Backfill completely above the water table or below the water table. 4-1.

Hu and Tan (2009) proposed a formula for passive earth pressure on cohesive soil. Lower values for silty sands, and higher values for other soils. Semi-empirical Mononobe-Okabe Method. q= 10.0 kn/m^2 surcharge. I calcualte the k 0 = 1 sin ; = function Bearing pressure resultants. The degree of relative compaction of the wall backfill within the active or at-rest envelopes. The resultant force due to the earth pressure acting on a basement wall can be calculated as. This can be done using the coefficient of earth pressure at rest, as coined by Terzaghi (1920). Coefficient of active earth pressure at rest: When the retaining wall is at

Active earth pressure is the one that is exerted by the soil that tends to overturn or slide the retaining wall. Check bearing capacity. 1.0 - 2.0 low density to high density concrete. (3) Earth pressure at rest as expressed by equation (1.2.5) may be used when there is little 2. The pressure exerted by a fluid at equilibrium at any point of time due to the force of gravity. The way of computing the earth pressure at rest can be therefore influenced by the selection of the type of soil (cohesive, cohesionless) when inputting its EARTH PRESSURE THEORY AND APPLICATION The horizontal stress (h) is linearly proportional to depth and is a multiple of vertical stress (v) as shown in. By generalizing Coulombs formula, Motta (1994) obtained the active earth pressure acting on a wall by a uniformly-distributed surcharge. In other words, because of the large lateral extent of the soil Eq. For better prediction, the The active state occurs when a retained soil mass is allowed to relax or deform laterally and outward (away from the soil mass) to the point of mobilizing its available full shear resistance (or engaging its shear strength) in trying to resist lateral deformation. C_2 is 0.22 in the published formula, and is stored in the Coefficient_Lateral_Earth_Pressure_2_C2 field. The image below shows schematically the pressure states of a soil mass, as well as the Rankine formula of Kp for granular soils, where is the internal friction angle. If, on the other hand the wall was pushed horizontally towards the right the earth pressure on the back of the wall would increase instead of decreasing. The pressure applied in the horizontal direction due to backfill is called the horizontal pressure or laterla earth pressure. In this study, active earth pressure behind retaining walls under seismic loading was discussed from no 5) When computing the pressure at rest for cohesive soils r using the Jky formula for the determination of coefficient of earth pressure at rest K r, it is recommended to use the alternate (1.2.5) where K0 : coefficient of earth pressure at rest (4) Angle of Internal Friction of Soil (2002) estimated the passive earth pressure by introducing the critical state concept to either Terzaghi or Coulomb theory. 1.5 - 4.0 low density to high density timber.

Passive Earth Pressure - The Mller - Breslau Theory; Passive Earth Pressure - The Absi Theory; Passive Earth Pressure - The Sokolovski Theory; Passive Earth Pressure - SP 22.13330.2016; Passive Earth Pressure - Total Stress; Earth Pressure at Rest. There is a check box to allow the applied seismic force to be reversed to that it acts in the direction that opposes the active lateral earth pressure. 4-1 . Earth Pressure at Rest GL In a homogeneous natural soil deposit, X h v the ratio h/ v is a constant known as coefficient of earth pressure at rest (K 0). The total horizontal force from the retained earth acting on the wall surface is: P = 19.34 3.6 = 34.84 kN. If pile-soil friction is to be ignored, then we can use Rankine Method. The coefficient of earth pressure at rest (K 0) is an important soil parameter which still remains one of the most difficult parameters to be accurately measured. 7, 1944, pp. The following table provides the earth pressure coefficient formula for a different types of soils. where K o at-rest earth pressure coefficient. When a soil mass gets deposited naturally or artificially, the coefficient of earth pressure attains a value known as coefficient of earth pressure at rest (K 0) which is This value can be further reduced as follows: K p (mobilized) = (Thermal Movement/ (0.05 * Wall Height)) * K p ; Provided K p >= 0.5. The passive pressure coefficient Kp is defined as the ratio of the horizontal to vertical stress. The lateral earth pressure has a triangular distribution, whereas the surcharge pressure has a rectangular distribution. K a = 1 sin ( ) 1 + sin ( ) = tan 2 ( 45 2) Sometimes it is also defined as the neutral lateral earth pressure or the lateral earth pressure at consolidated equilibrium. Active earth pressure coefficient (Ka): It is the ratio of horizontal and vertical principal effective stresses when a retaining wall moves away (by a small amount) from the retained soil. Results indicated that the measured horizontal earth force is about three times the value calculated by classical at-rest earth pressure theory. Fa = resultant force acting on the basement wall (kN) hs = height of backfill soil (m) = specific weight of backfill soil (kN/m3) K = coefficient of earth pressure at rest. Fa = 0.5 K hs2 (1a) where. Of course, K0 = 1 for water.

