suction on the wall back, any tendency for this to occur ceases rapidly as the soil shrinks away from the soil back, leading to what is called a 'tension crack' from the ground surface down to the water table. Such a crack can fill with rain water or other run-off and lead to hydrostatic pressure behind the top of the wall. This must be avoided by grading the ground surface away from the wall back, and sealing the surface of the backfill. The theoretical methods of estimating K_a and K_p in gravity retaining wall design involve certain assumptions. The simplest assumes a horizontal ground surface, a vertical wall back, a cohesionless soil, and zero relative movement between the wall back and the soil. This latter assumption is often called 'zero wall friction', but this is misleading. It may happen that, as the wall moves away from the soil the ground beneath it compresses just enough to match the tendency of a wedge of soil to slip down behind the wall. It may happen that, as the wall moves towards the soil, it is pushed upwards and moves together with the wedge of soil being displaced behind it. An analysis of the compressibility of the soil beneath the wall base in the case of active stress, or the direction of the overall passive force being applied to the wall, is needed in order to estimate the likely amount of relative movement between wall back and retained soil and, therefore, whether a frictional component of stress is likely to be generated on the wall back. Obviously, if the wall is founded on rock it is highly likely that the maximum relative movement between wall and soil will occur in the active situation, and that the coefficient of wall friction μ will be that of the soil on the wall material - timber, steel or concrete. This is also possible in the passive case, but each situation must be evaluated on its own merits. Usually, some proportion of the maximum possible wall friction is used in design. In many cases the ground surface is not horizontal and the wall back is not vertical. Also, the soil may have a cohesive component of strength as well as a frictional one, or the design may be done in terms of total stress or in terms of effective stress. The common methods of estimating Ka and Kp allow for these types of situations. When a retaining wall is not free to rotate about its base or to move laterally, the simple triangular or near-triangular active and passive stress distributions no longer apply. Calculation of the likely stress distribution is not possible, and design methods rely on measurements of stress distributions in actual construction situations. The best-known of these is due to Terzaghi and Peck who produced envelopes of likely maximum stress distributions obtained from strut load measurements in deep trenches in several soil types. Basement walls, bridge abutments and reinforced soil are common cases of propped retaining walls. They continue to represent a great challenge to geotechnical engineers in producing safe and economical designs. Because the word 'drainage' is used, it is a common misconception that the principal purpose of weep holes through the stems of walls, or gravel layers or geo-synthetic drains down the backs of walls, is to remove water. Their purpose is actually to introduce zones of air at atmospheric pressure into the soil immediately behind the wall. When this is done, a hydraulic gradient is set up between the water some distance behind the wall and the water in the air spaces in the drain, such that seepage occurs towards the wall. At the wall back, the water pressure is zero, and a simple flow net may be used to verify that, as seepage approaches the wall, the water table slopes rapidly downwards and meets the wall at or near its base. Of course, some water seeps out of the soil and is removed by the drains, but the quantity is generally very small. When the force applied on the back of a retaining wall due to a hydrostatic stress is estimated and compared with the effective active stress, it will be seen to be very large compared with the soil force. It is much cheaper to add drainage than to resist water pressure.

[edit] Coulomb and surcharge?

Is it possible for anyone to include in the article how surface surcharges are accounted on Coulomb's wedge analysis? --Mecanismo | Talk 23:05, 23 January 2008 (UTC)