【正文】 同樣，大多數(shù)彈塑性模型將包含某種彈性其中往往充滿塑性變形。許多構(gòu)模式，采取了務(wù)實的超彈性方式和單純定義應(yīng)力狀態(tài)模量或不關(guān)心熱力后果的應(yīng)變狀態(tài)。我們已經(jīng)注意到小規(guī)模的非均質(zhì)性季節(jié)性分層—可能導(dǎo)致在典型樣本的范圍內(nèi)剛度(和其他)性能的各向異性。但是，我們?nèi)韵Ｍ_定其性能。在一個小規(guī)模范圍內(nèi)， 繆意爾對于＜，那么，這意味著等效剪切剛度與土的剛度矩陣比的比值: 這兩個表達(dá)式，（）和（），對于模量比。他們發(fā)現(xiàn)：粘土/砂石系統(tǒng)的所有性能受土基質(zhì)控制。接收機(jī)將顯示通過這種非均質(zhì)路線最快波的旅行時間。)—冰磧和殘積土中往往在不同土樣基質(zhì)中含有漂石顆粒。各向異性和非線性均可能偏離簡單各向同性線彈性的假設(shè)。這種剛度變化的方程式，原則上應(yīng)當(dāng)是基于微分偶然的發(fā)現(xiàn)彈性應(yīng)變能量密度函數(shù)，因此彈性不應(yīng)違反熱力學(xué)定律。彈性參數(shù)隨應(yīng)變而變化，而不是隨方向變化。豪斯柏（1985）建議一個可以接受的應(yīng)變能函數(shù)可為： 更近一步地，這意味著剛度矩陣再次包含顯示變形的體積和剪切元素耦合的對角線量。當(dāng)以對數(shù)壓縮平面（ ）作圖時，其中是比容，這種關(guān)系的結(jié)合顯示粘土的彈性卸載形成一條直線反應(yīng)。對于和泊松比，意味的常體積應(yīng)變曲線，—由鮑耶斯對小應(yīng)變回彈彈性參數(shù)測試的路基材料得到的典型值。體積作用和剪切作用之間再次是共軛的（對于各向異性模型）。 舉例來說， 如果我們假定土體體積彈性模量隨平均有效壓力變化，但泊松比(即剪切模量和體積模量的比值)是恒定的話，我們會發(fā)現(xiàn),，違反熱力學(xué)第一定律創(chuàng)造一個永動機(jī)，能量將增加(或失去)，這不會是一個保守體系。這些關(guān)系符合和的預(yù)期范圍，但對于和， ()有奇異的倒轉(zhuǎn)。 事實上，對于，其關(guān)系其實并不單調(diào)，并且有效應(yīng)力路徑方向超出了明顯的界限 ()。實際上，不排水試驗的有效應(yīng)力路徑的斜率，形式（） 從我們對孔壓參數(shù) (167。 這是書寫的楊氏模量，在垂直方向楊氏模量，泊松比， 連同第三個參數(shù)。如果我們對于垂直軸與三軸儀主軸平行的試樣，就徑向和軸向的應(yīng)力和應(yīng)變書寫()，我們發(fā)現(xiàn)： 柔度矩陣不是對稱的，因為在三軸試驗環(huán)境中，應(yīng)變增量和應(yīng)力增量不是完全共軛的?，F(xiàn)在柔度矩陣的形式為: 并且我們可以寫為： 這被形容為橫向各向同性或六邊形對稱的交叉各向異性。不過，如果巖土工程材料具有一定的組構(gòu)對稱性，減少獨立彈性參數(shù)的數(shù)量，顯然是很方便的，正如料想的那樣，受構(gòu)造力、冰、或人推動的大部分材料，將不再擁有任何這類對稱性，只要有一個域的彈性反應(yīng)，我們應(yīng)該期望要求全部21個彈性參數(shù)獨立。對于一個完全整體各向異性彈性材料 其中，每個字母，...是，在原理上是一個獨立的彈性參數(shù)，彈性材料剛度矩陣必要的對稱性已推導(dǎo)出獨立參數(shù)的最大值為21。然而，我們知道土已經(jīng)以某種方式沉積—例如，沉積性土在垂直方向受重力作用而沉積。Contours of constant volumetric strain are shown in Fig for and Poisson’s ratio implying —values typical for the road subbase materials being tested by Boyce for their small strain, resilient elastic properties.Similarly the path followed in a purely volumetric deformation will develop some change in distortional stress. For an initial state ,the effective stress path for such a test is Contours of constant distortional strain are also shown in Fig for n = .Figure : Contours of constant volumetric strain (solid lines) and constantdistortional strain (dotted lines) for nonlinear elastic model of Boyce (1980)It is often proposed that the elastic volumetric stiffness—bulk modulus—of clays should be directly proportional to mean effective stress: .Integration of this relationship shows that elastic unloading of clays produces a straight line response when plotted in a logarithmic pression plane(Fig ) where v is specific volume. But what assumption should we make about shear modulus? If we simply assume that Poisson’s ratio is constant, so that the ratio of shear modulus to bulk modulus is constant, then we will emerge with a nonconservative material (Zytynski et al., 1978). If we assume a constant value of shear modulus, independent of stress level, we will obtain a conservative material but may find that we have physically surprising values of implied Poisson’s ratio for certain high or low stress levels. Again we need to find a strain or plementary energy function that will give us the basic modulus variation that we desire.Houlsby (1985) suggests that an acceptable strain energy function could be: : Linear logarithmic relationship between and for elastic materialwith bulk modulus proportional to Incrementally this implies a stiffness matrix which, once again, contains off diagonal terms indicating coupling between volumetric and distortional elements of deformation: It can be deduced that so that contours of constant distortional strain are lines of constant stress ratio η(Fig ). Constant volume (undrained) stress paths are found to be parabolae (Fig ): All parabolae in this family touch the line.Figure : Contours of constant volumetric strain (solid lines) and constantdistortional strain (dotted lines) for nonlinear elastic model of Houlsby (1985)The nonlinearity that has been introduced in these two models is still associated with an isotropic elasticity. The elastic properties vary with deformation but not with direction.Although it tends to be assumed that