Earth Pressure at Rest for Partially Submerged Soil Consider H is the height of retaining wall and 'H1' is the depth(from top) below which water table is there. Broms: 0.5 - 1.0 for low density to high density steel. Common simplified approaches to calculate seismic active pressure are described below: 1. Eq. At-Rest Pressure Based on Expansive Soil Condition for basement wall designs shall be limited to only basement walls that serve as site walls and are not structural elements of habitable structures. This equation, which derived by William Rankine, is the development of the coulomb formula. Passive earth pressure is the one exerted from the other side and that tends to stabilize it. At any depth Z (Z Pressure Unit in SI. Under normal conditions, the lateral earth pressure is at rest condition. Generally, it is applied near the "toe" of the wall. carried out a series The equivalent lateral pressure is 40psf / ft of depth. r/Geotech is for all topics related to geotechnical issues of earth materials. Below a level ground surface, the horizontal 1. h is referred to as the at-rest earth pressure. The total active pressure at depth z acting on the back of the retaining wall is: pA = pA' + u = b gz KA + q KA + w gz (12.8) This coefficient contains the words at rest since the soil was deposited under conditions of zero horizontal strain. Professor Whitney Clark Huntington in his publication, Earth Pressures and Retaining Walls, said The equivalent fluid method is commonly misused by applying it to walls which retain earth with a sloping ground surface At Rest Lateral Earth Pressure: The wall may be restrained Download Solution PDF. Where: OCR is taken from the Overconsolidation_Ratio_5 field on the CPT_DATA table. The minimum value of K p (mobilized) that we allow by the above equation is 0.5 (the at-rest value for average soil). For a full discussion of earth pressure and the design of earth-retaining structures the reader is referred to Clayton and Milititsky.35. When computing the pressure at rest for cohesive soils r using the Jky formula for the determination of coefficient of earth pressure at rest K r, it is recommended to use the alternate angle of internal friction n.. * If the retained earth has a Pressure problems solving numerical with pressure formula. (3) Earth pressure at rest as expressed by equation (1.2.5) may be used when there is little displacement because of the wall being confined. ADVERTISEMENTS: where K p the Rankines coefficient of passive earth pressure, is given by . K0 = the coefficient of earth pressure at rest for normally consolidated soil; and Ko* = the coefficient of earth pressure at rest for overconsolidated soil that is pres ently subjected to Note that the factored load combinations are used in this stage. It can be shown to be some multiple of the vertical stress at any points. Equation (15.57) indicates that the The program then applies the appropriate Load Factors (1.0 for concrete design and 0.7 for serviceability checks). Hydrostatic pressure comes under the study of hydrostatics or fluid statics. Lateral earth pressure is the pressure that soil exerts in the horizontal direction. Importantly, at K 0 state, there Rankine's theory (maximum-normal stress theory), developed in 1857 by William John Macquorn Rankine, is a stress field solution that predicts active and passive earth pressure.

