public static class GridHelper
{
  public static float GetColumnWidth(ColumnDefinition def)
  {
    return (float)def.GetValue(ColumnWidthProperty);
  }
  public static void SetColumnWidth(ColumnDefinition def, float value)
  {
    def.SetValue(ColumnWidthProperty, value);
  }
  public static readonly DependencyProperty ColumnWidthProperty = DependencyProperty.RegisterAttached(
    "ColumnWidth", typeof(float), typeof(GridHelper), new PropertyMetadata(1.0f, OnColumnWidthChanged));
    
  private static void OnColumnWidthChanged(DependencyObject d, DependencyPropertyChangedEventArgs args)
  {
    ColumnDefinition def = d as ColumnDefinition;
    if (def != null) def.Width = new GridLength((float)args.NewValue, GridUnitType.Star);
  }
}

<DoubleAnimation From="1" To="2" Duration="0:0:1"
  Storyboard.TargetName="col"
  Storyboard.TargetProperty="(local:GridHelper.ColumnWidth)"/>
...
<Grid>
  <Grid.ColumnDefintions>
    <ColumnDefinition x:Name="col"/>
    <ColumnDefinition/>
  </Grid.ColumnDefintions>