Pengaruh Kadar Bentonit Terhadap Kekuatan Geser Dari Cetakan Pasir

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KEKUATAN GESER TANAHDefinisi:perlawananinternaltanahtiapsatuanluasterhadapkeruntuhanatau pergeseran sepanjang bidang runtuh dalam satu elemen tanah Tujuan Studi kekuatan geser tanah: Untuk analisis masalah kestabilan tanah, seperti : daya dukung stabilitas talud (lereng) tekanan tanah ke samping pada turap/tembok penahan dll KEKUATAN GESER TANAHDasarTeori (Hukum Gesekan Newton): W T R | T > Wgeser T < Wdiam T = Wlabil |ot |= = == =tan:tanAWATtegangan dalamWTKEKUATAN GESER TANAH Basic mechanics applied to soils Equilibrium and compatibility The principle of equilibrium states that if a body is in state of rest, the net force acting on the body in any direction is zero. Thus, in the figure above, the sums of forces in the horizontal and vertical directions will be zero: AH = H1 + H2 + H3 + H4 AV = V1 + V2 + V3 + V4 The principle of compatibility states that any movements or changes in shape or volume must be compatible with no material being lost or gained. When loads are applied to bodies of soil it is assumed that the solid content remains constant (though displaced or re-arranged), but that there may be changes in the volume of water and or air. KEKUATAN GESER TANAH Mechanical Characteristic of soils Soils are not solid materials, as are steel and concrete, but are made up of separate particles, surrounded by voids, which may contain water or air or both. The particles in sands are rotund, while in clays they are flaky. Changes in shape and volume, and the strength of soil, are controlled by effective stress, i.e. the difference between the (external) total stress and the (internal) pore pressure. Under different circumstances of occurrence soils may be: - very dense, ranging through dense, intermediate and loose, to very loose - very dry and hard, ranging through stiff and soft, to very wet and soft. KEKUATAN GESER TANAH Compressibility Characteristic of soils Soils are compressible if the voids contain air. Soils saturated with water are compressible ONLY if drainage can take place. Compression results in a change in the volume of voids (changes in the volume of the grains are negligible) Loose sands are more compressible than dense sands. Wet or soft clays are more compressible than dry or hard clays. Normally consolidated clays are more compressible than overconsolidated clays. KEKUATAN GESER TANAH Strength Characteristic of soils Soil strength is basically frictional, and is controlled by effective stress. The strength of a soil is defined as the maximum sustainable shear stress that can be developed under certain specified conditions: Undrained strength:(e.g. in saturated clay) is constant with respect to effective normal stress, but decreases with increasing water content. Drained strength:increases with effective normal stress. KEKUATAN GESER TANAH Stiffness and Elasticity Stiffness is the relationship between strain and the stress that will induce it. Stiffness behavior relates to the changes in strain that accompany changes in stress (due to loading and unloading). A stress-strain curve is used to characterize stiffness behavior. The stiffness modulus is simply the slope of the stress-strain curve. KEKUATAN GESER TANAH Stiffness Moduli When the loading on a body changes the strain induced will be one or a combination of three types: oDirect or linear strain:changes in length, breadth, diameter, etc. oVolumetric strain:changes in volume oShear strain:changes in shape KEKUATAN GESER TANAH Stiffness Moduli In bodies of elastic material the three stiffness moduli (E, K and G) are related to each other and to Poissons ratio (u). It assumed that the material is elastic and isotropic (i.e. linear stiffness is equal in all directions). The following relationships can be demonstrated (for proofs refer to a text on the strength of materials) G = E/ 2(1-u) K = E/ 3(1-2u) u=Poissons ratio for soils, is in the range 0.2 - 0.5 KEKUATAN GESER TANAH Stress-Strain Behaviour of Soils The stress-strain behaviour of soils is similar to that of other engineering materials, i.e. elastic and plastic deformation occur as in steel, concrete, etc. It is the variability in behaviour that distinguishes soils from other materials. For example, the same soil at different water contents or states of compaction will exhibit a wide range of stiffness and strength characteristics. Relatively recent soils (< 1 Ma old)tend to deform plastically at relatively low stresses, but with deformation related linearly to the logarithm of stress. Geologically old soils, soils that have been overlain by other soils, rocks or ice, are harder and tend to behave elastically (or nearly so) at the levels of stress associated with civil engineering projects. KEKUATAN GESER TANAH Behaviour of Soft Soils Soft soils (including recent natural soils and reconstituted soils) with no history of previous greater loading behave inelastically; the