The magnitude of Bowles: 0.6 - 1.25. The magnitude and direction of is acting on a retaining structure and foundation depends largely upon relative strain of the soil behind the structure. Mayne (2007), NCHRP Synthesis 368 p 43. We can determine the backfill earth pressure using Rankine, Coulomb, Boussinesq, Muller-Breslau or Terzaghi & Peck method. The calculated values agree well with those from physical tests in the previous literature. (2) The earth pressure at permanent situation is based on Coulomb's earth pressure theory. The Rankine formula for earth pressure differs from Coulomb's by ignoring the friction between the wall and the backfill, AngF = 0.0 degrees. Georgiadis and Anagnostopoulos (1998) compared the results of pressure applied to sheet piles under strip loading with those obtained from the distribution of the elastic stresses technique, the 45 Ka being the coefficient of active earth pressure. Note the maximum stress level corresponding to the passive state. For a vertical wall retaining a horizontal backfill and for which the friction is equal to , = 90, = 0, and = , and Kp The surcharge is Compare this result with the liquid pressure in Example 1. If the top surface is not horizontal then the soil can be partially saturated. The horizontal force resulting from this earth pressure increases to a maximum value P P as shown in Figure 12.2(c). When the effective stresses of Equation 5.2 correspond to the at-rest state, the coefficient is named the coefficient of earth pressure at-rest, as indicated above (Equation 5.1). Calculate the eccentricity, maximum and minimum soil pressure beneath the base of a retaining wall. Rankine's theory, is a stress field solution that predicts active and passive earth pressure. Rankine's theory, is a stress field solution that predicts active and passive earth pressure. For a vertical wall retaining a horizontal backfill for which the angle of wall friction is equal to , Ka reduces to (Eq. The Rankine method of Lateral Earth Pressure Calculation. In addition, the location of the EFP refers to "Equivalent Fluid Pressure," where you can enter a lateral soil pressure in psf per foot of depth. effects of the earth pressure from the backfill. It should be noted that the design engineer should make sure the fully where K 0 is the coefficient of the earth pressure at rest and z is the vertical stress due to the self-weight of the soil at depth z, where the earth pressure at rest is to be computed K 0 = Earth pressure at-rest (Jaky formula) o For a dense, compacted sand backfill, may grossly We all have are well familiar with Sir Active Pressure (or At-Rest Pressure for Restrained Walls): This value will be computed using the Coulomb formulas. (2) The earth pressure at permanent situation is based on Coulomb's earth pressure theory. c=0. It is the minimum theoretical lateral pre The point of application of the active earth pressure is also obtained. Backfill Earth Pressure. Hydrostatic pressure is proportional to the depth measured from the surface as the weight of the fluid increases when a downward force is applied. 4-2 . The unit of pressure in the SI system is the pascal, abbreviated Pa. One pascal is equal to a force of 1 N applied over an area of 1 m^2, or 1 Pa = 1 N/m^2. But, if the wall deflects slightly, stresses were exerted in the soil, these are; a passive earth pressure ( PP) in front of the wall, and an active earth pressure (P ) behind the wall. C_1 is 0.192 in the published formula, and is stored in the Coefficient_Lateral_Earth_Pressure_2_C1 field. Often, we need the soils friction angle and the soil unit weight. Earth pressure coefficient (k 0) 1) Cohesionless soils. Eq. At-Rest 0.4 0.6 0.4 0.8 At-Rest Earth Pressure Under conditions of zero horizontal displacement, the soil is said to be at-rest: Ko 1- sin (granular soils) Active Earth Hydrostatic pressure is defined as. or Coulomb formula. 1. That is, the soil is at the point of incipient failure by shearing due to unloading in the lateral direction. Lateral earth pressure is the pressure that soil exerts in the horizontal direction. Reference values of the coefficient of lateral In the above equations, K O is the earth pressure coefficient at rest, F is the frictional resistance and Q u is the ultimate holding capacity. Earth Pressure at Rest. At rest coefficient of earth The widely used Jaky coefficient of earth pressure at rest, K 0, is revisited. where K'o = coefficient of earth pressure at rest in terms of effective stresses (see equation (3.7)). Because earth loads are applied as uniformly increasing loads (triangular distribution against the back of wall). In the above equations, K O is the earth pressure coefficient at rest, F is the frictional resistance and Q u is the ultimate holding capacity. Hydrostatic pressure comes under the study of hydrostatics or fluid statics. Another popular method to estimate the earth pressure is the logarithmic-spiral method proposed by Terzaghi (1943). At present, the calculation of active earth pressure behind retaining walls is mainly based on the hypothesis that the fracture surface of rolling earth behind retaining walls is straight-running through wall heels. The pressure applied in the horizontal direction due to backfill is called the horizontal pressure or laterla earth pressure. Gravity always acts towards the centre of the Earth. phi= 28. Eccentricity, max and min soil pressure. The dynamic earth pressure coefficient for passive state is calculated according to EN1998-5 equation (E.4) as: KPE = p12 / ( p2 p32) = 0.9516 2 / (0.95610.6035 2) = 2.600. Fang et al. Hydrostatics is the study of fluids and its behaviour at rest. Hydrostatics is the study of fluids and its behaviour at rest. Coefficient of active earth pressure at rest: When the retaining wall is at rest then the ratio between the lateral earth pressure and the vertical pressure is called the co-efficient of the earth pressure at rest, The degree of saturation of the wall backfill in the zone of active or at-rest earth pressure. Example 5.1 Determine the ultimate holding capacity for 355-358. 2. 0. earth pressure against the wall following either Coulomb or Rankine's theory. Kp being the coefficient of passive earth pressure. 1. 4.3k. For normally So if you find your active pressure coefficient using one of the formulas below say Ka=0.33 and multiply this by the soil density say 120 pcf you get about 40pcf. C_3 is 0.31 in the Then ph = pw + ps At Rest Lateral Earth Pressure: The wall may be restrained from moving, for example; basement wall is restrained to move due to slab of the basement and the lateral earth force in this case can (for example basement wall) 11. Jaky J, "The coefficient of earth pressure at rest", Journal of the Society of Hungarian Architects and Engineers, Vol. E a = 0.283 19 3.6 = 19.34 kN/m. Here you can choose between E.F.P. Calculate the bearing pressure resultants for the toe and heel of a concrete cantilever retaining wall to be used in the reinforcement calculations. earth pressure coefficient for the at rest condition in granular soil is: Ko = 1 sin() (1.0) Where: Ko is the at rest earth pressure coefficient and is the soil friction value. Valid for cohesionless soil. This Civil Engineering App uses the Fadum's Chart to determine the stress increment - which is a key concept in civil engineering / goetechnical engineering. This statement was made in 1957, approx. Kp = (1+sin) / (1-sin) If the wall is in a passive state, we can use this coefficient to calculate the earth pressure. K p = tan 2 = (1 + sin)/ (1 sin) (15.58) = 45 + /2. The simplest method to approximate seismic active pressure is to use the approach of Mononobe-Okabe (M-O) which is originally based on Coulombs theory of static earth pressures. Type of Soil. The image below shows schematically the pressure states of a soil mass, as well as the Rankine formula of Kp for granular soils, where is the internal friction angle. It is of advantages to calculate the individual components, especially if you need to know the E a figure. It is reasonable to assume that the water table can be at the surface after prolonged rain, therefore, the lateral pressure comprises two components: 1. water pressure pw = 9.807*z and 2. soil pressure ps = (q + (gam_sat 9.807)*z)*K0 where gam_sat is the saturated unit weight of the soil. Site walls maybe structuralelementsofdecks,carports,patios,storagebuildings,etc. 3. The seismic pressure is trapezoidal with the resultant applied at 0.6H, as shown below. At Rest Lateral Earth Pressure: The wall may be restrained from moving, for example; basement wall is restrained to move due to slab of the basement and the lateral earth force in this case can be termed as" P o ". Lateral Earth Pressure 0 2 0 1 2 0 2 1 P =P +P =qK H + H K At Rest q H z h c K0 q K0 (q+H) 1 2 P1 P2 P0 H/3 H/2 z' K0: coefficient of at-rest earth pressure The total force: h =K v +u 0 When distance D is far enough, the direction of active earth pressure will be constant and is parallel to backfill ground line which is equal to the original Rankines assumption.20 The direction of active earth pressure as obtained is However, most experiments have proven that this hypothesis is false. At-rest Ko It occurs when the wall experiences no lateral movement. primary concern are the lateral earth pressures induced by the retained soil. Calculate the total lateral FORCE per meter on a retaining wall AT REST given: H= 4m (wall height) Gamma = 16.0 kn/m^3.