stress-strain diagram being curved even at low stresses. The slope of the curve (E = doa/dca) decreases as the stress increases, eventually reaching an ultimate stress which remains constant as straining continues. Irreversible plastic strain occurs, so that upon unloading permanent deformation ( cp) remains. KEKUATAN GESER TANAH Behaviour of Soft Soils Stiffness values vary with different stress regimes, e.g. uniaxial, triaxial, one-dimensional. Typical values should not be used in design, except in preliminary stages, feasibility studies, etc. Compression tests are required to ascertain reliable and representative values (refer to the Soil Mechanics Reference: Compression and swelling) Typical E range(MPa) Normally consolidated clays0.2 - 4 Organic alluvial clays and peats0.1 - 0.6 KEKUATAN GESER TANAH Behaviour of Hard Soils Stiff and hard soils have often become overconsolidated, i.e. they have a stress history in which loading has increased stresses and then unloading has decreased them. Deformation is a consequence of changes in effective stress. A low stresses the behaviour is elastic (or nearly so), with the stiffness remain almost constant. After the yield point has been reached, plastic deformation occurs Work softening occurs in heavily overconsolidated soils, so that the ultimate stress will be lower than the peak stress. KEKUATAN GESER TANAH Behaviour of Hard Soils Stiffness values vary with different stress regimes, e.g. uniaxial, triaxial, one-dimensional. Typical values should not be used in design, except in preliminary stages, feasibility studies, etc. Compression tests are required to ascertain reliable and representative values (refer to the Soil mechanics Reference: Compression and swelling) Typical E range(MPa) Unweathered overconsolidated clays20 - 50 Boulder clay10 - 20 Keuper Marl (unweathered)>150 Keuper Marl (moderately weathered)30 - 150 Weathered overconsolidated clays3 -10 KEKUATAN GESER TANAH State of Stress and Strain The three orthogonal axial directions are defined in soil mechanics similarly to other engineering disciplines, except that some special considerations apply. The direction of the z-axis is usually vertical; with positive = downward-with-depth in site problems. Stresses relating to soil masses are almost always compressive. Distinction must be made between total stresses and effective stresses, e.g. o =total normal stress o=effective normal stress (note the prime) oz oy ox KEKUATAN GESER TANAH State of Stress and Strain oz oa =total axial compressive stress oa=effective axial stress=oa - u u = internal pore pressure ca =axial strain (due to oa) Uniaxial stress and strain KEKUATAN GESER TANAH State of Stress and Strain Triaxial stresses and strains KEKUATAN GESER TANAH State of Stress and Strain Biaxially symmetrical stresses and strains In a triaxial arrangement, normal stresses (ox, o y, o z) and normal strains (cx, cy, cz) are aligned on three orthogonal axes. In the triaxial test, axial directions are referred to as axial or radial. Also the two radial values will be equaly, i.e. are biaxially symmetrical. oz = oa= total axial stress ox = oy = or= total radial stress oz = oa= effective axial stress = oa - u ox = oy = or = effective radial stress = or - u u = pore pressure ca = axial strain cr = radial strain KEKUATAN GESER TANAH State of Stress and Strain Biaxially symmetrical stresses and strains The normal stresses are principal stresses (o1, o2, o3) The deviator and mean normal stresses are defined as: q = deviator stress = oa - or = oa - or(= o1 - o3) p= mean total normal stress= 1/3 (o1 + o2 + o3) = 1/2 (oa + 2or) p = mean effective normal stress= 1/3 (o1 + o2 + o3) = 1/2 (oa + 2 or) = p - u KEKUATAN GESER TANAH State of Stress and Strain Plane strain Plane strain conditions occur, for example, under the centre of long strip footings and retaining walls. Strains only occur in a vertical plane, perpendicular to this plane the strain is zero. ozor ov= vertical total stress ozor ov= vertical effective stress czor cv= vertical strain oxor oh= horizontal total stress oxor oh= horizontal effective stress oy = horizontal stress in the direction of zero strain =K0 ov (where K0 = coefficient of earth pressure at rest) KEKUATAN GESER TANAH State of Stress and Strain Plane strain Mohr circle and the invariants s and t KEKUATAN GESER TANAH Shear Stress and Strain Engineers shear strain is defined as the angle of distortion of a rectilinear element. t=shear stress (acting tangentially) =shear strain (angular distortion due to the shear stress) On either side of a slip plane the shear stress (t) has reached a limiting value (tf), which may be termed shear strength,e.g. as in the shear box (or direct shear) test The stress-displacement (t/dx) curve will have characteristics similar to those of a shear-stress/shear-strain curve, but cannot be used to measure shear stiffness. KEKUATAN GESER TANAH State of Stress and Strain Stiffness Parameters: Changes in volume in soil masses are due to changes in effective stress. Changes in shape can be related to both total and effective stresses. E= Stiffness (Youngs) modulus for direct (axial) straining, i.e. when oor = 0 = ooa/ ocai.e.. in terms of total stresses Eu= Stiffness modulus measured in undrained conditions, i.e. when ocv = 0 E= Stiffnessmodulus for direct (axial) straining, i.e. when oor = 0 =ooa/ oca i.e. in terms of total stresses Eo= Youngs modulus for one-dimensional compression, i.e. when ocr = 0 K= Bulk modulus (isotropic stress)= oo/ ocv G= Shear modulus=ot/o KEKUATAN GESER TANAH State of Stress and Strain Stiffness Parameters: Tangent and Secant values of E Since the stress-strain behaviour of soil produces a curve, E is not constant, but decreases with increasing stress.Practical measures of the slope (e.g. to obtain an E value for design) can be either a secant value or a tangent value. For problems where the stress is simply raised from zero by Ds, the secant value is appropriate. For problems involving small strains around a given level of stress (point A), the tangent value is more suitable. STRENGTHANDFAILURE KEKUATAN GESER TANAH Strength and Failure The strength of a material is often expressed in terms of the applied stress, e.g. - in a tie rod: tensile strength - a concrete cube: compressive strength - in bolts: shear strength In all cases, however, strength is related to a characteristic maximum shear stress. The magnitude of maximum shear stress is given by the radius of the Mohr circle. KEKUATAN GESER TANAHKriteria Keruntuhan Menurut MOHR-COLOUMB Keruntuhanterjadipadasuatumaterialakibatkombinasikritis antarategangannormaldangeser,danbukanhanyaakibat tegangan normal maksimum atau tegangan geser maksimum saja. tf = f(o)| : sudut geser-internal c : kohesi tf = c + o tan|KEKUATAN GESER TANAHMohr circle for tensile strength In soil mechanics, since stresses are invariably compressive, the sign convention for the Mohr circle axes is:compressive stresses are positive and plotted on thex-axis to the right. Note that the tensile strength will be given by otf= diameter of the Mohr circle. The shear strength (tf) is given by the radius of the Mohr circle KEKUATAN GESER TANAHMohr circle for compressive strength Note that the angle of the potential plane of failure is 45 Maximum shear strength = 1/2 oc KEKUATAN GESER TANAHMohr circle for shear strength The example in the figure is that of a saturated clay slope, but the same concept of shear strength applies in all soil constructions. The stresses at failure (slipping in this case) are: tf= shear stress = radius of the Mohr circle on = normal effective stress = the x-coordinate of the circle centre KEKUATAN GESER TANAHMohr circle for water The stresses at a point within a liquid are equal;they plot at a single point. Thus, liquids have no shear strength. KEKUATAN GESER TANAHStrength Criteria Strength criteria relate to the maximum sustainable shear stress, i.e. the shear stress at failure. For soils, there are really two criteria by which strength (and therefore failure) may be defined, but one of these is modified to provide a third. oTresca - applies to failure in metals and undrained soils oMohr-Coulomb (when c = 0) - applies the critical state failures in soils oMohr-Coulomb (when c > 0) - applies to peak state failures in soils. KEKUATAN GESER TANAHThe Tresca Criterion At any level of normal stress the Mohr circle diameter (oa - or) remains constant. The failure envelope is therefore parallel to the on axis and the strength independent of normal stress. Failure occurs when the Mohr circle increases in diameter to touch the failure envelope: Undrained shear strength, tf=cu(or su)=oa - or=constant Strength criteria Related to undrained condition In terms of total stresses KEKUATAN GESER TANAHThe Mohr-Coulomb (c = 0) Criterion The Mohr-Coulomb (c = 0) criterion relates to the drained critical state strength of soils. Shear strength increases linearly with normal stress; the strength being zero at zero normal stress. As the normal stress increases the Mohr circle diameters increase; circles representing failure stress ultimately touch a straight-line failure envelope. o Critical state shear strength, tf =on tan | o |(or |c)= the critical angle of friction Strength criteria Related to drained critical state strength of soils KEKUATAN GESER TANAHThe Mohr-Coulomb (c > 0) Criterion Strength increases linearly with normal stress, i.e. circle Mohr diameters increase; circles representing failure stress touch a failure envelope. At low stresses the failure envelope is curved, but for practical purpose a straight line is fitted with a practical normal stress range which gives the cohesion intercept on the shear stress axis. Peak state shear strength, tf =c + on tan |p o c=the cohesion intercept o|p= the peak angle of friction Strength criteria Related to drained peak state strength of condition KEKUATAN GESER TANAHThe Mohr-Coulomb (c > 0) Criterion Strength increas...